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 η = 0.75 w (0) = 1 (a) Simple form of Hebb’s rule (Activity Product Rule) Δ w ( n ) = η x ( n ) y ( n ) w ( n +1) = w ( n ) + Δ w ( n ) = 2.08 w ( n ) n w ( n ) y ( n ) Δ w ( n ) 0 1 1.2 1.08 1 2.08 2.496 2.246 2 4.326 5.19 4.67 … … … … k (2.08) k 1.2 (2.08) k 1.08 (2.08) k … … … … b The weight increases exponentially with the number of iterations k . (b) Modified form of Hebb’s rule (Generalized Activity Product Rule) (i) η = 0.75, a = 2 Δ w ( n ) = 0.75 x ( n ) y ( n ) – 2 y ( n ) w ( n ) w ( n +1) = w ( n ) ( 2.08 – 2.4 ( w ( n ) ) n w ( n ) y ( n ) Δ w ( n ) 0 1 1.2 –1.32 1 –0.32 –0.384 –0.591 2 –0.911 –1.09 –2.98 3 –3.889 –4.667 –40.499 4 –44.38 –53.27 –4776 5 –4820 –5785 –5.6 x 10 7 6 –5.6 x 10 7 –6.7 x 10 7 –7.5 x 10 15 … … … … b The weight magnitude increases even faster, cannot achieve the regulation purpose as a (forgetting term parameter) is much larger than η (learning rate parameter). 2 (ii) η = 0.75, a = 0.75 Δ w ( n ) =...
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tut2_sol - 1 EE4210 Solution to Tutorial 2 1. Hebbian...

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