hw4_Solution_Part I - CS 6375 Homework 4 Chenxi Zeng, UTD...

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CS 6375 Homework 4 Chenxi Zeng, UTD ID: 11124236 Part I 1. Let is the correct output and is the actual output of the neural network, then Err= = , E= t o to 2 z te 2 1 () 2 . Let input x G = 01 { , ,..., } n x xx , and weight β JG = , then we have { , ,..., } n ww w j E w = j EE r r Err w ∂∂ × Err = × j Err w = Err × 2 x j w −• G = Err × 2( ) x GJ G × 2 x e G × j x . The gradient descent is E = ( , ,..., ) n E w . So the gradient descent training rule for a single Gaussian unit is j w j j , and j w Δ = 2 2( ) x j Err x e x ηβ ×× × × G G , η is the learning rate. 2. Learning rate is 0.05, = =1, t=1. We assume (i=0, 1, 2) and (j=0, 1, 2; k=1, 2) are the weights from node to and 1 i 2 i 1 hio w ijhk w i h 1 o j i to . k h Firstly, we compute all the outputs at each layer: 1 h = =g(0.02)= 1 ( ijh j j gwi × ) 0.02 1 1 e + =0.505
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2 h = =g(0.01)= 2 ( ijh j j gwi × ) 0.01 1 1 e + =0.502 1 o = =g(0.025)= 1 ( hio i i gw h × ) 0.025 1 1 e + =0.506 Then, we use the Backpropagation Algorithm with Sigmoid units: 1 o δ = =0.123 11 (1 )( ) oo t o −− 1 1 01 ho w = + w 0 o h η ×× =-0.02+ (-0.006) = -0.026
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This note was uploaded on 01/25/2012 for the course CS 6375 taught by Professor Yangliu during the Spring '09 term at University of Texas at Dallas, Richardson.

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hw4_Solution_Part I - CS 6375 Homework 4 Chenxi Zeng, UTD...

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