# tut2_sol - 1 EE4210 Solution to Tutorial 2 1 Hebbian...

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Unformatted text preview: 1 EE4210 Solution to Tutorial 2 1. Hebbian Learning y ( n ) = w ( n ) x ( n ) = 1.2 w ( n ) since x ( n ) = 1.2 for all n Î· = 0.75 w (0) = 1 (a) Simple form of Hebbâ€™s rule (Activity Product Rule) Î” w ( n ) = Î· x ( n ) y ( n ) w ( n +1) = w ( n ) + Î” w ( n ) = 2.08 w ( n ) n w ( n ) y ( n ) Î” w ( n ) 0 1 1.2 1.08 1 2.08 2.496 2.246 2 4.326 5.19 4.67 â€¦ â€¦ â€¦ â€¦ k (2.08) k 1.2 (2.08) k 1.08 (2.08) k â€¦ â€¦ â€¦ â€¦ b The weight increases exponentially with the number of iterations k . (b) Modified form of Hebbâ€™s rule (Generalized Activity Product Rule) (i) Î· = 0.75, a = 2 Î” w ( n ) = 0.75 x ( n ) y ( n ) â€“ 2 y ( n ) w ( n ) w ( n +1) = w ( n ) ( 2.08 â€“ 2.4 ( w ( n ) ) n w ( n ) y ( n ) Î” w ( n ) 0 1 1.2 â€“1.32 1 â€“0.32 â€“0.384 â€“0.591 2 â€“0.911 â€“1.09 â€“2.98 3 â€“3.889 â€“4.667 â€“40.499 4 â€“44.38 â€“53.27 â€“4776 5 â€“4820 â€“5785 â€“5.6 x 10 7 6 â€“5.6 x 10 7 â€“6.7 x 10 7 â€“7.5 x 10 15 â€¦ â€¦ â€¦ â€¦ b The weight magnitude increases even faster, cannot achieve the regulation purpose as a (forgetting term parameter) is much larger than Î· (learning rate parameter). 2 (ii) Î· = 0.75, a = 0.75 Î” w ( n ) =...
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## This note was uploaded on 04/14/2011 for the course EE 4210 taught by Professor Wong during the Spring '10 term at City University of Hong Kong.

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tut2_sol - 1 EE4210 Solution to Tutorial 2 1 Hebbian...

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