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# tut4_sol - 1 EE4210 Solution to Tutorial 4 Backpropagation...

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Unformatted text preview: 1 EE4210 Solution to Tutorial 4 Backpropagation Training in Multilayer Perceptron 1. X 1 =0, X 2 =1, d =0.9, Î· =0.7, Ï• ( ) exp( ) v v = +- 1 1 . (a) Feedforward Phase: H 1 : v H1 = (- 0.5)(0)+(0.1)(1)+(- 0.6)(- 1) = 0.7 =&amp;gt; y H1 = Ï• (0.7) = 0.668 H 2 : v H2 = (- 0.4)(0)+(0.2)(1)+(0.3)(- 1) = -0 .1 =&amp;gt; y H2 = Ï• (- 0.1) = 0.475 Y 1 : v Y1 = (0.6)(0.668)+(- 0.7)(0.475)+(- 0.8)(- 1) = 0.868 =&amp;gt; y Y1 = Ï• (0.868) = 0.704 Error = ( d - y Y1 ) = 0.9 â€“ 0.704 = 0.196 (b) Backward Phase: (i) Î´ Y1 = ( d- y Y1 ) y Y1 (1- y Y1 ) = (0.9- 0.704)(0.704)(1- 0.704) = 0.041 (ii) Î” w Y1H1 = Î· Î´ Y1 y H1 = (0.7)(0.041)(0.668) = 0.019 Î” w Y1H2 = Î· Î´ Y1 y H2 = (0.7)(0.041)(0.475) = 0.014 Î” b Y1 = Î· Î´ Y1 (- 1) = (0.7)(0.041)(- 1) = - 0.0285 (iii) Î´ H1 = âˆ‘ k kH k H w v 1 1 ' ) ( Î´ Ï• = ( Î´ Y1 w Y1H1 ) y H1 (1â€“ y H1 ) = (0.041) (0.6) (0.668)(1â€“0.668) = 0.0054 Î´ H2 = âˆ‘ k kH k H w v 2 2 ' ) ( Î´ Ï• = ( Î´ Y1 w Y1H2 ) y H2 (1â€“ y H2 ) = (0.041) (â€“0.7) (0.475)(1â€“0.475) = â€“0.007 (iv) Î”...
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tut4_sol - 1 EE4210 Solution to Tutorial 4 Backpropagation...

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