hw4_Solution

hw4_Solution - CS 6375 Homework 4 Chenxi Zeng, UTD ID:...

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CS 6375 Homework 4 Chenxi Zeng, UTD ID: 11124236 Part I 1. Let t is the correct output and o is the actual output of the neural network, then Err= t o - = 2 z t e - - , E= 2 1 ( ) 2 t o - . Let input x r = 0 1 { , ,..., } n x x x , and weight β ur = 0 1 { , ,..., } n w w w , then we have j E w = j E Err Err w × = Err × j Err w = Err × 2 ( ) ( ) x j t e w - - r ur = Err × 2( ) x r ur × 2 ( ) x e - r ur × j x . The gradient descent is E = 0 1 ( , ,..., ) n E E E w w w . So the gradient descent training rule for a single Gaussian unit is j w ¬ j j w w + ∆ , and j w = 2 ( ) 2 ( ) x j Err x e x η - - × × × × r ur r ur , is the learning rate. 2. Learning rate is 0.05, 1 i = 2 i =1, t=1. We assume 1 hio w (i=0, 1, 2) and ijhk w (j=0, 1, 2; k=1, 2) are the weights from node i h to 1 o and j i to k h . Firstly, we compute all the outputs at each layer:
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hw4_Solution - CS 6375 Homework 4 Chenxi Zeng, UTD ID:...

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