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Prove the updating equation for the Backpropagation:

Prove the updating equation for the Backpropagation:

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Prove the updating equation for the Backpropagation:

 

Step 1. Show that for the Logistic Activation function for the neurons as below: 1 1+ exp(-v) o(v) = Then the derivative is as following: q'(t) = y(t)(1- q(t)) Step 2. Using the model of a single neuron, calculate the input of the neuron j, netj, as: Σ(WX+Threshold) where X, is the activation of previous layer neuron i W₁ is the weight of going from node i to node j ☐p is the number of neurons in the previous layer Step 3. Using the error function below, = 1/2 k=1 jk E(x)= (yk (x)-1(x))² Take the partial derivative with respect to the weight as: JE (x) owjk Use chain rule of calculus and simplify it using results of steps 1 and 2, show that: dE (x) =-y; 9(net) (1-9 (net;)) (t; − y;) dw
Transcribed Image Text:Step 1. Show that for the Logistic Activation function for the neurons as below: 1 1+ exp(-v) o(v) = Then the derivative is as following: q'(t) = y(t)(1- q(t)) Step 2. Using the model of a single neuron, calculate the input of the neuron j, netj, as: Σ(WX+Threshold) where X, is the activation of previous layer neuron i W₁ is the weight of going from node i to node j ☐p is the number of neurons in the previous layer Step 3. Using the error function below, = 1/2 k=1 jk E(x)= (yk (x)-1(x))² Take the partial derivative with respect to the weight as: JE (x) owjk Use chain rule of calculus and simplify it using results of steps 1 and 2, show that: dE (x) =-y; 9(net) (1-9 (net;)) (t; − y;) dw
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