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}for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{
counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef
/_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave -1 534 218 170 rectclip -1 534 218 170 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 4 539 208 160 rectfill 4.000000 539.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 208 160 rectclip 0.394687 0.394089 scale -10 -279 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef
/upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch
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y(\()p Fu(x)490 1643 y Fr(1)508 1637 y Fu(;)7 b(:)g(:)g(:)e(;)i(x)625 1643 y Ft(n)647 1637 y Fx(\).)33 b(When)19 b(w)o(e)g(w)o(an)o(t)f(to)h (distinguish)f(among)e(di\013eren)o(t)k(feature)g(v)o(ec-)450 1686 y(tors,)c(w)o(e)g(will)e(attac)o(h)i(subscripts,)h(suc)o(h)g(as)e Fy(X)1212 1692 y Ft(i)1226 1686 y Fx(.)23 b(The)16 b(comp)q(onen)o(ts)g(of)f Fy(X)g Fx(can)h(b)q(e)450 1736 y(an)o(y)f(real-v)n(alued)f(n)o(um)o(b)q(ers,) h(but)g(w)o(e)h(often)f(sp)q(ecialize)h(to)f(the)h(binary)e(n)o(um)o(b)q(ers) h(0)450 1786 y(and)g(1.)21 b(The)16 b(w)o(eigh)o(ts)f(of)f(a)h(TLU)g(are)g (represen)o(ted)j(b)o(y)d(an)g Fu(n)p Fx(-dimensional)d Fs(weight)450 1836 y(ve)n(ctor)p Fx(,)f Fy(W)h Fx(=)g(\()p Fu(w)732 1842 y Fr(1)751 1836 y Fu(;)7 b(:)g(:)g(:)t(;)g(w)873 1842 y Ft(n)895 1836 y Fx(\).)17 b(Its)12 b(comp)q(onen)o(ts)e(are)i(real-v)n(alued)e(n)o(um) o(b)q(ers)g(\(but)i(w)o(e)450 1886 y(sometimes)e(sp)q(ecialize)j(to)f(in)o (tegers\).)19 b(The)13 b(TLU)f(has)g(output)g(1)g(if)1525 1855 y Fj(P)1569 1865 y Ft(n)1569 1898 y(i)p Fr(=1)1631 1886 y Fu(x)1655 1892 y Ft(i)1669 1886 y Fu(w)1699 1892 y Ft(i)1724 1886 y Fw(\025)g Fu(\022)q Fx(;)450 1936 y(otherwise)20 b(it)f(has)g(output)g(0.)34 b(The)20 b(w)o(eigh)o(ted)f(sum)f(that)h(is)g(calculated)g(b)o(y)g(the)450 1985 y(TLU)g(can)h(b)q(e)g(simply)d(represen)o(ted)22 b(as)d(a)g(v)o(ector)i (dot)e(pro)q(duct,)i Fy(X)p Fm(\017)p Fy(W)p Fx(.)e(\(If)g(the)450 2035 y(pattern)g(and)f(w)o(eigh)o(t)f(v)o(ectors)i(are)f(though)o(t)g(of)g (as)g(\\column")d(v)o(ectors,)20 b(this)e(dot)450 2085 y(pro)q(duct)d(is)f (then)h(sometimes)e(written)h(as)h Fy(X)1178 2070 y Ft(t)1192 2085 y Fy(W)q Fx(,)f(where)i(the)f(\\ro)o(w")e(v)o(ector)i Fy(X)1743 2070 y Ft(t)1772 2085 y Fx(is)450 2135 y(the)h(transp)q(ose)h(of)e Fy(X)p Fx(.\))23 b(Often,)16 b(the)g(threshold,)g Fu(\022)q Fx(,)g(of)f(the)i(TLU)e(is)g(\014xed)h(at)g(0;)f(in)450 2185 y(that)i(case,)g(arbitrary)g(thresholds)g(are)g(ac)o(hiev)o(ed)g(b)o(y)f (using)g(\()p Fu(n)11 b Fx(+)h(1\)-dimensional)450 2234 y(\\augmen)o(ted")k (v)o(ectors,)i Fy(Y)p Fx(,)f(and)f Fy(V)p Fx(,)h(whose)h(\014rst)f Fu(n)g Fx(comp)q(onen)o(ts)g(are)g(the)h(same)450 2284 y(as)g(those)g(of)f Fy(X)g Fx(and)h Fy(W)p Fx(,)f(resp)q(ectiv)o(ely)m(.)30 b(The)18 b(\()p Fu(n)11 b Fx(+)h(1\)-st)18 b(comp)q(onen)o(t,)f Fu(x)1672 2290 y Ft(n)p Fr([phone] y Fx(,)h(of)450 2334 y(the)13 b(augmen)o(ted)e(feature)i(v)o(ector,)g Fy(Y)p Fx(,)f(alw)o(a)o(ys)f(has)i(v) n(alue)e(1;)i(the)f(\()p Fu(n)6 b Fx(+)g(1\)-st)13 b(comp)q(o-)450 2384 y(nen)o(t,)g Fu(w)584 2390 y Ft(n)p Fr([phone] y Fx(,)f(of)f(the)i (augmen)o(ted)e(w)o(eigh)o(t)h(v)o(ector,)h Fy(V)p Fx(,)f(is)g(set)h(equal)e (to)h(the)h(negativ)o(e)450 2434 y(of)k(the)i(desired)g(threshold)g(v)n (alue.)30 b(\(When)18 b(w)o(e)h(w)o(an)o(t)e(to)h(emphasize)g(the)h(use)g(of) 450 2539 y Fo(Intr)n(o)n(duction)14 b(to)k(Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 41 3 41 2 bop 150 275 a Fp(4.1.)31 b(THRESHOLD)14 b(LOGIC)f(UNITS)654 b Fx(41)150 391 y(augmen)o(ted)13 b(v)o(ectors,)h(w)o(e'll)f(use)i(the)f Fy(Y)p Fx(,)p Fy(V)g Fx(notation;)e(ho)o(w)o(ev)o(er)i(when)h(the)f(con)o (text)150 441 y(of)h(the)h(discussion)g(mak)o(es)e(it)i(clear)f(ab)q(out)h (what)f(sort)h(of)f(v)o(ectors)i(w)o(e)e(are)h(talking)150 491 y(ab)q(out,)d(w)o(e'll)f(lapse)h(bac)o(k)h(in)o(to)e(the)i(more)f(famili) o(ar)e Fy(X)p Fx(,)p Fy(W)i Fx(notation.\))k(In)c(the)h Fy(Y)p Fx(,)p Fy(V)150 541 y Fx(notation,)f(the)j(TLU)e(has)h(an)f(output)h(of)f(1)g (if)g Fy(Y)p Fm(\017)p Fy(V)g Fw(\025)f Fx(0.)20 b(Otherwise,)c(the)f(output) 150 591 y(is)f(0.)212 668 y(W)m(e)19 b(can)f(giv)o(e)h(an)f(in)o(tuitiv)o (ely)f(useful)i(geometric)f(description)h(of)f(a)h(TLU.)f(A)150 718 y(TLU)c(divides)g(the)g(input)g(space)h(b)o(y)e(a)h(h)o(yp)q(erplane)g (as)g(sk)o(etc)o(hed)i(in)d(Fig.)k(4.2.)h(The)150 768 y(h)o(yp)q(erplane)d (is)e(the)i(b)q(oundary)f(b)q(et)o(w)o(een)i(patterns)f(for)e(whic)o(h)h Fy(X)p Fw(\017)p Fy(W)d Fx(+)e Fu(w)1359 774 y Ft(n)p Fr(+1)1435
768 y Fu(>)j Fx(0)150 817 y(and)20 b(patterns)i(for)e(whic)o(h)g Fy(X)p Fw(\017)p Fy(W)14 b Fx(+)g Fu(w)799 823 y Ft(n)p Fr(+1)886 817 y Fu(<)22 b Fx(0.)37 b(Th)o(us,)22 b(the)f(equation)f(of)f(the)150 867 y(h)o(yp)q(erplane)11 b(itself)g(is)g Fy(X)p Fw(\017)p Fy(W)t Fx(+)s Fu(w)672 873 y Ft(n)p Fr(+1)749 867 y Fx(=)g(0.)17 b(The)12 b(unit)e(v)o(ector)i(that)f(is)g(normal)e(to)h(the)150 926 y(h)o(yp)q(erplane)i(is)f Fy(n)g Fx(=)496 909 y Fy(W)p 486 916 70 2 v 486 946 a Fi(j)p Fy(W)q Fi(j)561 926 y Fx(,)g(where)h Fw(j)p Fy(W)q Fw(j)f Fx(=)830 890 y Fj(p)p 871 890 284 2 v 871 926 a Fx(\()p Fu(w)918 912 y Fr(2)917 937 y(1)946 926 y Fx(+)f Fu(:)d(:)g(:)g Fx(+)j Fu(w)1118 914 y Fr(2)1117 936 y Ft(n)1139 926 y Fx(\))h(is)g(the)h(length)f(of)f(the)150 1003 y(v)o(ector)h Fy(W)p Fx(.)f(\(The)g Fs(normal)h(form)f Fx(of)f(the)i(h)o(yp)q(erplane)f(equation)g(is)g Fy(X)p Fw(\017)p Fy(n)q Fx(+)1331 986 y Fy(W)p 1321 993 70 2 v 1321 1023 a Fi(j)p Fy(W)q Fi(j)1408 1003 y Fx(=)i(0.\))150 1068 y(The)k(distance)h(from)d(the)i (h)o(yp)q(erplane)g(to)g(the)g(origin)f(is)1084 1047 y Ft(w)1108 1051 y Fl(n)p Fk(+1)p 1084 1058 80 2 v 1089 1088 a Fi(j)p Fy(W)q Fi(j)1168 1068 y Fx(,)h(and)g(the)g(distance)150 1149 y(from)e(an)i (arbitrary)h(p)q(oin)o(t,)e Fy(X)p Fx(,)i(to)f(the)h(h)o(yp)q(erplane)f(is) 1069 1128 y Fy(X)p Fi(\017)p Fy(W)q Fr(+)p Ft(w)1221 1132 y Fl(n)p Fk(+1)p 1069 1139 209 2 v 1138 1169 a Fi(j)p Fy(W)q Fi(j)1282 1149 y Fx(.)25 b(When)16 b(the)150 1212 y(distance)11 b(from)d(the)j(h)o(yp)q(erplane)f(to)g(the)h(origin)d(is)i(negativ)o(e)g (\(that)g(is,)g(when)h Fu(w)1392 1218 y Ft(n)p Fr([phone] y Fu(<)150 1262 y Fx(0\),)16 b(then)i(the)f(origin)e(is)h(on)g(the)h(negativ) o(e)g(side)f(of)g(the)h(h)o(yp)q(erplane)g(\(that)g(is,)f(the)150 1311 y(side)e(for)g(whic)o(h)g Fy(X)p Fw(\017)o Fy(W)d Fx(+)e Fu(w)603 1317 y Ft(n)p Fr([phone] y Fu(<)j Fx(0\).)212 1389 y(Adjusting)j(the)g(w)o(eigh)o(t)g(v)o(ector,)g Fy(W)q Fx(,)g(c)o(hanges)g(the)h(orien)o(tation)e(of)g(the)h(h)o(yp)q(er-)150 1439 y(plane;)h(adjusting)g Fu(w)489 1445 y Ft(n)p Fr([phone] y Fx(c)o(hanges)h(the)f(p)q(osition)g(of)f(the)i(h)o(yp)q(erplane)f (\(relativ)o(e)g(to)150 1488 y(the)e(origin\).)j(Th)o(us,)d(training)e(of)h (a)g(TLU)h(can)g(b)q(e)g(ac)o(hiev)o(ed)g(b)o(y)f(adjusting)g(the)h(v)n(al-) 150 1538 y(ues)j(of)e(the)i(w)o(eigh)o(ts.)24 b(In)15 b(this)h(w)o(a)o(y)g (the)g(h)o(yp)q(erplane)g(can)h(b)q(e)f(mo)o(v)o(ed)e(so)i(that)g(the)150 1588 y(TLU)e(implemen)o(ts)d(di\013eren)o(t)k(\(linearly)e(separable\))i (functions)f(of)f(the)i(input.)150 1764 y Fz(4.1.2)55 b(Sp)r(ecial)18 b(Cases)h(of)g(Linearly)d(Separable)j(F)-5 b(unctions)150 1875 y Fy(T)l(erms)150 1985 y Fx(An)o(y)13 b(term)g(of)f(size)i Fu(k)g Fx(can)g(b)q(e)g(implem)o(en)o(ted)d(b)o(y)i(a)g(TLU)g(with)g(a)g(w)o (eigh)o(t)g(from)e(eac)o(h)150 2035 y(of)i(those)h(inputs)g(corresp)q(onding) g(to)g(v)n(ariables)e(o)q(ccurring)i(in)f(the)i(term.)i(A)c(w)o(eigh)o(t)150 2085 y(of)e(+1)g(is)g(used)h(from)d(an)i(input)g(corresp)q(onding)h(to)f(a)g (p)q(ositiv)o(e)g(literal,)f(and)i(a)e(w)o(eigh)o(t)150 2135 y(of)15 b Fw(\000)p Fx(1)h(is)g(used)h(from)d(an)h(input)h(corresp)q(onding)h (to)e(a)h(negativ)o(e)g(literal.)23 b(\(Literals)150 2185 y(not)14 b(men)o(tioned)f(in)h(the)h(term)e(ha)o(v)o(e)h(w)o(eigh)o(ts)g(of)g (zero|that)h(is,)e(no)h(connection)h(at)150 2234 y(all|from)d(their)17 b(inputs.\))24 b(The)16 b(threshold,)h Fu(\022)q Fx(,)g(is)e(set)i(equal)f (to)f Fu(k)1231 2240 y Ft(p)1261 2234 y Fw(\000)c Fx(1)p Fu(=)p Fx(2,)k(where)150 2284 y Fu(k)172 2290 y Ft(p)206 2284 y Fx(is)f(the)i(n)o (um)o(b)q(er)e(of)h(p)q(ositiv)o(e)f(literals)h(in)f(the)i(term.)k(Suc)o(h)c (a)e(TLU)h(implemen)o(ts)150 2334 y(a)h(h)o(yp)q(erplane)h(b)q(oundary)f (that)g(is)g(parallel)g(to)g(a)g(subface)h(of)e(dimension)g(\()p Fu(n)c Fw(\000)g Fu(k)q Fx(\))150 2384 y(of)j(the)i(unit)f(h)o(yp)q(ercub)q (e.)24 b(W)m(e)14 b(sho)o(w)h(a)g(three-dimensional)f(example)g(in)g(Fig.)21 b(4.3.)150 2434 y(Th)o(us,)14 b(linearly)f(separable)h(functions)g(are)g(a)g
(sup)q(erset)i(of)d(terms.)150 2539 y Fo(Intr)n(o)n(duction)h(to)k(Machine)e (L)n(e)n(arning)757 2538 y Fn(c)746 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e (Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 42 4 42 3 bop 450 275 a Fx(42)579 b Fp(CHAPTER)14 b(4.)32 b(NEURAL)14 b(NETW)o(ORKS)719 1312 y @beginspecial 8 @llx 481 @lly 203 @urx 712 @ury 1950 @rwi @setspecial %%BeginDocument: Four/geometry.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def
gsave 8 481 195 231 rectclip 8 481 195 231 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 13 486 185 221 rectfill 13.000000 486.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 185 221 rectclip 0.332136 0.330838 scale -1 -28 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop
}for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc
} def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 1 28 557 668 rectclip 1 28 557 668 rectclip 0 setgray 0.333333 setgray 0 0 3.384615 setup 0 setgray 1 setalpha 435 -333 46 511 line grestore 0 setgray 0.333333 setgray 0 0 4.410257 setup 0 setgray 1 setalpha 58 67 87 214 line 49.119637 145 281 arrow grestore 0 0 0.102564 setup gsave /Helvetica findfont 20 scalefont [1 0 0 -1 0 0] makefont 500 exch defineuserobject 500 execuserobject setfont 0 setgray [1 0 0 -1 0 854] concat 500 execuserobject setfont 0 setgray 204 417 moveto (X) show 0 -8 rmoveto (.) show 0 8 rmoveto (W + w) show 0 9 rmoveto (n+1) show 0 -9 rmoveto ( > 0) show 204 450 moveto (on this side) show grestore grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 63.768291 0 62 353.358978 line grestore 0 0 0.102564 setup gsave 500 execuserobject setfont
0 setgray [1 0 0 -1 0 643.423096] concat /Helvetica-Bold findfont 36 scalefont [1 0 0 -1 0 0] makefont 1189 exch defineuserobject 1189 execuserobject setfont 0 setgray 77.158539 333 moveto (W) show grestore grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 0 -38.75 117.670731 343.423096 line grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 0 -38.75 70.097565 342.429504 line grestore 0 setgray 0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 78 -58 10 271 line grestore 0 setgray 0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 37 50 21 263 line 233.500137 21 263 arrow grestore 0 setgray 0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 33 42 113 391 line 51.844303 146 433 arrow grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 991] concat 1189 execuserobject setfont 0 setgray 445 508 moveto (X) show grestore grestore 0 setgray
0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 40 54 447 399 line 53.472721 487 453 arrow grestore 0 setgray 0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 29 40 360 272 line 234.059479 360 272 arrow grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 201 0 333 333 line grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 602.423096] concat 1189 execuserobject setfont 0 setgray 412.158539 310 moveto (W) show grestore grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 0 -38.75 452.670715 326.423096 line grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 0 -38.75 405.097565 325.429504 line grestore 0 setgray 0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 33 -26 466 471 line grestore 0 0 2.666667 setup 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 280] concat
1189 execuserobject setfont 0 setgray 111 153 moveto (n =) show grestore grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 312] concat 1189 execuserobject setfont 0 setgray 194 169 moveto (W) show grestore grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 220] concat /Helvetica findfont 36 scalefont [1 0 0 -1 0 0] makefont 582 exch defineuserobject 582 execuserobject setfont 0 setgray 188 123 moveto (|) show 1189 execuserobject setfont (W) show 582 execuserobject setfont (|) show grestore grestore 0 0 2.666667 setup 0 setgray 1 setalpha 63.768291 0 181 135.359009 line grestore grestore 0 0 0.102564 setup gsave 582 execuserobject setfont 0 setgray [1 0 0 -1 0 384] concat /Helvetica-Oblique findfont 24 scalefont [1 0 0 -1 0 0] makefont 1190 exch defineuserobject 1190 execuserobject setfont 0 setgray 24 195 moveto (Origin) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.666667 setup 0 setgray 1 setalpha 40 -82 124 252 line
116.001465 124 252 arrow grestore 0 0 0.102564 setup gsave 1190 execuserobject setfont 0 setgray [1 0 0 -1 0 126] concat 1190 execuserobject setfont 0 setgray 87 57 moveto (Unit vector normal) show 87 86 moveto (to hyperplane) show grestore grestore 0 0 0.102564 setup gsave 1190 execuserobject setfont 0 setgray [1 0 0 -1 0 1234] concat 1189 execuserobject setfont 0 setgray 74 622 moveto (W) show 582 execuserobject setfont ( + w) show 0 14 rmoveto (n+1) show 0 -14 rmoveto ( = 0) show grestore grestore 0 0 0.102564 setup gsave 582 execuserobject setfont 0 setgray [1 0 0 -1 0 1241] concat 1189 execuserobject setfont 0 setgray 26 631 moveto (X) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.102564 setup 0 setgray 1 setalpha 10 9 58 618 oval fill grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 1037] concat 1189 execuserobject setfont 0 setgray 74 512 moveto (n) show 582 execuserobject setfont ( + = 0) show grestore grestore 0 0 0.102564 setup
gsave 582 execuserobject setfont 0 setgray [1 0 0 -1 0 1067] concat 1189 execuserobject setfont 0 setgray 20 544 moveto (X) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.102564 setup 0 setgray 1 setalpha 10 9 52 531 oval fill grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 1340] concat 1190 execuserobject setfont 0 setgray 9 673 moveto (Equations of hyperplane:) show grestore grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 92 -0.359009 136 534.359009 line grestore 0 0 0.102564 setup gsave 1190 execuserobject setfont 0 setgray [1 0 0 -1 0 1125] concat 582 execuserobject setfont 0 setgray 139 568 moveto (w) show 0 14 rmoveto (n+1) show 0 -14 rmoveto grestore grestore 0 0 0.102564 setup gsave 582 execuserobject setfont 0 setgray [1 0 0 -1 0 1017] concat 582 execuserobject setfont 0 setgray 157 521 moveto (|W|) show grestore grestore 0 0 0.102564 setup gsave 582 execuserobject setfont
0 setgray [1 0 0 -1 0 761] concat 582 execuserobject setfont 0 setgray 53 386 moveto (w) show 0 14 rmoveto (n+1) show 0 -14 rmoveto grestore grestore 0 0 0.102564 setup gsave 582 execuserobject setfont 0 setgray [1 0 0 -1 0 715] concat 1189 execuserobject setfont 0 setgray 381 361 moveto (W) show 582 execuserobject setfont ( + w) show 0 14 rmoveto (n+1) show 0 -14 rmoveto grestore grestore 0 0 0.102564 setup gsave 582 execuserobject setfont 0 setgray [1 0 0 -1 0 729] concat 1189 execuserobject setfont 0 setgray 341 375 moveto (X) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.102564 setup 0 setgray 1 setalpha 10 9 367 363 oval fill grestore 0 setgray 0.333333 setgray 0 0 2.666667 setup 0 setgray 1 setalpha 374 257 88 214 line 34.496536 462 471 arrow grestore 0 0 0.102564 setup gsave 1189 execuserobject setfont 0 setgray [1 0 0 -1 0 513] concat 500 execuserobject setfont 0 setgray 197 249 moveto (X) show 0 -8 rmoveto
(.) show 0 8 rmoveto (W + w) show 0 9 rmoveto (n+1) show 0 -9 rmoveto ( < 0) show 197 282 moveto (on this side) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 878 1404 a Fx(Figure)g(4.2:)j(TLU)d(Geometry)450 1534 y Fy(Clauses)450 1621 y Fx(The)f(negation)f(of)g(a)h(clause)g(is)g(a)f (term.)17 b(F)m(or)12 b(example,)g(the)h(negation)f(of)g(the)h(clause)450 1671 y Fu(f)18 b Fx(=)c Fu(x)558 1677 y Fr(1)586 1671 y Fx(+)d Fu(x)653 1677 y Fr(2)681 1671 y Fx(+)f Fu(x)747 1677 y Fr(3)781 1671 y Fx(is)15 b(the)g(term)p 997 1637 25 2 v 15 w Fu(f)j Fx(=)p 1081 1648 43 2 v 14 w Fu(x)1105 1677 y Fr(1)p 1138 1648 V 1138 1671 a Fu(x)1162 1677 y Fr(2)p 1196 1648 V 1196 1671 a Fu(x)1220 1677 y Fr(3)1238 1671 y Fx(.)j(A)16 b(h)o(yp)q(erplane)f(can)g(b) q(e)h(used)g(to)450 1721 y(implemen)o(t)c(this)i(term.)20 b(If)14 b(w)o(e)h(\\in)o(v)o(ert")f(the)h(h)o(yp)q(erplane,)f(it)h(will)e(implem)o (en)o(t)f(the)450 1771 y(clause)f(instead.)17 b(In)o(v)o(erting)10 b(a)g(h)o(yp)q(erplane)h(is)f(done)h(b)o(y)f(m)o(ultiplyi)o(ng)d(all)i(of)h (the)h(TLU)450 1821 y(w)o(eigh)o(ts|ev)o(en)k Fu(w)751 1827 y Ft(n)p Fr([phone] y Fx(|b)o(y)f Fw(\000)p Fx(1.)21 b(This)15 b(pro)q(cess)h(simply)d(c)o(hanges)i(the)h(orien)o(tation)450 1870 y(of)c(the)i(h)o(yp)q(erplane|\015ipping)e(it)g(around)h(b)o(y)f(180)g (degrees)j(and)e(th)o(us)g(c)o(hanging)f(its)450 1920 y(\\p)q(ositiv)o(e)i (side.")21 b(Therefore,)15 b(linearly)f(separable)h(functions)g(are)g(also)f (a)h(sup)q(erset)450 1970 y(of)e(clauses.)19 b(W)m(e)14 b(sho)o(w)g(an)f (example)g(in)g(Fig.)18 b(4.4.)450 2097 y Fz(4.1.3)55 b(Error-Correction)17 b(T)-5 b(raining)19 b(of)g(a)g(TLU)450 2185 y Fx(There)h(are)g(sev)o(eral)f (pro)q(cedures)j(that)d(ha)o(v)o(e)g(b)q(een)h(prop)q(osed)g(for)f(adjusting) f(the)450 2234 y(w)o(eigh)o(ts)13 b(of)g(a)h(TLU.)f(W)m(e)g(presen)o(t)i (next)f(a)f(family)d(of)j Fs(incr)n(emental)g Fx(training)g(pro)q(ce-)450 2284 y(dures)k(with)f(parameter)g Fu(c)p Fx(.)25 b(These)18 b(metho)q(ds)e(mak)o(e)f(adjustmen)o(ts)g(to)i(the)f(w)o(eigh)o(t)450 2334 y(v)o(ector)e(only)e(when)i(the)g(TLU)f(b)q(eing)g(trained)h(mak)o(es)e (an)h(error)h(on)f(a)g(training)f(pat-)450 2384 y(tern;)g(they)f(are)g (called)g Fs(err)n(or-c)n(orr)n(e)n(ction)d Fx(pro)q(cedures.)19
b(W)m(e)10 b(use)i Fs(augmente)n(d)f Fx(feature)450 2434 y(and)j(w)o(eigh)o (t)f(v)o(ectors)i(in)f(describing)g(them.)450 2539 y Fo(Intr)n(o)n(duction)g (to)k(Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o (ed.)p eop %%Page: 43 5 43 4 bop 150 275 a Fp(4.1.)31 b(THRESHOLD)14 b(LOGIC)f(UNITS)654 b Fx(43)542 1062 y @beginspecial 0 @llx 0 @lly 136 @urx 171 @ury 1360 @rwi @setspecial %%BeginDocument: Four/term.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show
3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq
{NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /_NXfindfont /findfont load def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {_NXfindfont} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {_NXfindfont dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string __NXdef}ifelse __NXImageString}__NXbdef /_NXDoImageOp{ 3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def chans 2 add 2 roll parr 0 chans getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /totbytes exch def pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore {0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end }__NXbdef /alphaimage{1 add _NXDoImageOp}def _NXLevel2{ /NXCalibratedRGBColorSpace where{pop}{ /NXCalibratedRGBColorSpace {mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped {cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin /MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def /WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse /nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef /nxsetgray{dup dup nxsetrgbcolor}__NXbdef /_NXCalibratedImage{exch{array astore dup length true}{false}ifelse 8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if 8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def} {2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef } {
/setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /colorimage{2 copy 3 ne or{_NXDoImageOp}{4 index dup 8 ne exch 4 ne and{_NXDoImageOp}{ pop pop save 6 1 roll 12 dict begin/Proc exch def/Res 0 string def /Alloc{2 index length mul 2 add dup 2 index load length gt{1.2 mul round cvi string def}{pop pop}ifelse}def 1 index 8 eq{/Unpack{.34 Alloc}def}{ /Wid 4 index 3 mul def exch pop 8 exch/Str1 0 string def/Lim Wid def /Unpack{.67 Alloc/Str1 2 Alloc 0 exch Lim exch {dup -4 bitshift 17 mul Str1 exch 4 index exch put 15 and 17 mul Str1 exch 3 index 1 add exch put 2 sub dup 0 le{0 lt Wid exch{exch 1 sub exch}if}if exch 2 add exch }forall/Lim exch def Str1 exch 0 exch getinterval }def }ifelse /Ops[{.3 mul add 1}{.59 mul add 2}{.11 mul add round cvi Res exch 2 index exch put 1 add 0.0 0}]def/Val 0.0 def/Phase 0 def {0 Val Phase Proc/Res Unpack{exch Ops exch get exec}forall/Phase exch def/Val exch def Res exch 0 exch getinterval} image end restore}ifelse}ifelse }__NXbdef /nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef /setpattern{pop .5 setgray}__NXbdef /_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef } ifelse /_NXSetCMYKOrRGB where{pop}{ mark{systemdict /currentwindow get exec}stopped {{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark }ifelse gsave /__NXbasematrix matrix currentmatrix def grestore gsave 0 0 136 171 rectclip [1 0 0 -1 -18 189] concat 18 18 136 171 rectclip gsave 18 18 135.620697 171 rectclip gsave 1 -1 scale gsave 18 -189 translate 0.294828 0.294828 scale -49 -46 translate /__NXEPSSave save def /showpage {} def _NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse /sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def /setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def /_NXcimage where{pop}{/_NXcimage /colorimage load def}ifelse /colorimage{dup 3 eq{true 2 index{1 index}{1}ifelse 7 add 1 roll _NXCalibratedImage}
{_NXcimage}ifelse}def}if 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /_NXfindfont /findfont load def /findfont{
% Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {_NXfindfont} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {_NXfindfont dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string __NXdef}ifelse __NXImageString}__NXbdef /_NXDoImageOp{ 3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def chans 2 add 2 roll parr 0 chans getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /totbytes exch def pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore {0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end }__NXbdef /alphaimage{1 add _NXDoImageOp}def _NXLevel2{ /NXCalibratedRGBColorSpace where{pop}{ /NXCalibratedRGBColorSpace {mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped {cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin /MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def /WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse /nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef /nxsetgray{dup dup nxsetrgbcolor}__NXbdef /_NXCalibratedImage{exch{array astore dup length true}{false}ifelse 8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if 8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def} {2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef } { /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /colorimage{2 copy 3 ne or{_NXDoImageOp}{4 index dup 8 ne exch 4 ne
and{_NXDoImageOp}{ pop pop save 6 1 roll 12 dict begin/Proc exch def/Res 0 string def /Alloc{2 index length mul 2 add dup 2 index load length gt{1.2 mul round cvi string def}{pop pop}ifelse}def 1 index 8 eq{/Unpack{.34 Alloc}def}{ /Wid 4 index 3 mul def exch pop 8 exch/Str1 0 string def/Lim Wid def /Unpack{.67 Alloc/Str1 2 Alloc 0 exch Lim exch {dup -4 bitshift 17 mul Str1 exch 4 index exch put 15 and 17 mul Str1 exch 3 index 1 add exch put 2 sub dup 0 le{0 lt Wid exch{exch 1 sub exch}if}if exch 2 add exch }forall/Lim exch def Str1 exch 0 exch getinterval }def }ifelse /Ops[{.3 mul add 1}{.59 mul add 2}{.11 mul add round cvi Res exch 2 index exch put 1 add 0.0 0}]def/Val 0.0 def/Phase 0 def {0 Val Phase Proc/Res Unpack{exch Ops exch get exec}forall/Phase exch def/Val exch def Res exch 0 exch getinterval} image end restore}ifelse}ifelse }__NXbdef /nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef /setpattern{pop .5 setgray}__NXbdef /_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef } ifelse /_NXSetCMYKOrRGB where{pop}{ mark{systemdict /currentwindow get exec}stopped {{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark }ifelse gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc closepath } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 509 626 rectclip 49 46 460 580 rectclip 0 setgray 0.333333 setgray 0 0 0.17 setup 0 nxsetgray 253 1 210 357 line 0.226471 463 358 arrow grestore 0 0 2.477692 setup 0 nxsetgray 205 357 171 165 rectstroke grestore 0 setgray 0.333333 setgray
0 0 0 setup gsave 1 2 translate 1 1 scale 0.549593 nxsetgray gsave newpath systemdict begin 224 261 345 475 setbbox 224 426 moveto 0 0 rlineto 118 49 rlineto 3 -158 rlineto -121 -56 rlineto 0 165 rlineto 0 0 rlineto end eofill grestore grestore 1 2 translate 1 1 scale 0 nxsetgray gsave newpath systemdict begin 224 261 345 475 setbbox 224 426 moveto 0 0 rlineto 118 49 rlineto 3 -158 rlineto -121 -56 rlineto 0 165 rlineto 0 0 rlineto end stroke grestore grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 nxsetgray 134 179 71 178 line 233.182922 71 178 arrow grestore 0 0 2.477692 setup 0 nxsetgray 69 94 306 426 line grestore 0 0 2.477692 setup 0 nxsetgray 72 97 303 260 line grestore 0 0 2.477692 setup 0 nxsetgray 135 262 170 165 rectstroke grestore
0 0 2.477692 setup 0 nxsetgray 68 94 136 427 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 nxsetgray 0 228 204 357 line 90.002655 204 585 arrow grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 nxsetgray 21 20 196 347 oval fill grestore 0 nxsetgray 21 20 196 347 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 nxsetgray 21 20 126 253 oval fill grestore 0 nxsetgray 21 20 126 253 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 nxsetgray 21 20 127 417 oval fill grestore 0 nxsetgray 21 20 127 417 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 nxsetgray 21 20 365 346 oval fill grestore 0 nxsetgray 21 20 365 346 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 nxsetgray 294 414 22 21 rectfill 0 nxsetgray 294 414 22 21 rectstroke grestore
defaultmatrix setmatrix stroke
defaultmatrix setmatrix stroke
defaultmatrix setmatrix stroke
defaultmatrix setmatrix stroke
0 setgray 0.333333 setgray 0 0 0.17 setup 0 nxsetgray 294 251 22 21 rectfill 0 nxsetgray 294 251 22 21 rectstroke grestore 0 0 0.17 setup gsave /Helvetica findfont 24 scalefont [1 0 0 -1 0 0] makefont 11 exch defineuserobject 11 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 792] concat 11 execuserobject setfont 0 nxsetgray 231 400 moveto (\(1,1,1\)) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 nxsetgray 21 20 194 510 oval fill grestore 0 nxsetgray 21 20 194 510 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 nxsetgray 21 20 365 510 oval fill grestore 0 nxsetgray 21 20 365 510 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0.17 setup gsave 11 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 512] concat 11 execuserobject setfont 0 nxsetgray 322 263 moveto (\(1,1,0\)) show grestore grestore 0 0 0 setup gsave 11 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 707] concat 11 execuserobject setfont 0 nxsetgray
468 357 moveto (x) show 0 7 rmoveto (2) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 11 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 318] concat 11 execuserobject setfont 0 nxsetgray 56 159 moveto (x) show 0 7 rmoveto (1) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 11 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 1209] concat gsave 207 588 39 33 rectclip 11 execuserobject setfont 0 nxsetgray 207 611 moveto (x) show 0 7 rmoveto (3) show 0 -7 rmoveto grestore grestore grestore 0 0 0 setup gsave 11 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 1164] concat /Helvetica findfont 44 scalefont [1 0 0 -1 0 0] makefont 12 exch defineuserobject 12 execuserobject setfont 0 nxsetgray 304 588 moveto (f = x) show 0 17 rmoveto (1) show 0 -17 rmoveto (x) show 0 17 rmoveto (2) show 0 -17 rmoveto grestore grestore 0 0 0 setup gsave 12 execuserobject setfont
0 nxsetgray [1 0 0 -1 0 186] concat /Helvetica findfont 31 scalefont [1 0 0 -1 0 0] makefont 13 exch defineuserobject 13 execuserobject setfont 0 nxsetgray 255 87 moveto (x) show 0 7 rmoveto (1) show 0 -7 rmoveto ( ) show /Helvetica findfont 38 scalefont [1 0 0 -1 0 0] makefont 14 exch defineuserobject 14 execuserobject setfont (+) show 13 execuserobject setfont ( x) show 0 7 rmoveto (2) show 0 -7 rmoveto ( - 3/2 = 0) show grestore grestore 0 0 0 setup 0 nxsetgray 35 -102 256 272 line 108.936913 256 272 arrow grestore 0 0 0 setup gsave 13 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 294] concat 11 execuserobject setfont 0 nxsetgray 218 152 moveto (Equation of plane is:) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 509 626 rectclip [1 0 0 -1 0 626] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore grestore grestore %%EndDocument @endspecial 521 1154 a(Figure)14 b(4.3:)j(Implemen)o(ting)11 b(a)j(T)m(erm)201 1290 y(1.)20 b(W)m(e)11 b(start)h(with)f(a)g(\014nite)h (training)e(set,)j(\004,)e(of)g(v)o(ectors,)h Fy(Y)1159 1296
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}{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /_NXfindfont /findfont load def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {_NXfindfont} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {_NXfindfont dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string __NXdef}ifelse __NXImageString}__NXbdef /_NXDoImageOp{ 3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def chans 2 add 2 roll parr 0 chans getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse
4 index mul /totbytes exch def pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore {0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end }__NXbdef /alphaimage{1 add _NXDoImageOp}def _NXLevel2{ /NXCalibratedRGBColorSpace where{pop}{ /NXCalibratedRGBColorSpace {mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped {cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin /MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def /WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse /nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef /nxsetgray{dup dup nxsetrgbcolor}__NXbdef /_NXCalibratedImage{exch{array astore dup length true}{false}ifelse 8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if 8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def} {2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef } { /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /colorimage{2 copy 3 ne or{_NXDoImageOp}{4 index dup 8 ne exch 4 ne and{_NXDoImageOp}{ pop pop save 6 1 roll 12 dict begin/Proc exch def/Res 0 string def /Alloc{2 index length mul 2 add dup 2 index load length gt{1.2 mul round cvi string def}{pop pop}ifelse}def 1 index 8 eq{/Unpack{.34 Alloc}def}{ /Wid 4 index 3 mul def exch pop 8 exch/Str1 0 string def/Lim Wid def /Unpack{.67 Alloc/Str1 2 Alloc 0 exch Lim exch {dup -4 bitshift 17 mul Str1 exch 4 index exch put 15 and 17 mul Str1 exch 3 index 1 add exch put 2 sub dup 0 le{0 lt Wid exch{exch 1 sub exch}if}if exch 2 add exch }forall/Lim exch def Str1 exch 0 exch getinterval }def }ifelse /Ops[{.3 mul add 1}{.59 mul add 2}{.11 mul add round cvi Res exch 2 index exch put 1 add 0.0 0}]def/Val 0.0 def/Phase 0 def {0 Val Phase Proc/Res Unpack{exch Ops exch get exec}forall/Phase exch def/Val exch def Res exch 0 exch getinterval} image end restore}ifelse}ifelse }__NXbdef /nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef /setpattern{pop .5 setgray}__NXbdef /_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef } ifelse
/_NXSetCMYKOrRGB where{pop}{ mark{systemdict /currentwindow get exec}stopped {{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark }ifelse gsave /__NXbasematrix matrix currentmatrix def grestore gsave 0 0 153 159 rectclip [1 0 0 -1 -36 177] concat 36 18 153 159 rectclip gsave 36 18 153 158.43895 rectclip gsave 1 -1 scale gsave 36 -176 translate 0.236476 0.236476 scale -30 -48 translate /__NXEPSSave save def /showpage {} def _NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse /sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def /setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def /_NXcimage where{pop}{/_NXcimage /colorimage load def}ifelse /colorimage{dup 3 eq{true 2 index{1 index}{1}ifelse 7 add 1 roll _NXCalibratedImage} {_NXcimage}ifelse}def}if 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
{gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /flushgraphics{}def
/setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /_NXfindfont /findfont load def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {_NXfindfont} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {_NXfindfont dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string __NXdef}ifelse __NXImageString}__NXbdef /_NXDoImageOp{ 3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def chans 2 add 2 roll parr 0 chans getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /totbytes exch def pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore {0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end }__NXbdef /alphaimage{1 add _NXDoImageOp}def
_NXLevel2{ /NXCalibratedRGBColorSpace where{pop}{ /NXCalibratedRGBColorSpace {mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped {cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin /MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def /WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse /nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef /nxsetgray{dup dup nxsetrgbcolor}__NXbdef /_NXCalibratedImage{exch{array astore dup length true}{false}ifelse 8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if 8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def} {2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef } { /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /colorimage{2 copy 3 ne or{_NXDoImageOp}{4 index dup 8 ne exch 4 ne and{_NXDoImageOp}{ pop pop save 6 1 roll 12 dict begin/Proc exch def/Res 0 string def /Alloc{2 index length mul 2 add dup 2 index load length gt{1.2 mul round cvi string def}{pop pop}ifelse}def 1 index 8 eq{/Unpack{.34 Alloc}def}{ /Wid 4 index 3 mul def exch pop 8 exch/Str1 0 string def/Lim Wid def /Unpack{.67 Alloc/Str1 2 Alloc 0 exch Lim exch {dup -4 bitshift 17 mul Str1 exch 4 index exch put 15 and 17 mul Str1 exch 3 index 1 add exch put 2 sub dup 0 le{0 lt Wid exch{exch 1 sub exch}if}if exch 2 add exch }forall/Lim exch def Str1 exch 0 exch getinterval }def }ifelse /Ops[{.3 mul add 1}{.59 mul add 2}{.11 mul add round cvi Res exch 2 index exch put 1 add 0.0 0}]def/Val 0.0 def/Phase 0 def {0 Val Phase Proc/Res Unpack{exch Ops exch get exec}forall/Phase exch def/Val exch def Res exch 0 exch getinterval} image end restore}ifelse}ifelse }__NXbdef /nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef /setpattern{pop .5 setgray}__NXbdef /_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef } ifelse /_NXSetCMYKOrRGB where{pop}{ mark{systemdict /currentwindow get exec}stopped {{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark }ifelse
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Fy(Y)1395 1920 y Ft(i)1423 1914 y Fx(,)g(and)h Fu(f)1549 1920 y Ft(i)1576 1914 y Fx(is)g(the)g(actual)554 1964 y(resp)q(onse)i(\(1)d(or)h (0\))g(for)f Fy(Y)973 1970 y Ft(i)987 1964 y Fx(.])554 2029 y(Note)k(also)f(that)g(b)q(ecause)j(the)e(w)o(eigh)o(t)f(v)o(ector)i Fy(V)e Fx(no)o(w)g(includes)h(the)h Fu(w)1736 2035 y Ft(n)p Fr([phone] y Fx(threshold)g(comp)q(onen)o(t,)f(the)h(threshold)g(of)f (the)h(TLU)g(is)f(also)g(c)o(hanged)h(b)o(y)554 2129 y(these)d(adjustmen)o (ts.)512 2224 y(W)m(e)f(iden)o(tify)f(t)o(w)o(o)g(v)o(ersions)i(of)e(this)h (pro)q(cedure:)512 2284 y(1\))i(In)f(the)i Fs(\014xe)n(d-incr)n(ement)g(pr)n (o)n(c)n(e)n(dur)n(e)p Fx(,)e(the)h(learning)f(rate)h(parameter,)g Fu(c)1731 2290 y Ft(i)1744 2284 y Fx(,)g(is)450 2334 y(the)g(same)e(\014xed,) h(p)q(ositiv)o(e)g(constan)o(t)g(for)g(all)f Fu(i)p Fx(.)21 b(Dep)q(ending)16 b(on)e(the)i(v)n(alue)e(of)h(this)450 2384 y(constan)o(t,)i(the)h(w)o(eigh)o(t)e(adjustmen)o(t)g(ma)o(y)f(or)h(ma)o(y)f (not)i(correct)h(the)g(resp)q(onse)g(to)450 2434 y(an)c(erroneously)g (classi\014ed)h(feature)f(v)o(ector.)450 2539 y Fo(Intr)n(o)n(duction)g(to)k (Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 45 7 45 6 bop 150 275 a Fp(4.1.)31 b(THRESHOLD)14 b(LOGIC)f(UNITS)654 b Fx(45)212 391 y(2\))22 b(In)g(the)h Fs(fr)n(actional-c)n(orr)n(e)n(ction)d (pr)n(o)n(c)n(e)n(dur)n(e)p Fx(,)j(the)g(parameter)f Fu(c)1305 397 y Ft(i)1340 391 y Fx(is)g(set)h(to)150 466 y Fu(\025)187 434 y Fy(Y)223 453 y(i)238 434 y Fi(\017)p Fy(V)p 179 456 120 2 v 179 487 a(Y)215 505 y(i)231 487 y Fi(\017)p Fy(Y)284 505 y(i)304 466 y Fx(,)d(where)h Fy(V)e Fx(is)g(the)h(w)o(eigh)o(t)f(v)o(ector)h Fs(b)n(efor)n(e)f Fx(it)f(is)i(c)o(hanged.)34 b(Note)20 b(that)150 538 y(if)c Fu(\025)f Fx(=)h(0,)h(no)f(correction)h(tak)o(es)g(place)g(at)f (all.)24 b(If)16 b Fu(\025)g Fx(=)g(1,)g(the)h(correction)h(is)e(just)150 588 y(su\016cien)o(t)e(to)g(mak)o(e)e Fh(Y)516 601 y(i)531 588 y Fm(\017)p Fh(V)g Fn(=)f(0)p Fx(.)18 b(If)13 b Fu(\025)f(>)g Fx(1,)h(the)h(error)h(will)e(b)q(e)h(corrected.)212 648 y(It)f(can)g(b)q(e)g (pro)o(v)o(ed)f(that)h(if)f(there)h(is)g(some)e(w)o(eigh)o(t)h(v)o(ector,)i Fy(V)p Fx(,)e(that)g(pro)q(duces)i(a)150 698 y(correct)g(output)f(for)f(all)g (of)g(the)h(feature)g(v)o(ectors)h(in)e(\004,)g(then)i(after)f(a)f(\014nite)h (n)o(um)o(b)q(er)150 748 y(of)d(feature)i(v)o(ector)g(presen)o(tations,)h (the)e(\014xed-incremen)o(t)g(pro)q(cedure)i(will)d(\014nd)h(suc)o(h)150 797 y(a)k(w)o(eigh)o(t)h(v)o(ector)g(and)g(th)o(us)g(mak)o(e)e(no)h(more)g(w) o(eigh)o(t)g(c)o(hanges.)24 b(The)16 b(same)f(result)150 847 y(holds)f(for)f(the)i(fractional-correction)e(pro)q(cedure)j(if)d(1)e Fu(<)h(\025)g Fw(\024)g Fx(2.)212 907 y(F)m(or)e(additional)e(bac)o(kground,) i(pro)q(ofs,)g(and)f(examples)g(of)g(error-correction)j(pro-)150 957 y(cedures,)j(see)h([Nilsson,)c(1990)o(].)878 b Fr(See)1529 990 y([Maass)11 b(&)h(T)m(ur\023)-17 b(an,)11 b(1994)o(])1529 1023 y(for)g(a)1529 1056 y(h)o(yp)q(erplane-)1529 1090 y(\014nding)1529 1123 y(pro)q(cedure)g(that)1529 1156 y(mak)o(es)h(no)f(more)1529 1189 y(than)1529 1222 y Ft(O)q Fr(\()p Ft(n)1589 1210 y Fg(2)1612 1222 y Fr(log)5 b Ft(n)p Fr(\))1529 1256 y(mistak)o(es.)150 1082 y Fz(4.1.4)55 b(W)-5 b(eigh)n(t)19 b(Space)150 1168 y Fx(W)m(e)f(can)g(giv)o(e)g(an)g(in)o(tuitiv)o(e)f(idea)h(ab)q(out)g(ho)o(w)f (these)j(pro)q(cedures)g(w)o(ork)e(b)o(y)g(con-)150 1218 y(sidering)e(what)g (happ)q(ens)h(to)e(the)i(augmen)o(ted)e(w)o(eigh)o(t)h(v)o(ector)g(in)g(\\w)o (eigh)o(t)f(space")150 1268 y(as)f(corrections)i(are)f(made.)i(W)m(e)d(use)h (augmen)o(ted)f(v)o(ectors)h(in)f(our)g(discussion)h(here)150 1318 y(so)i(that)h(the)f(threshold)h(function)f(compares)g(the)h(dot)f(pro)q (duct,)i Fy(Y)1270 1324 y Ft(i)1284 1318 y Fw(\017)o Fy(V)q Fx(,)f(against)150 1368 y(a)h(threshold)h(of)e(0.)34 b(A)19 b(particular)g(w)o(eigh)o(t)g(v)o(ector,)i Fy(V)p Fx(,)d(then)i(corresp)q
(onds)h(to)e(a)150 1418 y(p)q(oin)o(t)e(in)g(\()p Fu(n)12 b Fx(+)g(1\)-dimensional)j(w)o(eigh)o(t)i(space.)30 b(No)o(w,)17 b(for)g(an)o(y)g(pattern)i(v)o(ector,)150 1467 y Fy(Y)186 1473 y Ft(i)200 1467 y Fx(,)12 b(consider)h(the)g(lo)q(cus)f(of)g(all)f(p)q(oin)o (ts)h(in)g(w)o(eigh)o(t)g(space)h(corresp)q(onding)g(to)f(w)o(eigh)o(t)150 1517 y(v)o(ectors)i(yielding)d Fy(Y)480 1523 y Ft(i)494 1517 y Fw(\017)p Fy(V)h Fx(=)g(0.)18 b(This)12 b(lo)q(cus)h(is)g(a)g(h)o(yp)q (erplane)g(passing)g(through)f(the)150 1567 y(origin)g(of)g(the)h(\()p Fu(n)7 b Fx(+)h(1\)-dimensional)i(space.)19 b(Eac)o(h)13 b(pattern)h(v)o (ector)f(will)f(ha)o(v)o(e)g(suc)o(h)150 1617 y(a)j(h)o(yp)q(erplane)h (corresp)q(onding)h(to)e(it.)23 b(W)m(eigh)o(t)14 b(p)q(oin)o(ts)i(in)f(one)h (of)f(the)h(half-spaces)150 1667 y(de\014ned)g(b)o(y)e(this)h(h)o(yp)q (erplane)g(will)e(cause)j(the)f(corresp)q(onding)g(pattern)h(to)e(yield)g(a) 150 1716 y(dot)d(pro)q(duct)h(less)g(than)g(0,)f(and)g(w)o(eigh)o(t)g(p)q (oin)o(ts)g(in)g(the)h(other)g(half-space)f(will)f(cause)150 1766 y(the)k(corresp)q(onding)h(pattern)g(to)f(yield)f(a)h(dot)f(pro)q(duct)i (greater)g(than)f(0.)212 1826 y(W)m(e)f(sho)o(w)h(a)f(sc)o(hematic)h (represen)o(tation)h(of)e(suc)o(h)h(a)f(w)o(eigh)o(t)g(space)i(in)e(Fig.)k (4.5.)150 1876 y(There)f(are)g(four)f(pattern)h(h)o(yp)q(erplanes,)g(1,)f(2,) g(3,)g(4)g(,)g(corresp)q(onding)i(to)e(patterns)150 1926 y Fy(Y)186 1932 y Fr(1)205 1926 y Fx(,)f Fy(Y)267 1932 y Fr(2)286 1926 y Fx(,)h Fy(Y)349 1932 y Fr(3)368 1926 y Fx(,)f Fy(Y)430 1932 y Fr(4)449 1926 y Fx(,)h(resp)q(ectiv)o(ely)m(,)g(and)g(w)o(e)g (indicate)g(b)o(y)g(an)g(arro)o(w)f(the)i(half-space)150 1975 y(for)c(eac)o(h)h(in)f(whic)o(h)h(w)o(eigh)o(t)f(v)o(ectors)h(giv)o(e)f(dot)h (pro)q(ducts)h(greater)f(than)g(0.)k(Supp)q(ose)150 2025 y(w)o(e)11 b(w)o(an)o(ted)f(w)o(eigh)o(t)g(v)n(alues)h(that)f(w)o(ould)g(giv)o(e)g(p)q (ositiv)o(e)g(resp)q(onses)j(for)d(patterns)i Fy(Y)1470 2031 y Fr(1)1488 2025 y Fx(,)150 2075 y Fy(Y)186 2081 y Fr(3)205 2075 y Fx(,)g(and)g Fy(Y)344 2081 y Fr(4)363 2075 y Fx(,)g(and)g(a)g(negativ) o(e)g(resp)q(onse)j(for)d(pattern)h Fy(Y)1072 2081 y Fr(2)1090 2075 y Fx(.)18 b(The)13 b(w)o(eigh)o(t)f(p)q(oin)o(t,)f Fy(V)p Fx(,)150 2125 y(indicated)j(in)f(the)i(\014gure)f(is)g(one)g(suc)o(h)h(set)g (of)e(w)o(eigh)o(t)g(v)n(alues.)212 2185 y(The)j(question)g(of)e(whether)j (or)e(not)g(there)i(exists)f(a)f(w)o(eigh)o(t)g(v)o(ector)h(that)f(giv)o(es) 150 2234 y(desired)e(resp)q(onses)i(for)d(a)g(giv)o(en)g(set)h(of)f(patterns) h(can)g(b)q(e)f(giv)o(en)g(a)g(geometric)g(in)o(ter-)150 2284 y(pretation.)21 b(T)m(o)14 b(do)h(so)g(in)o(v)o(olv)o(es)f(rev)o(ersing)h (the)h(\\p)q(olarit)o(y")d(of)h(those)i(h)o(yp)q(erplanes)150 2334 y(corresp)q(onding)h(to)g(patterns)g(for)f(whic)o(h)g(a)g(negativ)o(e)h (resp)q(onse)h(is)e(desired.)27 b(If)16 b(w)o(e)150 2384 y(do)e(that)h(for)f (our)g(example)f(ab)q(o)o(v)o(e,)h(w)o(e)h(get)f(the)h(w)o(eigh)o(t)f(space)i (diagram)c(sho)o(wn)i(in)150 2434 y(Fig.)j(4.6.)150 2539 y Fo(Intr)n(o)n(duction)d(to)k(Machine)e(L)n(e)n(arning)757 2538 y Fn(c)746 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 46 8 46 7 bop 450 275 a Fx(46)579 b Fp(CHAPTER)14 b(4.)32 b(NEURAL)14 b(NETW)o(ORKS)754 1008 y @beginspecial 4 @llx 550 @lly 182 @urx 708 @ury 1780 @rwi @setspecial %%BeginDocument: Four/weight1.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval
/UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat
strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known
{pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 4 550 178 158 rectclip 4 550 178 158 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 9 555 168 148 rectfill 9.000000 555.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 168 148 rectclip 0.416873 0.414566 scale -32 -232 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch
def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def
/findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 32.794872 232.794876 401.205139 355.410248 rectclip 32.794872 232.794876 401.205139 355.410248 rectclip 0 0 2.205128 setup 0 setgray 1 setalpha 56 -310 181 550 line grestore
0 0 2.205128 setup 0 setgray 1 setalpha 116 281 147 257 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 284 76 65 367 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 318 -115 40 465 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 254 537 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 355 exch defineuserobject 355 execuserobject setfont 0 setgray [1 0 0 -1 0 1104] concat /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 39 exch defineuserobject 39 execuserobject setfont 0 setgray 265 558 moveto (2) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 164 550 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 1118] concat 39 execuserobject setfont 0 setgray 173 559 moveto (3) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 359 328 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup
gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 686] concat 39 execuserobject setfont 0 setgray 370 349 moveto (4) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 349 432 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 894] concat 39 execuserobject setfont 0 setgray 360 453 moveto (1) show grestore grestore 0 0 4.666667 setup 0 setgray 1 setalpha 29 2 193 487 line 3.945303 222 489 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 28 -10 226 526 line 160.345596 226 526 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 10 24 331 360 line 67.382126 341 384 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 11 -26 317 435 line -67.069878 328 409 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 381 395 oval fill grestore 0 setgray 1 setalpha 10 10 381 395 oval matrix defaultmatrix setmatrix stroke
grestore 0 0 0 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 825] concat 355 execuserobject setfont 0 setgray 396 419 moveto (V) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 895 1099 a Fx(Figure)g(4.5:)j(W)m(eigh)o(t)c(Space)512 1226 y(If)i(a)f(w)o(eigh)o(t)g(v)o(ector)h(exists)h(that)f(correctly)g (classi\014es)h(a)e(set)i(of)e(patterns,)h(then)450 1276 y(the)e(half-spaces) f(de\014ned)h(b)o(y)f(the)h(correct)h(resp)q(onses)g(for)e(these)h(patterns)h (will)c(ha)o(v)o(e)450 1326 y(a)17 b(non-empt)o(y)e(in)o(tersection,)j (called)f(the)g(solution)f(region.)27 b(The)17 b(solution)f(region)450 1376 y(will)10 b(b)q(e)i(a)f(\\h)o(yp)q(er-w)o(edge")h(region)g(whose)g(v)o (ertex)g(is)f(at)h(the)g(origin)e(of)h(w)o(eigh)o(t)g(space)450 1426 y(and)i(whose)i(cross-section)g(increases)g(with)e(increasing)h (distance)h(from)c(the)k(origin.)450 1476 y(This)i(region)g(is)f(sho)o(wn)h (shaded)h(in)e(Fig.)27 b(4.6.)f(\(The)17 b(b)q(o)o(xed)h(n)o(um)o(b)q(ers)e (sho)o(w,)h(for)450 1525 y(later)c(purp)q(oses,)i(the)f(n)o(um)o(b)q(er)f(of) f(errors)j(made)d(b)o(y)h(w)o(eigh)o(t)g(v)o(ectors)i(in)e(eac)o(h)h(of)e (the)450 1575 y(regions.\))20 b(The)14 b(\014xed-incremen)o(t)h (error-correction)h(pro)q(cedure)g(c)o(hanges)f(a)f(w)o(eigh)o(t)450 1625 y(v)o(ector)d(b)o(y)g(mo)o(ving)d(it)i(normal)e(to)j(an)o(y)f(pattern)h (h)o(yp)q(erplane)g(for)f(whic)o(h)h(that)f(w)o(eigh)o(t)450 1675 y(v)o(ector)j(giv)o(es)e(an)h(incorrect)h(resp)q(onse.)19 b(Supp)q(ose)13 b(in)f(our)g(example)e(that)i(w)o(e)g(presen)o(t)450 1725 y(the)i(patterns)g(in)f(the)h(sequence)h Fy(Y)1010 1731 y Fr(1)1029 1725 y Fx(,)d Fy(Y)1089 1731 y Fr(2)1108 1725 y Fx(,)h Fy(Y)1169 1731 y Fr(3)1188 1725 y Fx(,)f Fy(Y)1248 1731 y Fr(4)1267 1725 y Fx(,)h(and)g(start)h(the)f(pro)q(cess)i(with)e(a)450 1774 y(w)o(eigh)o(t)g(p)q(oin)o(t)g Fy(V)725 1780 y Fr(1)743 1774 y Fx(,)g(as)h(sho)o(wn)f(in)g(Fig.)k(4.7.)g(Starting)c(at)g Fy(V)1411 1780 y Fr(1)1430 1774 y Fx(,)g(w)o(e)g(see)i(that)e(it)g(giv)o(es) 450 1824 y(an)h(incorrect)i(resp)q(onse)h(for)d(pattern)i Fy(Y)1100 1830 y Fr(1)1118 1824 y Fx(,)f(so)f(w)o(e)h(mo)o(v)o(e)e Fy(V)1402 1830 y Fr(1)1435 1824 y Fx(to)i Fy(V)1523 1830 y Fr(2)1556
1824 y Fx(in)f(a)h(direction)450 1874 y(normal)h(to)h(plane)h(1.)29 b(\(That)17 b(is)h(what)f(adding)g Fy(Y)1278 1880 y Fr(1)1314 1874 y Fx(to)h Fy(V)1405 1880 y Fr(1)1441 1874 y Fx(do)q(es.\))30 b Fy(Y)1614 1880 y Fr(2)1651 1874 y Fx(giv)o(es)17 b(an)450 1924 y(incorrect)j(resp)q(onse)g(for)e(pattern)h Fy(Y)1056 1930 y Fr(2)1074 1924 y Fx(,)g(and)f(so)h(on.)31 b(Ultimately)m(,)16 b(the)j(resp)q(onses)450 1974 y(are)g(only)e(incorrect)j(for)e(planes)g(b)q (ounding)g(the)h(solution)e(region.)32 b(Some)17 b(of)g(the)450 2023 y(subsequen)o(t)i(corrections)f(ma)o(y)d(o)o(v)o(ersho)q(ot)i(the)g (solution)g(region,)f(but)i(ev)o(en)o(tually)450 2073 y(w)o(e)13 b(w)o(ork)f(our)g(w)o(a)o(y)g(out)g(far)g(enough)h(in)f(the)h(solution)f (region)g(that)g(corrections)i(\(for)450 2123 y(a)f(\014xed)g(incremen)o(t)g (size\))h(tak)o(e)f(us)g(within)g(it.)k(The)d(pro)q(ofs)f(for)f(con)o(v)o (ergence)j(of)d(the)450 2173 y(\014xed-incremen)o(t)i(rule)g(mak)o(e)f(this)g (in)o(tuitiv)o(e)g(argumen)o(t)g(precise.)450 2298 y Fz(4.1.5)55 b(The)19 b(Widro)n(w-Ho\013)f(Pro)r(cedure)450 2384 y Fx(The)e(Widro)o (w-Ho\013)f(pro)q(cedure)j(\(also)d(called)g(the)i Fs(LMS)f Fx(or)g(the)g Fs(delta)g Fx(pro)q(cedure\))450 2434 y(attempts)9 b(to)g(\014nd)h(w)o(eigh)o(ts)f(that)g(minimi)o(ze)e(a)j(squared-error)h (function)e(b)q(et)o(w)o(een)h(the)450 2539 y Fo(Intr)n(o)n(duction)k(to)k (Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 47 9 47 8 bop 150 275 a Fp(4.1.)31 b(THRESHOLD)14 b(LOGIC)f(UNITS)654 b Fx(47)358 1108 y @beginspecial 4 @llx 528 @lly 228 @urx 710 @ury 2240 @rwi @setspecial %%BeginDocument: Four/weight2.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef
/xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
/flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for
_NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 4 528 224 182 rectclip 4 528 224 182 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 9 533 214 172 rectfill 9.000000 533.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 214 172 rectclip 0.480899 0.481793 scale -32 -232 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse
}__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
}repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{
1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 32.794872 232.794876 443.205139 355.410248 rectclip 32.794872 232.794876 443.205139 355.410248 rectclip 0 setgray 0.333333 setgray 0 0 0 setup gsave -0.787079 5.235291 translate 1.003802 0.986928 scale 0.710746 setgray 1 setalpha gsave newpath systemdict begin 207 324 470 477 setbbox 207 404 moveto 263 73 rlineto -50 -153 rlineto -212 82 rlineto -1 -1 rlineto 0 -1 rlineto end eofill grestore grestore -0.787079 5.235291 translate 1.003802 0.986928 scale 0 setgray 1 setalpha gsave
newpath systemdict begin 207 324 470 477 setbbox 207 404 moveto 263 73 rlineto -50 -153 rlineto -212 82 rlineto -1 -1 rlineto 0 -1 rlineto end stroke grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 56 -310 181 550 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 116 281 147 257 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 284 76 65 367 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 318 -115 40 465 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 254 537 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave /Helvetica findfont 24 scalefont [1 0 0 -1 0 0] makefont 71 exch defineuserobject 71 execuserobject setfont 0 setgray [1 0 0 -1 0 1104] concat /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 39 exch defineuserobject 39 execuserobject setfont 0 setgray 265 558 moveto (2) show grestore grestore 0 0 2.205128 setup 0 setgray
1 setalpha 31 31 164 550 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 1118] concat 39 execuserobject setfont 0 setgray 173 559 moveto (3) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 359 328 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 686] concat 39 execuserobject setfont 0 setgray 370 349 moveto (4) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 349 432 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 894] concat 39 execuserobject setfont 0 setgray 360 453 moveto (1) show grestore grestore 0 0 4.666667 setup 0 setgray 1 setalpha 29 2 193 487 line 3.945303 222 489 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 27 -9 254 516 line -18.435492 281 507 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 10 24 331 360 line
67.382126 341 384 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 11 -26 317 435 line -67.069878 328 409 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 381 395 oval fill grestore 0 setgray 1 setalpha 10 10 381 395 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 781] concat /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 355 exch defineuserobject 355 execuserobject setfont 0 setgray 398 397 moveto (V) show grestore grestore 0 0 0 setup gsave 355 execuserobject setfont 0 setgray [1 0 0 -1 0 858] concat 71 execuserobject setfont 0 setgray 424 433 moveto (0) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 1059] concat 71 execuserobject setfont 0 setgray 374 538 moveto (1) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 575] concat
71 execuserobject setfont 0 setgray 310 296 moveto (1) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 1091] concat 71 execuserobject setfont 0 setgray 217 554 moveto (2) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 1061] concat 71 execuserobject setfont 0 setgray 107 539 moveto (3) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 535] concat 71 execuserobject setfont 0 setgray 187 276 moveto (2) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 653] concat 71 execuserobject setfont 0 setgray 93 335 moveto (3) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 829] concat 71 execuserobject setfont 0 setgray 50 423 moveto (4) show grestore grestore 0 0 1.435897 setup 0 setgray 1 setalpha 43 398 29 29 rectstroke
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0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse
}ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave -1 529 233 185 rectclip -1 529 233 185 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 4 534 223 175 rectfill 4.000000 534.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 223 175 rectclip 0.492274 0.490196 scale -23 -232 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef
/defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse
{//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 23 232.794876 453 355.410248 rectclip 23 232.794876 453 355.410248 rectclip 0 setgray 0.333333 setgray 0 0 0 setup gsave -0.787079 6.235291 translate 1.003802 0.986928 scale 0.710746 setgray 1 setalpha gsave newpath systemdict
begin 207 324 470 477 setbbox 207 404 moveto 263 73 rlineto -50 -153 rlineto -212 82 rlineto -1 -1 rlineto 0 -1 rlineto end eofill grestore grestore -0.787079 6.235291 translate 1.003802 0.986928 scale 0 setgray 1 setalpha gsave newpath systemdict begin 207 324 470 477 setbbox 207 404 moveto 263 73 rlineto -50 -153 rlineto -212 82 rlineto -1 -1 rlineto 0 -1 rlineto end stroke grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 56 -310 181 550 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 116 281 147 257 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 284 76 65 367 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 318 -115 41 465 line grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 254 537 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont
85 exch defineuserobject 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1104] concat 85 execuserobject setfont 0 setgray 265 558 moveto (2) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 164 550 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1118] concat 85 execuserobject setfont 0 setgray 173 559 moveto (3) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 359 328 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 686] concat 85 execuserobject setfont 0 setgray 370 349 moveto (4) show grestore grestore 0 0 2.205128 setup 0 setgray 1 setalpha 31 31 349 432 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.205128 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 894] concat 85 execuserobject setfont 0 setgray 360 453 moveto (1) show grestore grestore 0 0 4.666667 setup 0 setgray 1 setalpha
29 2 193 487 line 3.945303 222 489 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 27 -9 254 516 line -18.435492 281 507 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 10 24 344 356 line 67.382126 354 380 arrow grestore 0 0 4.666667 setup 0 setgray 1 setalpha 11 -26 336 439 line -67.069878 347 413 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 381 395 oval fill grestore 0 setgray 1 setalpha 10 10 381 395 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 787] concat /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 738 exch defineuserobject 738 execuserobject setfont 0 setgray 396 400 moveto (V) show grestore grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 52 482 oval fill grestore 0 setgray 1 setalpha 10 10 52 482 oval matrix defaultmatrix setmatrix stroke grestore
0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 76 399 oval fill grestore 0 setgray 1 setalpha 10 10 76 399 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 2.153846 setup 0 setgray 1 setalpha 22 -77 57 487 line -74.056786 79 410 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 154 365 oval fill grestore 0 setgray 1 setalpha 10 10 154 365 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 2.153846 setup 0 setgray 1 setalpha 73 -33 82 403 line -24.326292 155 370 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 240 378 oval fill grestore 0 setgray 1 setalpha 10 10 240 378 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 2.153846 setup 0 setgray 1 setalpha 76 11 165 371 line 8.235862 241 382 arrow
grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 268 465 oval fill grestore 0 setgray 1 setalpha 10 10 268 465 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 2.153846 setup 0 setgray 1 setalpha 25 76 247 389 line 71.793633 272 465 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 setgray 1 setalpha 10 10 295 381 oval fill grestore 0 setgray 1 setalpha 10 10 295 381 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 2.153846 setup 0 setgray 1 setalpha 23 -72 275 464 line -72.286339 298 392 arrow grestore 0 0 0 setup gsave 738 execuserobject setfont 0 setgray [1 0 0 -1 0 1010] concat 738 execuserobject setfont 0 setgray 52 508 moveto (V) show 85 execuserobject setfont 0 7 rmoveto (1) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray
[1 0 0 -1 0 802] concat 738 execuserobject setfont 0 setgray 43 404 moveto (V) show 85 execuserobject setfont 0 7 rmoveto (2) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 688] concat 738 execuserobject setfont 0 setgray 131 347 moveto (V) show 85 execuserobject setfont 0 7 rmoveto (3) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 706] concat 738 execuserobject setfont 0 setgray 240 356 moveto (V) show 85 execuserobject setfont 0 7 rmoveto (4) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 974] concat 738 execuserobject setfont 0 setgray 297 490 moveto (V) show 85 execuserobject setfont 0 7 rmoveto (5) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 790] concat 738 execuserobject setfont 0 setgray
302 398 moveto (V) show 85 execuserobject setfont 0 7 rmoveto (6) show 0 -7 rmoveto grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 720 1212 a Fx(Figure)g(4.7:)j(Mo)o(ving)12 b(In)o(to)i(the)h (Solution)d(Region)450 1341 y(of)k(\004)g(at)g(a)h(time,)e(compute)h(the)h (gradien)o(t)f(of)g(the)h(single-pattern)g(squared)g(error,)450 1391 y Fu(")469 1397 y Ft(i)483 1391 y Fx(,)d(mak)o(e)f(the)i(appropriate)g (adjustmen)o(t)f(to)g(the)h(w)o(eigh)o(ts,)f(and)h(then)g(try)g(another)450 1440 y(mem)o(b)q(er)h(of)g(\004.)28 b(Of)17 b(course,)h(the)g(results)h(of)d (the)i(incremen)o(tal)e(v)o(ersion)h(can)h(only)450 1490 y(appro)o(ximate)10 b(those)j(of)f(the)h(batc)o(h)f(one,)g(but)h(the)f(appro)o(ximation)e(is)i (usually)f(quite)450 1540 y(e\013ectiv)o(e.)19 b(W)m(e)14 b(will)e(b)q(e)j (describing)f(the)h(incremen)o(tal)e(v)o(ersion)h(here.)512 1600 y(The)h Fu(j)r Fx(-th)f(comp)q(onen)o(t)f(of)g(the)i(gradien)o(t)f(of)f (the)h(single-pattern)h(error)f(is:)872 1707 y Fu(@)r(")915 1713 y Ft(i)p 865 1725 72 2 v 865 1763 a Fu(@)r(w)919 1769 y Ft(j)953 1735 y Fx(=)d Fw(\000)p Fx(2\()p Fu(d)1087 1741 y Ft(i)1110 1735 y Fw(\000)1152 1683 y Ft(n)p Fr([phone] y Fj(X)1154 1784 y Ft(j)r Fr(=1)1221 1735 y Fu(x)1245 1741 y Ft(ij)1274 1735 y Fu(w)1304 1741 y Ft(j)1321 1735 y Fx(\))p Fu(x)1361 1741 y Ft(ij)450 1874 y Fx(An)i(adjustmen)o(t)f(in)g(the)i (direction)e(of)h(the)g(negativ)o(e)g(gradien)o(t)f(w)o(ould)g(then)i(c)o (hange)450 1924 y(eac)o(h)g(w)o(eigh)o(t)g(as)g(follo)o(ws:)889 2029 y Fu(w)919 2035 y Ft(j)948 2029 y Fw( )-7 b(\000)11 b Fu(w)1056 2035 y Ft(j)1082 2029 y Fx(+)f Fu(c)1142 2035 y Ft(i)1156 2029 y Fx(\()p Fu(d)1194 2035 y Ft(i)1216 2029 y Fw(\000)g Fu(f)1278 2035 y Ft(i)1292 2029 y Fx(\))p Fu(x)1332 2035 y Ft(ij)450 2132 y Fx(where)j Fu(f)588 2138 y Ft(i)614 2132 y Fx(=)658 2101 y Fj(P)702 2111 y Ft(n)p Fr([phone] y Ft(j)r Fr(=1)773 2132 y Fu(x)797 2138 y Ft(ij)826 2132 y Fu(w)856 2138 y Ft(j)873 2132 y Fx(,)f(and)g Fu(c)994 2138 y Ft(i)1020 2132 y Fx(go)o(v)o(erns)g(the)h(size)g(of)e(the)i(adjustmen)o(t.)j(The)d(en-) 450 2182 y(tire)e(w)o(eigh)o(t)e(v)o(ector)j(\(in)d(augmen)o(ted,)h(or)g Fy(V)q Fx(,)h(notation\))e(is)h(th)o(us)h(adjusted)g(according)450 2231 y(to)j(the)g(follo)o(wing)d(rule:)901 2337 y Fy(V)h Fw( )-7 b(\000)11 b Fy(V)f Fx(+)g Fu(c)1133 2343 y Ft(i)1147 2337 y
Fx(\()p Fu(d)1185 2343 y Ft(i)1208 2337 y Fw(\000)f Fu(f)1269 2343 y Ft(i)1283 2337 y Fx(\))p Fy(Y)1335 2343 y Ft(i)450 2434 y Fx(where,)15 b(as)f(b)q(efore,)g Fy(Y)805 2440 y Ft(i)832 2434 y Fx(is)g(the)h Fu(i)p Fx(-th)f(augmen)o(ted)f(pattern)i(v)o(ector.)450 2539 y Fo(Intr)n(o)n(duction)f(to)k(Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 49 11 49 10 bop 150 275 a Fp(4.1.)31 b(THRESHOLD)14 b(LOGIC)f(UNITS)654 b Fx(49)212 391 y(The)20 b(Widro)o(w-Ho\013)d(pro)q(cedure)k(mak)o(es)d (adjustmen)o(ts)g(to)h(the)h(w)o(eigh)o(t)e(v)o(ector)150 441 y(whenev)o(er)c(the)f(dot)g(pro)q(duct)g(itself,)f Fh(Y)772 445 y Ff(i)786 441 y Fm(\017)p Fh(V)q Fx(,)g(do)q(es)i(not)e(equal)g(the)i (sp)q(eci\014ed)g(desired)150 491 y(target)20 b(v)n(alue,)f Fu(d)425 497 y Ft(i)458 491 y Fx(\(whic)o(h)g(is)g(either)h(1)f(or)g Fw(\000)p Fx(1\).)34 b(The)20 b(learning-rate)f(factor,)h Fu(c)1475 497 y Ft(i)1488 491 y Fx(,)150 541 y(migh)o(t)10 b(decrease)j(with)f(time)e (to)o(w)o(ard)h(0)h(to)f(ac)o(hiev)o(e)h(asymptotic)f(con)o(v)o(ergence.)19 b(The)150 591 y(Widro)o(w-Ho\013)13 b(form)o(ula)e(for)j(c)o(hanging)f(the)i (w)o(eigh)o(t)e(v)o(ector)i(has)f(the)h(same)e(form)f(as)150 640 y(the)i(standard)h(\014xed-incremen)o(t)f(error-correction)h(form)o(ula.) h(The)e(only)f(di\013erence)150 690 y(is)k(that)h Fu(f)309 696 y Ft(i)341 690 y Fx(is)f(the)h(thresholded)h(resp)q(onse)g(of)e(the)h (TLU)g(in)f(the)h(error-correction)150 740 y(case)d(while)e(it)h(is)g(the)g (dot)g(pro)q(duct)h(itself)e(for)h(the)g(Widro)o(w-Ho\013)f(pro)q(cedure.)212 795 y(Finding)k(w)o(eigh)o(t)g(v)n(alues)g(that)g(giv)o(e)g(the)h(desired)g (dot)f(pro)q(ducts)i(corresp)q(onds)150 845 y(to)f(solving)f(a)h(set)h(of)f (linear)f(equalities,)i(and)f(the)g(Widro)o(w-Ho\013)g(pro)q(cedure)i(can)150 895 y(b)q(e)25 b(in)o(terpreted)h(as)e(a)g(descen)o(t)i(pro)q(cedure)g(that)e (attempts)g(to)g(minimi)o(ze)e(the)150 945 y(mean-squared-error)k(b)q(et)o(w) o(een)g(the)g(actual)f(and)h(desired)g(v)n(alues)f(of)g(the)h(dot)150 994 y(pro)q(duct.)40 b(\(F)m(or)20 b(more)g(on)g(Widro)o(w-Ho\013)g(and)h (other)g(related)g(pro)q(cedures,)k(see)150 1044 y([Duda)13 b(&)h(Hart,)g(1973)o(,)f(pp.)18 b(151\013].\))788 b Fr(Examples)12 b(of)1529 1078 y(training)g(curv)o(es)1529 1111 y(for)f(TLU's;)1529 1144 y(p)q(erformance)g(on)1529 1177 y(training)h(set;)1529 1210 y(p)q(erformance)f(on)1529 1244 y(test)g(set;)1529 1277 y(cum)o(ulativ)o(e)1529 1310 y(n)o(um)o(b)q(er)h(of)1529 1343 y(corrections.)150 1163 y Fz(4.1.6)55 b(T)-5 b(raining)13 b(a)f(TLU)g(on)h (Non-Linearly-Separable)c(T)-5 b(rain-)321 1221 y(ing)19 b(Sets)150 1303 y Fx(When)d(the)h(training)e(set)j(is)e(not)g(linearly)f(separable)i (\(p)q(erhaps)g(b)q(ecause)h(of)e(noise)150 1353 y(or)g(p)q(erhaps)h(inheren) o(tly\),)f(it)f(ma)o(y)f(still)h(b)q(e)h(desired)h(to)f(\014nd)g(a)f(\\b)q (est")i(separating)150 1403 y(h)o(yp)q(erplane.)23 b(T)o(ypically)m(,)13 b(the)i(error-correction)i(pro)q(cedures)h(will)c(not)h(do)g(w)o(ell)f(on)150 1452 y(non-linearly-separable)h(training)f(sets)j(b)q(ecause)g(they)f(will)e (con)o(tin)o(ue)h(to)h(attempt)150 1502 y(to)i(correct)i(inevitable)d (errors,)j(and)e(the)h(h)o(yp)q(erplane)f(will)f(nev)o(er)i(settle)g(in)o(to) e(an)150 1552 y(acceptable)e(place.)212 1607 y(Sev)o(eral)i(metho)q(ds)e(ha)o (v)o(e)h(b)q(een)h(prop)q(osed)g(to)f(deal)g(with)g(this)g(case.)25 b(First,)17 b(w)o(e)150 1657 y(migh)o(t)10 b(use)i(the)h(Widro)o(w-Ho\013)d (pro)q(cedure,)k(whic)o(h)e(\(although)f(it)g(will)g(not)g(con)o(v)o(erge)150 1707 y(to)i(zero)h(error)g(on)f(non-linearly)f(separable)i(problems\))e(will) g(giv)o(e)g(us)i(a)f(w)o(eigh)o(t)g(v)o(ec-)150 1757 y(tor)e(that)g(minim)o (izes)e(the)j(mean-squared-error.)17 b(A)11 b(mean-squared-error)h(criterion) 150 1807 y(often)k(giv)o(es)g(unsatisfactory)h(results,)g(ho)o(w)o(ev)o(er,)g (b)q(ecause)h(it)e(prefers)i(man)o(y)c(small)150 1856 y(errors)j(to)e(a)g (few)g(large)g(ones.)23 b(As)16 b(an)f(alternativ)o(e,)g(error)h(correction)h (with)e(a)g(con-)150 1906 y(tin)o(uous)g(decrease)i(to)o(w)o(ard)e(zero)h(of)
e(the)i(v)n(alue)f(of)f(the)i(learning)e(rate)i(constan)o(t,)g Fu(c)p Fx(,)150 1956 y(will)9 b(result)j(in)e(ev)o(er)i(decreasing)g(c)o (hanges)f(to)g(the)g(h)o(yp)q(erplane.)18 b(Duda)10 b([Duda,)i(1966)o(])150 2006 y(has)j(suggested)g(k)o(eeping)g(trac)o(k)g(of)e(the)i(a)o(v)o(erage)g (v)n(alue)f(of)g(the)h(w)o(eigh)o(t)f(v)o(ector)h(dur-)150 2056 y(ing)e(error)h(correction)g(and)g(using)f(this)g(a)o(v)o(erage)h(to)f (giv)o(e)g(a)g(separating)g(h)o(yp)q(erplane)150 2105 y(that)20 b(p)q(erforms)f(reasonably)h(w)o(ell)f(on)g(non-linearly-separable)h (problems.)34 b(Gal-)150 2155 y(lan)o(t)16 b([Gallan)o(t,)11 b(1986)o(])17 b(prop)q(osed)h(what)e(he)i(called)e(the)i(\\p)q(o)q(c)o(k)o (et)f(algorithm.")24 b(As)150 2205 y(describ)q(ed)16 b(in)d([Hertz,)h(Krogh,) g(&)g(P)o(almer,)e(1991)o(,)h(p.)19 b(160]:)254 2284 y(.)32 b(.)f(.)h(the)19 b(p)q(o)q(c)o(k)o(et)g(algorithm)d(.)32 b(.)g(.)f(consists) 20 b(simply)c(in)i(storing)254 2334 y(\(or)c(\\putting)g(in)f(y)o(our)h(p)q (o)q(c)o(k)o(et"\))h(the)g(set)g(of)f(w)o(eigh)o(ts)g(whic)o(h)g(has)g(had) 254 2384 y(the)i(longest)g(unmo)q(di\014ed)f(run)i(of)e(successes)k(so)d (far.)24 b(The)17 b(algorithm)254 2434 y(is)d(stopp)q(ed)g(after)h(some)e(c)o (hosen)h(time)f Fu(t)h Fx(.)k(.)g(.)150 2539 y Fo(Intr)n(o)n(duction)c(to)k (Machine)e(L)n(e)n(arning)757 2538 y Fn(c)746 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 50 12 50 11 bop 450 275 a Fx(50)579 b Fp(CHAPTER)14 b(4.)32 b(NEURAL)14 b(NETW)o(ORKS)450 391 y Fx(After)f(stopping,)f(the)h(w)o(eigh)o(ts)g(in)f (the)h(p)q(o)q(c)o(k)o(et)h(are)f(used)g(as)g(a)f(set)h(that)g(should)g(giv)o (e)450 441 y(a)h(small)f(n)o(um)o(b)q(er)h(of)g(errors)i(on)e(the)i(training) d(set.)22 b(Error-correction)16 b(pro)q(ceeds)h(as)450 491 y(usual)d(with)f(the)i(ordinary)e(set)i(of)e(w)o(eigh)o(ts.)-954 b Fr(Also)11 b(see)196 524 y(metho)q(ds)196 557 y(prop)q(osed)g(b)o(y)196 591 y([John,)h(1995)n(])196 624 y(and)f(b)o(y)196 657 y([Marc)o(hand)g(&)h (Golea,)f(1993)n(].)196 690 y(The)g(latter)g(is)196 723 y(claimed)h(to)196 757 y(outp)q(erform)f(the)196 790 y(p)q(o)q(c)o(k)o(et)196 823 y(algorithm.)450 635 y FA(4.2)70 b(Linear)22 b(Mac)n(hines)450 735 y Fx(The)13 b(natural)g(generalization)f(of)h(a)f(\(t)o(w)o(o-category\)) h(TLU)g(to)g(an)g Fu(R)p Fx(-category)g(clas-)450 785 y(si\014er)18 b(is)g(the)g(structure,)i(sho)o(wn)d(in)g(Fig.)29 b(4.8,)17 b(called)g(a)g Fs(line)n(ar)h(machine)p Fx(.)29 b(Here,)450 834 y(to)15 b(use)g(more)f(familia)o(r)e(notation,)i(the)h Fy(W)p Fx(s)h(and)e Fy(X)h Fx(are)g(mean)o(t)f(to)g(b)q(e)i(augmen)o(ted)450 884 y(v)o(ectors)f(\(with)f(an)g(\(n+1\)-st)h(comp)q(onen)o(t\).)j(Suc)o(h)c (a)g(structure)i(is)e(also)g(sometimes)450 934 y(called)i(a)h(\\comp)q (etitiv)o(e")e(net)i(or)f(a)h(\\winner-tak)o(e-all")e(net.)27 b(The)17 b(output)f(of)g(the)450 984 y(linear)g(mac)o(hine)e(is)i(one)g(of)g (the)g(n)o(um)o(b)q(ers,)g Fw(f)p Fx(1)p Fu(;)7 b(:)g(:)g(:)t(;)g(R)p Fw(g)p Fx(,)15 b(corresp)q(onding)i(to)f(whic)o(h)450 1034 y(dot)f(pro)q(duct)g(is)g(largest.)20 b(Note)15 b(that)g(when)g Fu(R)e Fx(=)g(2,)h(the)h(linear)g(mac)o(hine)e(reduces)450 1084 y(to)h(a)f(TLU)h(with)g(w)o(eigh)o(t)f(v)o(ector)i Fy(W)d Fx(=)g(\()p Fy(W)1157 1090 y Fr(1)1186 1084 y Fw(\000)d Fy(W)1276 1090 y Fr(2)1295 1084 y Fx(\).)733 1565 y @beginspecial 6 @llx 607 @lly 194 @urx 709 @ury 1880 @rwi @setspecial %%BeginDocument: Four/linear.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{
array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{
exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 6 607 188 102 rectclip 6 607 188 102 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 11 612 178 92 rectfill 11.000000 612.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 178 92 rectclip 0.403628 0.405286 scale -61 -350 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth
0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 61 350 441 227 rectclip 61 350 441 227 rectclip 0 0 2.682821 setup 0 setgray 1 setalpha 66 0 421 464 line
0 487 464 arrow grestore 0 0 0.17 setup gsave /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 355 exch defineuserobject 355 execuserobject setfont 0 setgray [1 0 0 -1 0 931] concat 355 execuserobject setfont 0 setgray 69 472 moveto (X) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 33.000004 32.275864 172 498.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 33.000004 32.275864 175 398.43103 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.734103 setup 0 setgray 1 setalpha 83 -1 206 513 line -0.690298 289 512 arrow grestore 0 0 2.734103 setup 0 setgray 1 setalpha 79 -1 210 414 line -0.725246 289 413 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 75 -40 96 561 line -28.073315 171 521 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 71 -37 99 458 line -27.526037 170 421 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 78 41 98 366 line 27.729076 176 407 arrow
grestore 0 0 2.990513 setup 0 setgray 1 setalpha 73 43 99 462 line 30.500734 172 505 arrow grestore 0 0 2.990513 setup gsave 355 execuserobject setfont 0 setgray [1 0 0 -1 0 1024] concat 355 execuserobject setfont 0 setgray 111 515 moveto (W) show /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 39 exch defineuserobject 39 execuserobject setfont 0 7 rmoveto (1) show 0 -7 rmoveto grestore grestore 0 0 2.990513 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 822] concat 355 execuserobject setfont 0 setgray 113 414 moveto (W) show 39 execuserobject setfont 0 7 rmoveto (R) show 0 -7 rmoveto grestore grestore 0 0 2.990513 setup gsave 39 execuserobject setfont 0 setgray [1 0 0 -1 0 940] concat /Helvetica-Bold findfont 24 scalefont [1 0 0 -1 0 0] makefont 27 exch defineuserobject 27 execuserobject setfont 0 setgray 168 479 moveto (. . .) show grestore grestore 0 0 2.990513 setup gsave 27 execuserobject setfont 0 setgray [1 0 0 -1 0 996] concat /Symbol findfont 24 scalefont [1 0 0 -1 0 0] makefont
310 exch defineuserobject 310 execuserobject setfont 0 setgray 181 490 moveto (S) show grestore grestore 0 0 2.990513 setup gsave 310 execuserobject setfont 0 setgray [1 0 0 -1 0 796] concat 310 execuserobject setfont 0 setgray 185 390 moveto (S) show grestore grestore 0 0 2.990513 setup 0 setgray 1 setalpha 293 392 126 143 rectstroke grestore 0 0 2.990513 setup gsave 310 execuserobject setfont 0 setgray [1 0 0 -1 0 918] concat /Helvetica findfont 24 scalefont [1 0 0 -1 0 0] makefont 71 exch defineuserobject 71 execuserobject setfont 0 setgray 301 464 moveto (ARGMAX) show grestore grestore 0 0 2.682821 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 1075] concat 355 execuserobject setfont 0 setgray 223 548 moveto (W) show 39 execuserobject setfont 0 7 rmoveto (1) show 0 -7 rmoveto /Helvetica findfont 27 scalefont [1 0 0 -1 0 0] makefont 455 exch defineuserobject 455 execuserobject setfont 0 -7 rmoveto (.) show 0 7 rmoveto 355 execuserobject setfont (X) show
grestore grestore 0 0 2.682821 setup gsave 355 execuserobject setfont 0 setgray [1 0 0 -1 0 763] concat 355 execuserobject setfont 0 setgray 220 392 moveto (W) show 39 execuserobject setfont 0 7 rmoveto (R) show 0 -7 rmoveto 455 execuserobject setfont 0 -7 rmoveto (.) show 0 7 rmoveto 355 execuserobject setfont (X) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 854 1656 a(Figure)14 b(4.8:)j(A)d(Linear)g(Mac)o(hine)512 1750 y(The)20 b(diagram)e(in)h(Fig.)35 b(4.9)18 b(sho)o(ws)i(the)h(c)o (haracter)g(of)e(the)h(regions)g(in)f(a)g(2-)450 1800 y(dimensional)11 b(space)j(created)h(b)o(y)e(a)f(linear)h(mac)o(hine)f(for)h Fu(R)e Fx(=)h(5.)17 b(In)d Fu(n)f Fx(dimensions,)450 1849 y(ev)o(ery)j(pair)e (of)h(regions)g(is)g(either)g(separated)i(b)o(y)d(a)h(section)h(of)e(a)h(h)o (yp)q(erplane)g(or)g(is)450 1899 y(non-adjacen)o(t.)512 1958 y(T)m(o)h(train)g(a)h(linear)f(mac)o(hine,)f(there)j(is)e(a)h(straigh)o (tforw)o(ard)f(generalization)g(of)450 2008 y(the)f(2-category)e (error-correction)j(rule.)j(Assem)o(ble)13 b(the)i(patterns)g(in)e(the)i (training)450 2057 y(set)g(in)o(to)e(a)h(sequence)i(as)e(b)q(efore.)501 2148 y(1.)20 b(If)11 b(the)i(mac)o(hine)e(classi\014es)i(a)f(pattern)h (correctly)m(,)f(no)g(c)o(hange)h(is)f(made)e(to)i(an)o(y)554 2198 y(of)h(the)i(w)o(eigh)o(t)e(v)o(ectors.)501 2277 y(2.)20 b(If)14 b(the)g(mac)o(hine)f(mistak)o(enly)f(classi\014es)j(a)f(category)h Fu(u)f Fx(pattern,)g Fy(X)1642 2283 y Ft(i)1656 2277 y Fx(,)g(in)g(cat-)554 2327 y(egory)g Fu(v)h Fx(\()p Fu(u)d Fw(6)p Fx(=)f Fu(v)q Fx(\),)k(then:)995 2434 y Fy(W)1044 2440 y Ft(u)1077 2434 y Fw( )-7 b(\000)12
b Fy(W)1205 2440 y Ft(u)1236 2434 y Fx(+)d Fu(c)1295 2440 y Ft(i)1309 2434 y Fy(X)1345 2440 y Ft(i)450 2539 y Fo(Intr)n(o)n(duction)14 b(to)k(Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o (ed.)p eop %%Page: 51 13 51 12 bop 150 275 a Fp(4.3.)31 b(NETW)o(ORKS)14 b(OF)g(TLUS)765 b Fx(51)435 1133 y @beginspecial 10 @llx 509 @lly 197 @urx 697 @ury 1870 @rwi @setspecial %%BeginDocument: Four/voronoi.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop
}__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 252/thorn/ydieresis] 246/udieresis/yacute {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath
gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 10 509 187 188 rectclip 10 509 187 188 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 15 514 177 178 rectfill 15.000000 514.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 177 178 rectclip 0.473262 0.474667 scale -81 -193 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{
currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def
/showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore
/oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 81 193.100006 373.900024 374.799988 rectclip 81 193.100006 373.900024 374.799988 rectclip 0 0 0.9 setup 0 setgray 137 -102 93 562 line grestore 0 0 0.9 setup 0 setgray 117 81 231 458 line grestore 0 0 0.9 setup 0 setgray 6 86 225 373 line grestore 0 0 0.9 setup 0 setgray 116 -65 225 374 line grestore 0 0 0.9 setup 0 setgray 106 68 118 305 line grestore 0 0 0.9 setup 0 setgray 0 -110 340 309 line grestore 0 0 0.9 setup 0 setgray 99 73 339 309 line grestore 0 0 0.9 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 39 exch defineuserobject 39 execuserobject setfont 0 setgray [1 0 0 -1 0 1033] concat /Helvetica-Bold findfont 16 scalefont [1 0 0 -1 0 0] makefont 481 exch defineuserobject 481 execuserobject setfont 0 setgray 225 516 moveto (R) show 0 4 rmoveto (1) show
0 -4 rmoveto grestore grestore 0 0 0.9 setup gsave 481 execuserobject setfont 0 setgray [1 0 0 -1 0 817] concat 481 execuserobject setfont 0 setgray 309 408 moveto (R) show 0 4 rmoveto (3) show 0 -4 rmoveto grestore grestore 0 0 0.9 setup gsave 481 execuserobject setfont 0 setgray [1 0 0 -1 0 599] concat 481 execuserobject setfont 0 setgray 222 297 moveto (R) show 0 4 rmoveto (4) show 0 -4 rmoveto grestore grestore 0 0 0.9 setup gsave 481 execuserobject setfont 0 setgray [1 0 0 -1 0 536] concat 481 execuserobject setfont 0 setgray 402 266 moveto (R) show 0 4 rmoveto (5) show 0 -4 rmoveto grestore grestore 0 0 0.9 setup gsave 481 execuserobject setfont 0 setgray [1 0 0 -1 0 450] concat /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 355 exch defineuserobject 355 execuserobject setfont 0 setgray 121 234 moveto (X) show /Helvetica-Bold findfont 24 scalefont [1 0 0 -1 0 0] makefont 27 exch defineuserobject 27 execuserobject setfont
0 -7 rmoveto (.) show 0 7 rmoveto 355 execuserobject setfont (W) show 39 execuserobject setfont 0 7 rmoveto (4) show 0 -7 rmoveto ( ) show /Symbol findfont 18 scalefont [1 0 0 -1 0 0] makefont 489 exch defineuserobject 489 execuserobject setfont <b3> show 39 execuserobject setfont ( ) show 355 execuserobject setfont (X) show 27 execuserobject setfont 0 -7 rmoveto (.) show 0 7 rmoveto 355 execuserobject setfont (W) show 39 execuserobject setfont 0 7 rmoveto (i) show 0 -7 rmoveto ( for i ) show 489 execuserobject setfont <b92034> show grestore grestore 0 0 0.9 setup gsave 489 execuserobject setfont 0 setgray [1 0 0 -1 0 829] concat 481 execuserobject setfont 0 setgray 140 414 moveto (R) show 0 4 rmoveto (2) show 0 -4 rmoveto grestore grestore 0 0 0.9 setup gsave 481 execuserobject setfont 0 setgray [1 0 0 -1 0 493] concat 39 execuserobject setfont 0 setgray 92 249 moveto (In this region:) show grestore grestore 0 setgray
0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 445 1224 a(Figure)14 b(4.9:)j(Regions)c(F)m(or)h(a)f(Linear)h (Mac)o(hine)254 1353 y(and)697 1455 y Fy(W)746 1461 y Ft(v)777 1455 y Fw( )-7 b(\000)12 b Fy(W)905 1461 y Ft(v)934 1455 y Fw(\000)d Fu(c)993 1461 y Ft(i)1007 1455 y Fy(X)1043 1461 y Ft(i)254 1557 y Fx(and)k(all)g(other)i(w)o(eigh)o(t)e(v)o(ectors)i(are)f(not) g(c)o(hanged.)150 1654 y(This)i(correction)h(increases)g(the)g(v)n(alue)e(of) h(the)g Fu(u)p Fx(-th)g(dot)g(pro)q(duct)h(and)e(decreases)150 1704 y(the)e(v)n(alue)e(of)g(the)i Fu(v)q Fx(-th)f(dot)g(pro)q(duct.)18 b(Just)13 b(as)f(in)f(the)i(2-category)f(\014xed)g(incremen)o(t)150 1754 y(pro)q(cedure,)21 b(this)e(pro)q(cedure)i(is)e(guaran)o(teed)g(to)g (terminate,)g(for)f(constan)o(t)h Fu(c)1430 1760 y Ft(i)1444 1754 y Fx(,)h(if)150 1804 y(there)f(exists)g(w)o(eigh)o(t)e(v)o(ectors)j (that)e(mak)o(e)e(correct)k(separations)e(of)f(the)i(training)150 1853 y(set.)26 b(Note)17 b(that)f(when)h Fu(R)e Fx(=)h(2,)g(this)g(pro)q (cedure)i(reduces)g(to)e(the)h(ordinary)f(TLU)150 1903 y(error-correction)e (pro)q(cedure.)20 b(A)12 b(pro)q(of)g(that)g(this)g(pro)q(cedure)i (terminates)e(is)g(giv)o(en)150 1953 y(in)h([Nilsson,)g(1990)o(,)g(pp.)19 b(88-90])12 b(and)i(in)f([Duda)g(&)h(Hart,)g(1973)o(,)f(pp.)18 b(174-177].)150 2100 y FA(4.3)70 b(Net)n(w)n(orks)22 b(of)i(TLUs)150 2210 y Fz(4.3.1)55 b(Motiv)m(ation)18 b(and)h(Examples)150 2297 y Fy(La)o(y)o(ered)14 b(Net)o(w)o(orks)150 2384 y Fx(T)m(o)i(classify)h (correctly)h(all)e(of)h(the)h(patterns)g(in)f(non-linearly-separable)f (training)150 2434 y(sets)e(requires)f(separating)g(surfaces)h(more)d (complex)h(than)g(h)o(yp)q(erplanes.)18 b(One)c(w)o(a)o(y)150 2539 y Fo(Intr)n(o)n(duction)g(to)k(Machine)e(L)n(e)n(arning)757 2538 y Fn(c)746 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 52 14 52 13 bop 450 275 a Fx(52)579 b Fp(CHAPTER)14 b(4.)32 b(NEURAL)14 b(NETW)o(ORKS)450 391 y Fx(to)g(ac)o(hiev)o(e)h(more)e(complex)g(surfaces)j (is)e(with)g(net)o(w)o(orks)h(of)f(TLUs.)20 b(Consider,)14 b(for)450 441 y(example,)i(the)h(2-dimensional,)d(ev)o(en)j(parit)o(y)f (function,)h Fu(f)k Fx(=)16 b Fu(x)1493 447 y Fr(1)1512 441 y Fu(x)1536 447 y Fr(2)1565 441 y Fx(+)p 1609 418 43 2 v 12 w Fu(x)1633 447 y Fr(1)p 1667 418 V 1667 441 a Fu(x)1691 447 y Fr(2)1710 441 y Fx(.)26 b(No)450 491 y(single)12 b(line)g(through)h(the)g (2-dimensional)d(square)j(can)g(separate)h(the)f(v)o(ertices)h(\(1,1\))450 541 y(and)d(\(0,0\))g(from)f(the)j(v)o(ertices)g(\(1,0\))e(and)g(\(0,1\)|the) g(function)h(is)f(not)h(linearly)e(sep-)450 591 y(arable)i(and)h(th)o(us)g (cannot)g(b)q(e)g(implemen)o(ted)d(b)o(y)j(a)f(single)g(TLU.)h(But,)g(the)g (net)o(w)o(ork)450 640 y(of)k(three)i(TLUs)f(sho)o(wn)g(in)f(Fig.)29
b(4.10)16 b(do)q(es)j(implemen)o(t)c(this)i(function.)30 b(In)17 b(the)450 690 y(\014gure,)g(w)o(e)g(sho)o(w)f(the)h(w)o(eigh)o(t)f(v)n(alues) g(along)f(input)h(lines)h(to)f(eac)o(h)h(TLU)f(and)g(the)450 740 y(threshold)f(v)n(alue)e(inside)h(the)g(circle)h(represen)o(ting)g(the)g (TLU.)644 1202 y @beginspecial 7 @llx 617 @lly 238 @urx 715 @ury 2310 @rwi @setspecial %%BeginDocument: Four/parity.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave
7 617 231 98 rectclip 7 617 231 98 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 12 622 221 88 rectfill 12.000000 622.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 221 88 rectclip 0.513954 0.517647 scale -30 -376 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop
}__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line {
moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 30 376 430 170 rectclip 30 376 430 170 rectclip 0 setgray 0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 113 1 76 508 line 0.507044 189 509 arrow grestore 0 0 1.48718 setup gsave /Helvetica findfont 24 scalefont [1 0 0 -1 0 0] makefont 13 exch defineuserobject 13 execuserobject setfont 0 setgray [1 0 0 -1 0 913] concat 13 execuserobject setfont 0 setgray 439 465 moveto (f) show grestore grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 1014] concat 13 execuserobject setfont 0 setgray 43 511 moveto (x) show 0 9 rmoveto (1) show 0 -9 rmoveto grestore grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 836] concat 13 execuserobject setfont 0 setgray 43 422 moveto (x) show 0 9 rmoveto (2) show 0 -9 rmoveto grestore grestore 0 0 1.48718 setup
0 0 1.48718 setup 0 setgray 1 setalpha 45 45 190 486 oval matrix defaultmatrix setmatrix stroke grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 1000] concat 13 execuserobject setfont 0 setgray 194 499 moveto (1.5) show grestore grestore grestore 0 0 1.48718 setup 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 825] concat 13 execuserobject setfont 0 setgray 191 419 moveto (-0.5) show grestore grestore 0 0 1.48718 setup 0 setgray 1 setalpha 48 48 189 390 oval matrix defaultmatrix setmatrix stroke grestore grestore 0 0 1.48718 setup 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 901] concat 13 execuserobject setfont 0 setgray 324 454 moveto (0.5) show grestore grestore 0 0 1.48718 setup 0 setgray 1 setalpha 48 48 317 432 oval matrix defaultmatrix setmatrix stroke grestore grestore 0 setgray 0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 113 1 75 413 line 0.507044 188 414 arrow grestore 0 setgray
0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 116 -82 77 509 line -35.257397 193 427 arrow grestore 0 setgray 0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 119 81 76 414 line 34.243042 195 495 arrow grestore 0 setgray 0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 83 -38 236 507 line -24.600515 319 469 arrow grestore 0 setgray 0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 80 32 238 415 line 21.802052 318 447 arrow grestore 0 setgray 0.333333 setgray 0 0 1.48718 setup 0 setgray 1 setalpha 66 -1 365 456 line -0.868077 431 455 arrow grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 1041] concat 13 execuserobject setfont 0 setgray 155 529 moveto (1) show grestore grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 939] concat 13 execuserobject setfont 0 setgray 174 478 moveto (1) show grestore grestore
0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 953] concat 13 execuserobject setfont 0 setgray 85 483 moveto (-1) show grestore grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 803] concat 13 execuserobject setfont 0 setgray 93 410 moveto (-1) show grestore grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 833] concat 13 execuserobject setfont 0 setgray 281 425 moveto (1) show grestore grestore 0 0 1.48718 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 1003] concat 13 execuserobject setfont 0 setgray 277 510 moveto (1) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument
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/__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx
{/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont
}{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 11 559 276 158 rectclip 11 559 276 158 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 16 564 266 148 rectfill 16.000000 564.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 266 148 rectclip 0.491682 0.435294 scale -2 -290 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that
/currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 2 290.676147 540.323853 339.323853 rectclip 2 290.676147 540.323853 339.323853 rectclip 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 33.000004 32.275864 327 575.724121 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray
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count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 407 1099 a(Figure)14 b(4.11:)j(A)d(La)o(y)o(ered,)g(F)m(eedforw) o(ard)g(Net)o(w)o(ork)150 1226 y(function)d Fu(f)17 b Fx(=)11 b Fu(x)414 1232 y Fr(1)433 1226 y Fu(x)457 1232 y Fr(2)480 1226 y Fx(+)5 b Fu(x)541 1232 y Fr(2)p 559 1203 43 2 v 559 1226 a Fu(x)583 1232 y Fr(3)606 1226 y Fx(+)g Fu(x)667 1232 y Fr(1)p 685 1203 V 685 1226 a Fu(x)709 1232 y Fr(3)728 1226 y Fx(.)17 b(The)12 b(form)e(of)h(the)h(net)o(w)o(ork)g(that)f(implemen)o(ts) 150 1276 y(this)j(function)g(is)g(sho)o(wn)h(in)e(Fig.)19 b(4.12.)f(\(W)m(e)c (lea)o(v)o(e)g(it)f(to)i(the)f(reader)i(to)e(calculate)150 1325 y(appropriate)i(v)n(alues)g(of)f(w)o(eigh)o(ts)h(and)f(thresholds.\))25 b(The)17 b(3-cub)q(e)f(represen)o(tation)150 1375 y(of)h(the)h(function)f(is) h(sho)o(wn)f(in)g(Fig.)29 b(4.13.)e(The)18 b(net)o(w)o(ork)g(of)f(Fig.)28 b(4.12)17 b(can)g(b)q(e)150 1425 y(designed)c(so)f(that)g(eac)o(h)h(hidden)f (unit)g(implemen)o(ts)e(one)j(of)e(the)i(planar)e(b)q(oundaries)150 1475 y(sho)o(wn)j(in)f(Fig.)18 b(4.13.)413 2096 y @beginspecial 7 @llx 570 @lly 205 @urx 706 @ury 1980 @rwi @setspecial %%BeginDocument: Four/twolayer.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor
}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{
_NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 7 570 198 136 rectclip 7 570 198 136 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 12 575 188 126 rectfill 12.000000 575.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 188 126 rectclip 0.426304 0.425676 scale -40 -358 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec
}for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{
counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef
/_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 40 358 441 296 rectclip 40 358 441 296 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 1 setalpha 188 394 116 20 rectfill 1 setgray 1 setalpha 188 394 116 20 rectstroke grestore 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 1 setalpha 325 480 151 29 rectfill 1 setgray 1 setalpha 325 480 151 29 rectstroke grestore 0 0 0 setup 0 0 0 setup 1 setgray 45 373 410 239 rectfill 45.000000 373.000000 transform gsave __NXbasematrix setmatrix itransform translate
0 0 410 239 rectclip -67 -359 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 67.086411 359.086395 409.913574 238.913605 rectclip 67.086411 359.086395 409.913574 238.913605 rectclip
0 0 2.734103 setup 0 setgray 1 setalpha 25 25 252 558 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.734103 setup 0 setgray 1 setalpha 25 25 259 503 oval matrix defaultmatrix setmatrix stroke grestore 0 0 1.91359 setup 0 setgray 1 setalpha 131 51 121 515 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 132 0 119 571 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 138 100 118 461 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 138 0 120 516 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 143 -49 118 571 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 142 50 118 459 line grestore 0 0 1.91359 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 62 exch defineuserobject 62 execuserobject setfont 0 setgray [1 0 0 -1 0 1027] concat /Helvetica-Bold findfont 25 scalefont [1 0 0 -1 0 0] makefont 430 exch defineuserobject 430 execuserobject setfont 0 setgray 76 523 moveto (x) show grestore grestore 0 0 1.91359 setup
0 setgray 1 setalpha 77 0 388 516 line 0 465 516 arrow grestore 0 0 2.734103 setup 0 setgray 1 setalpha 25 25 261 450 oval matrix defaultmatrix setmatrix stroke grestore 0 0 1.91359 setup 0 setgray 1 setalpha 145 -96 119 569 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 140 -52 122 515 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 141 0 119 460 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 81 -45 278 566 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 25 25 361 503 oval matrix defaultmatrix setmatrix stroke grestore 0 0 1.91359 setup 0 setgray 1 setalpha 74 0 286 515 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 76 44 287 465 line grestore 0 0 1.91359 setup gsave 430 execuserobject setfont 0 setgray [1 0 0 -1 0 827] concat 62 execuserobject setfont 0 setgray 231 405 moveto (conjuncts) show grestore grestore 0 0 1.91359 setup gsave 62 execuserobject setfont 0 setgray
[1 0 0 -1 0 960] concat 62 execuserobject setfont 0 setgray 348 486 moveto (disjunct) show grestore grestore 0 0 1.91359 setup gsave 62 execuserobject setfont 0 setgray [1 0 0 -1 0 754] concat 62 execuserobject setfont 0 setgray 124 383 moveto (A Feedforward, 2-layer Network) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 0 0 setup 1 setgray 1 setalpha 95 380 270 69 rectfill 1 setgray 1 setalpha 95 380 270 69 rectstroke grestore 0 0 0 setup 1 setgray 1 setalpha 327 479 131 34 rectfill 1 setgray 1 setalpha 327 479 131 34 rectstroke grestore grestore 0 0 0 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 85 exch defineuserobject 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1276] concat 85 execuserobject setfont 0 setgray 299 644 moveto (TLUs) show grestore grestore 0 setgray
0.333333 setgray 0 0 0 setup 0 setgray 1 setalpha 31 31 263 602 line 225.001328 263 602 arrow grestore 0 setgray 0.333333 setgray 0 0 0 setup 0 setgray 1 setalpha 31 -66 314 627 line -64.842613 345 561 arrow grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 957] concat 85 execuserobject setfont 0 setgray 363 469 moveto (disjunction) show 363 491 moveto (of terms) show grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 820] concat 85 execuserobject setfont 0 setgray 191 380 moveto (conjunctions) show 191 402 moveto (of literals) show 191 424 moveto (\(terms\)) show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 505 2188 a(Figure)c(4.12:)j(A)d(Tw)o(o-La)o(y)o(er)f(Net)o(w)o (ork)212 2284 y(T)m(o)h(train)h(a)f(t)o(w)o(o-la)o(y)o(er)g(net)o(w)o(ork)h
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/yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line {
moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 12 509 169 201 rectclip 12 509 169 201 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 17 514 159 191 rectfill 17.000000 514.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 159 191 rectclip 0.341202 0.340463 scale -41 -140 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch
3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def
/currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef
/alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 41 140 466 561 rectclip 41 140 466 561 rectclip 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 253 1 199 356 line 0.226471 452 357 arrow grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 134 179 71 178 line 233.182922 71 178 arrow grestore 0 0 0.17 setup 0 setgray 1 setalpha 204 357 171 165 rectstroke grestore 0 0 0.17 setup 0 setgray 68 94 136 427 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 0 -208 204 565 line 89.997345 204 565 arrow grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 21 20 196 347 oval fill grestore 0 setgray 21 20 196 347 oval matrix defaultmatrix setmatrix stroke grestore
0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 21 20 127 417 oval fill grestore 0 setgray 21 20 127 417 oval matrix defaultmatrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 294 414 22 21 rectfill 0 setgray 294 414 22 21 rectstroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 295 250 22 21 rectfill 0 setgray 295 250 22 21 rectstroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 21 20 194 510 oval fill grestore 0 setgray 21 20 194 510 oval matrix defaultmatrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 21 20 365 510 oval fill grestore 0 setgray 21 20 365 510 oval matrix defaultmatrix grestore 0 0 0 setup gsave /Helvetica findfont 44 scalefont [1 0 0 27 exch defineuserobject 27 execuserobject setfont 0 setgray [1 0 0 -1 0 709] concat /Helvetica findfont 18 scalefont [1 0 0 67
setmatrix stroke
setmatrix stroke
setmatrix stroke
-1 0 0] makefont
-1 0 0] makefont
exch defineuserobject 67 execuserobject setfont 0 setgray 468 357 moveto (x) show 0 7 rmoveto (2) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 67 execuserobject setfont 0 setgray [1 0 0 -1 0 319] concat 67 execuserobject setfont 0 setgray 60 162 moveto (x) show 0 7 rmoveto (1) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 67 execuserobject setfont 0 setgray [1 0 0 -1 0 1163] concat 67 execuserobject setfont 0 setgray 207 584 moveto (x) show 0 7 rmoveto (3) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 67 execuserobject setfont 0 setgray [1 0 0 -1 0 1287] concat 27 execuserobject setfont 0 setgray 48 632 moveto (f = x) show 0 17 rmoveto (1) show 0 -17 rmoveto (x) show 0 17 rmoveto (2) show 0 -17 rmoveto ( + x) show 0 17 rmoveto (2) show 0 -17 rmoveto (x) show 0 17 rmoveto (3) show 0 -17 rmoveto
( + x) show 0 17 rmoveto (1) show 0 -17 rmoveto (x) show 0 17 rmoveto (3) show 0 -17 rmoveto grestore grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 365 347 22 21 rectfill 0 setgray 365 347 22 21 rectstroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 126 255 22 21 rectfill 0 setgray 126 255 22 21 rectstroke grestore 0 setgray 0.333333 setgray 0 0 2.170001 setup 0 setgray 1 setalpha 39 0 297 683 line grestore 0 setgray 0.333333 setgray 0 0 2.170001 setup 0 setgray 1 setalpha 39 0 445 685 line grestore 0 0 0.17 setup 0 setgray 1 setalpha 69 94 308 264 line grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave 0 3 translate 1 1 scale 0.243797 setgray 1 setalpha gsave newpath systemdict begin
135 314 345 350 setbbox 135 350 moveto 0 0 rlineto 171 -2 rlineto 39 -34 rlineto -172 1 rlineto -37 33 rlineto -1 2 rlineto end eofill grestore grestore 0 3 translate 1 1 scale 0 setgray 1 setalpha gsave newpath systemdict begin 135 314 345 350 setbbox 135 350 moveto 0 0 rlineto 171 -2 rlineto 39 -34 rlineto -172 1 rlineto -37 33 rlineto -1 2 rlineto end stroke grestore grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave -3 -1 translate 1 1 scale 0.582644 setgray 1 setalpha gsave newpath systemdict begin 234 264 348 479 setbbox 234 428 moveto 0 0 rlineto 110 51 rlineto 4 -164 rlineto -113 -51 rlineto 0 163 rlineto -1 1 rlineto end eofill grestore grestore -3 -1 translate 1 1 scale 0.466948 setgray
1 setalpha gsave newpath systemdict begin 234 264 348 479 setbbox 234 428 moveto 0 0 rlineto 110 51 rlineto 4 -164 rlineto -113 -51 rlineto 0 163 rlineto -1 1 rlineto end stroke grestore grestore 0 0 0.17 setup 0 setgray 1 setalpha 136 265 170 165 rectstroke grestore 0 0 0.17 setup 0 setgray 1 setalpha 69 94 305 427 line grestore 0 setgray 0.333333 setgray 0 0 2.769231 setup 0 setgray 1 setalpha 73 82 302 356 line grestore 0 setgray 0.333333 setgray 0 0 2.769231 setup 0.838847 setgray 1 setalpha 68 91 233 264 line grestore 0 setgray 0.333333 setgray 0 0 2.769231 setup 0.838847 setgray 1 setalpha 41 48 302 356 line grestore 0 setgray 0.333333 setgray 0 0 0 setup gsave -2 -1 translate 1 1 scale 0.247932 setgray 1 setalpha gsave newpath systemdict
begin 272 317 346 352 setbbox 272 351 moveto 0 0 rlineto 33 1 rlineto 41 -35 rlineto -32 0 rlineto -41 35 rlineto -1 -1 rlineto end eofill grestore grestore -2 -1 translate 1 1 scale 0 setgray 1 setalpha gsave newpath systemdict begin 272 317 346 352 setbbox 272 351 moveto 0 0 rlineto 33 1 rlineto 41 -35 rlineto -32 0 rlineto -41 35 rlineto -1 -1 rlineto end stroke grestore grestore 0 setgray 0.333333 setgray 0 0 2.769231 setup 0 setgray 1 setalpha 72 90 304 347 line grestore 0 setgray 0.333333 setgray 0 0 2.769231 setup 0 setgray 1 setalpha 71 87 234 262 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 293 417 22 21 rectfill 0 setgray 293 417 22 21 rectstroke grestore 0 setgray 0.333333 setgray gsave
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/xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
/flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for
_NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 0 488 207 218 rectclip 0 488 207 218 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 5 493 197 208 rectfill 5.000000 493.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 197 208 rectclip 0.362799 0.361739 scale -4 -8 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse
}__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
}repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{
1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 4 8.009487 543 574.981018 rectclip 4 8.009487 543 574.981018 rectclip 0 0 2.682821 setup 0 setgray 1 setalpha 51 -1 366 464 line -1.123336 417 463 arrow grestore 0 0 0.17 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 85 exch defineuserobject 85 execuserobject setfont 0 setgray [1 0 0 -1 0 632] concat /Helvetica-Bold findfont 30 scalefont [1 0 0 -1 0 0] makefont 347 exch defineuserobject 347 execuserobject setfont 0 setgray 17 327 moveto (X) show grestore grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray
1 setalpha 33.000004 32.275864 172 498.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 33.000004 32.275864 175 398.43103 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.734103 setup 0 setgray 1 setalpha 83 -1 206 513 line -0.690298 289 512 arrow grestore 0 0 2.734103 setup 0 setgray 1 setalpha 79 -1 210 414 line -0.725246 289 413 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 143 -27 28 548 line -10.692528 171 521 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 147 -125 23 546 line -40.377037 170 421 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 130 314 46 94 line 67.51181 176 408 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 141 390 35 111 line 70.125198 176 501 arrow grestore 0 0 2.990513 setup gsave 347 execuserobject setfont 0 setgray [1 0 0 -1 0 1104] concat /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 738 exch defineuserobject 738 execuserobject setfont 0 setgray 172 553 moveto (W) show 85 execuserobject setfont
0 -7 rmoveto (1) show 0 7 rmoveto grestore grestore 0 0 2.990513 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 708] concat 738 execuserobject setfont 0 setgray 183 342 moveto (W) show 85 execuserobject setfont 0 -7 rmoveto (1) show 0 7 rmoveto grestore grestore 0 0 2.990513 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 940] concat /Helvetica-Bold findfont 24 scalefont [1 0 0 -1 0 0] makefont 147 exch defineuserobject 147 execuserobject setfont 0 setgray 168 479 moveto (. . .) show grestore grestore 0 0 2.990513 setup gsave 147 execuserobject setfont 0 setgray [1 0 0 -1 0 996] concat /Symbol findfont 24 scalefont [1 0 0 -1 0 0] makefont 699 exch defineuserobject 699 execuserobject setfont 0 setgray 181 490 moveto (S) show grestore grestore 0 0 2.990513 setup gsave 699 execuserobject setfont 0 setgray [1 0 0 -1 0 819] concat 699 execuserobject setfont 0 setgray 184 413 moveto (S) show grestore grestore 0 0 2.990513 setup 0 setgray
1 setalpha 292 391 74 146 rectstroke grestore 0 0 2.990513 setup gsave 699 execuserobject setfont 0 setgray [1 0 0 -1 0 919] concat /Helvetica findfont 24 scalefont [1 0 0 -1 0 0] makefont 13 exch defineuserobject 13 execuserobject setfont 0 setgray 300 467 moveto (MAX) show grestore grestore 0 0 2.682821 setup 0 setgray 1 setalpha 50 -1 369 159 line -1.145797 419 158 arrow grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 33.000004 32.275864 185 198.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 33.000004 32.275864 188 98.43103 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.734103 setup 0 setgray 1 setalpha 73 0 219 213 line 0 292 213 arrow grestore 0 0 2.734103 setup 0 setgray 1 setalpha 69 2 223 115 line 1.660331 292 117 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 160 -308 24 534 line -62.550846 184 226 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 163 -400 20 521 line
-67.831108 183 121 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 142 18 47 89 line 7.224529 189 107 arrow grestore 0 0 2.990513 setup 0 setgray 1 setalpha 134 107 51 98 line 38.608765 185 205 arrow grestore 0 0 2.990513 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 340] concat 147 execuserobject setfont 0 setgray 181 179 moveto (. . .) show grestore grestore 0 0 2.990513 setup gsave 147 execuserobject setfont 0 setgray [1 0 0 -1 0 396] concat 699 execuserobject setfont 0 setgray 194 190 moveto (S) show grestore grestore 0 0 2.990513 setup gsave 699 execuserobject setfont 0 setgray [1 0 0 -1 0 196] concat 699 execuserobject setfont 0 setgray 198 90 moveto (S) show grestore grestore 0 0 2.990513 setup 0 setgray 1 setalpha 294 90 74 146 rectstroke grestore 0 0 2.990513 setup gsave 699 execuserobject setfont 0 setgray [1 0 0 -1 0 309] concat 13 execuserobject setfont 0 setgray 307 162 moveto (MAX) show grestore grestore
0 0 2.990513 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 636] concat 147 execuserobject setfont 0 setgray 307 327 moveto (. . .) show grestore grestore 0 0 2.990513 setup gsave 147 execuserobject setfont 0 setgray [1 0 0 -1 0 508] concat 738 execuserobject setfont 0 setgray 186 255 moveto (W) show 85 execuserobject setfont 0 -7 rmoveto (R) show 0 7 rmoveto grestore grestore 0 0 2.990513 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 104] concat 738 execuserobject setfont 0 setgray 190 40 moveto (W) show 85 execuserobject setfont 0 -7 rmoveto (R) show 0 7 rmoveto grestore grestore 0 0 2.990513 setup 0 setgray 1 setalpha 421 118 74 398 rectstroke grestore 0 0 2.990513 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 660] concat 13 execuserobject setfont 0 setgray 429 324 moveto (ARG) show 429 353 moveto (MAX) show grestore grestore 0 0 2.682821 setup 0 setgray 1 setalpha 36 -1 496 334 line -1.591187 532 333 arrow
grestore 0 0 0 setup gsave 13 execuserobject setfont 0 setgray [1 0 0 -1 0 972] concat /Helvetica findfont 25 scalefont [1 0 0 -1 0 0] makefont 269 exch defineuserobject 269 execuserobject setfont 0 setgray 381 495 moveto (1) show grestore grestore 0 0 0 setup gsave 269 execuserobject setfont 0 setgray [1 0 0 -1 0 362] concat 269 execuserobject setfont 0 setgray 384 190 moveto (R) show grestore grestore 0 0 0 setup gsave 269 execuserobject setfont 0 setgray [1 0 0 -1 0 1094] concat 85 execuserobject setfont 0 setgray 189 553 moveto (1) show 0 -7 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 713] concat 85 execuserobject setfont 0 setgray 201 359 moveto (N) show 0 -7 rmoveto 0 14 rmoveto (1) show 0 -14 rmoveto grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 492] concat 85 execuserobject setfont 0 setgray 203 252 moveto (1) show 0 -7 rmoveto
grestore grestore 0 0 0 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 105] concat 85 execuserobject setfont 0 setgray 208 55 moveto (N) show 0 -7 rmoveto 0 14 rmoveto (R) show 0 -14 rmoveto grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 751 2234 a(Figure)d(4.14:)j(A)d(Piecewise)h(Linear)f(Mac)o(hine) 512 2334 y(The)19 b(PWL)g(mac)o(hine)e(groups)i(its)g(w)o(eigh)o(ted)f (summing)e(units)j(in)o(to)e Fu(R)i Fx(banks)450 2384 y(corresp)q(onding)d (to)g(the)g Fu(R)f Fx(categories.)23 b(An)16 b(input)f(v)o(ector)h Fy(X)g Fx(is)f(assigned)h(to)f(that)450 2434 y(category)d(corresp)q(onding)h (to)f(the)h(bank)e(with)h(the)h(largest)f(w)o(eigh)o(ted)g(sum.)k(W)m(e)c (can)450 2539 y Fo(Intr)n(o)n(duction)i(to)k(Machine)e(L)n(e)n(arning)1057 2538 y Fn(c)1046 2539 y Fm(\015)q Fn(1996)i(Nils)h(J.)e(Nilsson.)32 b(All)19 b(righ)o(ts)f(reserv)o(ed.)p eop %%Page: 57 19 57 18 bop 150 275 a Fp(4.3.)31 b(NETW)o(ORKS)14 b(OF)g(TLUS)765 b Fx(57)150 391 y(use)15 b(an)g(error-correction)h(training)e(algorithm)e (similar)g(to)i(that)h(used)g(for)f(a)g(linear)150 441 y(mac)o(hine.)h(If)10 b(a)g(pattern)h(is)f(classi\014ed)g(incorrectly)m(,)h(w)o(e)f(subtract)h(\(a) f(constan)o(t)h(times\))150 491 y(the)g(pattern)h(v)o(ector)f(from)e(the)i(w) o(eigh)o(t)f(v)o(ector)i(pro)q(ducing)e(the)i(largest)f(dot)f(pro)q(duct)150 541 y(\(it)20 b(w)o(as)h(incorrectly)g(the)g(largest\))g(and)f(add)g(\(a)g (constan)o(t)h(times\))f(the)h(pattern)150 591 y(v)o(ector)12 b(to)f(that)g(w)o(eigh)o(t)g(v)o(ector)h(in)f(the)h(correct)h(bank)e(of)f(w)o (eigh)o(t)h(v)o(ectors)h(whose)g(dot)150 640 y(pro)q(duct)k(is)e(lo)q(cally)f (largest)i(in)f(that)h(bank.)20 b(\(Again,)14 b(w)o(e)h(use)g(augmen)o(ted)f (v)o(ectors)150 690 y(here.\))19 b(Unfortunately)m(,)12 b(there)i(are)f (example)e(training)h(sets)i(that)f(are)g(separable)g(b)o(y)150 740 y(a)e(giv)o(en)g(PWL)h(mac)o(hine)e(structure)k(but)e(for)f(whic)o(h)h
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/defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse
{//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 8 560 215 138 rectclip 8 560 215 138 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 13 565 205 128 rectfill 13.000000 565.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 205 128 rectclip 0.39961 0.4 scale -15 -372 translate
/__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 15.086411 372 512.913574 320 rectclip 15.086411 372 512.913574 320 rectclip 0 0 2.734103 setup 0 setgray
1 setalpha 25 25 199 624 oval matrix defaultmatrix setmatrix stroke grestore 0 0 2.734103 setup 0 setgray 1 setalpha 25 25 250 529 oval matrix defaultmatrix setmatrix stroke grestore 0 0 1.91359 setup 0 setgray 1 setalpha 130 25 69 605 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 131 -20 67 661 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 140 74 66 551 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 185 -59 68 606 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 189 -108 66 661 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 183 -8 66 549 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 41 -74 219 628 line grestore 0 0 1.91359 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 85 exch defineuserobject 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1207] concat /Helvetica-Bold findfont 25 scalefont [1 0 0 -1 0 0] makefont 1113 exch defineuserobject 1113 execuserobject setfont 0 setgray 24 613 moveto (x) show
grestore grestore 0 0 1.91359 setup 0 setgray 1 setalpha 60 0 389 430 line 0 449 430 arrow grestore 0 0 1.91359 setup gsave 1113 execuserobject setfont 0 setgray [1 0 0 -1 0 1331] concat 85 execuserobject setfont 0 setgray 211 668 moveto (L) show 0 7 rmoveto (1) show 0 -7 rmoveto grestore grestore 0 0 1.91359 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1029] concat 85 execuserobject setfont 0 setgray 266 517 moveto (L) show 0 7 rmoveto (2) show 0 -7 rmoveto grestore grestore 0 0 1.91359 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 864] concat 85 execuserobject setfont 0 setgray 458 438 moveto (output) show grestore grestore 0 0 2.734103 setup 0 setgray 1 setalpha 25 25 363 417 oval matrix defaultmatrix setmatrix stroke grestore 0 0 1.91359 setup 0 setgray 1 setalpha 294 -180 68 607 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 294 -222 68 657 line grestore
0 0 1.91359 setup 0 setgray 1 setalpha 299 -130 65 550 line grestore 0 0 1.91359 setup 0 setgray 1 setalpha 92 -94 274 535 line grestore 0 0 1.91359 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 797] concat 85 execuserobject setfont 0 setgray 367 401 moveto (L) show 0 7 rmoveto (3) show 0 -7 rmoveto grestore grestore 0 0 1.91359 setup 0 setgray 1 setalpha 150 -191 224 634 line grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore %%EndDocument @endspecial 828 1016 a Fx(Figure)g(4.15:)j(A)d(Cascade)h(Net)o(w)o(ork)715 1536 y @beginspecial 18 @llx 581 @lly 215 @urx 692 @ury 1970 @rwi @setspecial %%BeginDocument: Four/parallel.eps /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval
/UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat
strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known
{pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave 18 581 197 111 rectclip 18 581 197 111 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 23 586 187 101 rectfill 23.000000 586.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 187 101 rectclip 0.410088 0.412245 scale -48 -443 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch
def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def
/findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 48 443.035126 456 244.964874 rectclip 48 443.035126 456 244.964874 rectclip 0 0 3.964872 setup 0 setgray 1 setalpha 120 -100 164 584 line grestore
0 0 3.964872 setup 0 setgray 1 setalpha 120 -100 249 617 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 85 34 164 583 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 85 34 282 483 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 129 108 243 518 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 85 34 245 517 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 129 108 330 551 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 85 34 373 626 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 129 108 59 454 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 67 56 147 486 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 85 34 189 562 line grestore 0 0 3.964872 setup 0 setgray 1 setalpha 85 34 61 452 line grestore 0 0 3.964872 setup 0.690085 setgray 1 setalpha 62 52 215 543 line
grestore 0 0 1.91359 setup gsave /Helvetica findfont 18 scalefont [1 0 0 -1 0 0] makefont 85 exch defineuserobject 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1025] concat 85 execuserobject setfont 0 setgray 376 515 moveto (L) show 0 7 rmoveto (1) show 0 -7 rmoveto grestore grestore 0 0 1.91359 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 1323] concat 85 execuserobject setfont 0 setgray 468 664 moveto (L) show 0 7 rmoveto (2) show 0 -7 rmoveto grestore grestore 0 0 1.91359 setup gsave 85 execuserobject setfont 0 setgray [1 0 0 -1 0 983] concat 85 execuserobject setfont 0 setgray 62 494 moveto (L) show 0 7 rmoveto (2) show 0 -7 rmoveto grestore grestore 0 setgray 0.333333 setgray gsave 0 0 792 1008 rectclip [1 0 0 -1 0 1008] concat grestore count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end} repeat __NXEPSSave restore grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip
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/yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef /alphaimage{1 add _NXDoImageOp}def gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line {
moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def gsave -1 492 358 206 rectclip -1 492 358 206 rectclip 0 setgray 0.333333 setgray 0 0 0 setup 1 setgray 4 497 348 196 rectfill 4.000000 497.000000 transform gsave __NXbasematrix setmatrix itransform translate 0 0 348 196 rectclip 0.513274 0.474576 scale -28 -55 translate /__NXEPSSave save def /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch def /__NXEPSDictCount countdictstack def /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch
3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor }__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def
/currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {//findfont exec} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {//findfont exec dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXProcArray 5 array __NXdef /_NXChannels 0 __NXdef /_NXTotalBytes 0 __NXdef /_NXDoImageOp{ 1 index{dup}{1}ifelse /_NXChannels exch store _NXChannels 2 add 2 roll _NXProcArray 0 _NXChannels getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /_NXTotalBytes exch store pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore { 0 1 _NXChannels 1 sub{ _NXProcArray exch get exec length _NXTotalBytes exch sub /_NXTotalBytes exch store}for _NXTotalBytes 0 le{exit}if }loop /_NXProcArray 5 array def }__NXbdef /colorimage{_NXDoImageOp}__NXbdef
/alphaimage{1 add _NXDoImageOp}def gsave /__NXbasematrix matrix currentmatrix def grestore /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc } def /line { moveto rlineto stroke } def /setup { setlinewidth setlinecap setlinejoin gsave } def /arrow { newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto closepath gsave 0 setlinejoin stroke grestore fill neg rotate } def 0 0 792 1008 rectclip 28 55 678 413 rectclip 28 55 678 413 rectclip 0 setgray 0.333333 setgray 0 0 0.887949 setup 0.566118 setgray 1 setalpha 218 116 47 292 rectfill 0 setgray 1 setalpha 218 116 47 292 rectstroke grestore 0 0 2.734103 setup 0 setgray 1 setalpha 29 -16 266 159 line grestore 0 0 0.17 setup gsave /Helvetica findfont 16 scalefont [1 0 0 -1 0 0] makefont 71 exch defineuserobject 71 execuserobject setfont 0 setgray [1 0 0 -1 0 834] concat /Helvetica-Bold findfont 18 scalefont [1 0 0 -1 0 0] makefont 516 exch defineuserobject 516 execuserobject setfont 0 setgray 47 420 moveto (X) show 71 execuserobject setfont 0 -6 rmoveto (\(0\)) show 0 6 rmoveto grestore grestore 0 0 2.734103 setup 0 setgray 1 setalpha 28 17 266 300 line
grestore 0 0 2.734103 setup 0 setgray 1 setalpha 27 -6 266 336 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 84 37 66 347 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 89 -197 66 345 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 86 -55 62 296 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 80 -17 62 243 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 86 177 68 197 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 81 73 68 246 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 30 -14 187 315 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 30 8 188 333 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 27 -16 265 249 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 28 0 190 396 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha
32 17 264 196 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 80 -52 68 191 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 41.290333 39.143902 149 368.5802 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 40 40 149 304.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 42 40 141 207.862061 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 149 114.43103 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0.17 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 556] concat /Helvetica findfont 28 scalefont [1 0 0 -1 0 0] makefont 478 exch defineuserobject 478 execuserobject setfont 0 setgray 36 288 moveto (. . .) show grestore grestore 0 0 0.17 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 354] concat 478 execuserobject setfont 0 setgray 153 187 moveto (. . .) show grestore grestore 0 setgray
0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 293 305.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 291 204.862061 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 292 114.43103 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0.17 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 606] concat 478 execuserobject setfont 0 setgray 148 313 moveto (. . .) show grestore grestore 0 0 0.17 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 356] concat 478 execuserobject setfont 0 setgray 293 188 moveto (. . .) show grestore grestore 0 0 2.734103 setup 0 setgray 1 setalpha 29 -16 189 379 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 26 0 266 394 line grestore 0 0 0 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 515] concat 516 execuserobject setfont 0 setgray 136 259 moveto (W) show 71 execuserobject setfont
0 6 rmoveto (i) show 0 -6 rmoveto 0 -6 rmoveto (\(1\)) show 0 6 rmoveto grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 623] concat 516 execuserobject setfont 0 setgray 557 315 moveto (W) show 71 execuserobject setfont 0 -6 rmoveto (\(k\)) show 0 6 rmoveto grestore grestore 0 0 0.17 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 834] concat 516 execuserobject setfont 0 setgray 189 420 moveto (X) show 71 execuserobject setfont 0 -6 rmoveto (\(1\)) show 0 6 rmoveto grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 159] concat /Helvetica-Oblique findfont 16 scalefont [1 0 0 -1 0 0] makefont 510 exch defineuserobject 510 execuserobject setfont 0 setgray 118 82 moveto (m) show 0 6 rmoveto (1) show 0 -6 rmoveto 71 execuserobject setfont ( TLUs) show grestore grestore 0 0 2.717949 setup 0 setgray 1 setalpha 89 -1 602 260 line
-0.643765 691 259 arrow grestore 0 0 2.528975 setup 0 setgray 1 setalpha 25 16 267 361 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 26 0 267 134 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 1 setalpha 12 12 55 340 oval fill grestore 0 setgray 1 setalpha 12 12 55 340 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 1 setalpha 12 12 56 289 oval fill grestore 0 setgray 1 setalpha 12 12 56 289 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 1 setalpha 12 12 57 237 oval fill grestore 0 setgray 1 setalpha 12 12 57 237 oval matrix grestore 0 setgray 0.333333 setgray 0 0 0.17 setup gsave 0 setgray 1 setalpha 12 12 58 186 oval fill grestore 0 setgray 1 setalpha 12 12 58 186 oval matrix
defaultmatrix setmatrix stroke
defaultmatrix setmatrix stroke
defaultmatrix setmatrix stroke
defaultmatrix setmatrix stroke
grestore 0 0 0.17 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 612] concat 478 execuserobject setfont 0 setgray 292 316 moveto (. . .) show grestore grestore 0 0 0 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 501] concat 516 execuserobject setfont 0 setgray 279 252 moveto (W) show 71 execuserobject setfont 0 6 rmoveto (i) show 0 -6 rmoveto 0 -6 rmoveto (\(j\)) show 0 6 rmoveto grestore grestore 0 0 2.734103 setup 0 setgray 1 setalpha 39 -26 178 216 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 41 16 178 238 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 29 -1 190 132 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 30 8 189 143 line grestore 0 setgray 0.333333 setgray 0 0 0.887949 setup 0.566118 setgray 1 setalpha 362 115 47 292 rectfill 0 setgray 1 setalpha 362 115 47 292 rectstroke grestore 0 0 2.734103 setup
0 setgray 1 setalpha 29 -16 410 158 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 28 17 410 299 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 27 -6 410 335 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 30 -14 331 314 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 30 8 332 332 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 27 -16 409 248 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 34 -1 328 396 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 23 17 411 204 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 437 304.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 435 204.862061 oval matrix defaultmatrix setmatrix stroke grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 436 113.43103 oval matrix defaultmatrix setmatrix stroke
grestore 0 0 0.17 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 354] concat 478 execuserobject setfont 0 setgray 437 187 moveto (. . .) show grestore grestore 0 0 2.734103 setup 0 setgray 1 setalpha 33 -15 328 379 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 26 0 410 393 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 434 366.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0.17 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 834] concat 516 execuserobject setfont 0 setgray 335 420 moveto (X) show 71 execuserobject setfont 0 -6 rmoveto (\(j\)) show 0 6 rmoveto grestore grestore 0 0 2.528975 setup 0 setgray 1 setalpha 28 16 411 360 line grestore 0 0 2.528975 setup 0 setgray 1 setalpha 26 0 411 133 line grestore 0 0 0.17 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 610] concat 478 execuserobject setfont 0 setgray
436 315 moveto (. . .) show grestore grestore 0 0 0 setup gsave 478 execuserobject setfont 0 setgray [1 0 0 -1 0 510] concat gsave 420 241 86 28 rectclip 516 execuserobject setfont 0 setgray 420 262 moveto (W) show 71 execuserobject setfont 0 6 rmoveto (i) show 0 -6 rmoveto 0 -6 rmoveto (\(k-1\)) show 0 6 rmoveto grestore grestore grestore 0 0 2.734103 setup 0 setgray 1 setalpha 34 -27 329 216 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 33 20 330 233 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 29 -1 334 131 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 31 6 332 144 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 98 -109 475 384 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 85 -56 478 321 line grestore 0 0 2.734103 setup 0 setgray 1 setalpha 85 26 477 225 line grestore 0 0 2.734103 setup
0 setgray 1 setalpha 95 108 477 132 line grestore 0 setgray 0.333333 setgray 0 0 0.17 setup 0 setgray 1 setalpha 40 40 562 237.293091 oval matrix defaultmatrix setmatrix stroke grestore 0 0 0.17 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 836] concat 516 execuserobject setfont 0 setgray 495 422 moveto (X) show 71 execuserobject setfont 0 -6 rmoveto (\(k-1\)) show 0 6 rmoveto grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 155] concat 510 execuserobject setfont 0 setgray 282 80 moveto (m) show 0 6 rmoveto (j) show 0 -6 rmoveto 71 execuserobject setfont ( TLUs) show grestore grestore 0 0 0 setup gsave 71 execuserobject setfont 0 setgray [1 0 0 -1 0 152] concat 510 execuserobject setfont 0 setgray 428 75 moveto (m) show 71 execuserobject setfont 0 6 rmoveto (\() show 0 -6 rmoveto 510 execuserobject setfont 0 6 rmoveto (k-1) show 0...