Prove the updating equation for the Backpropagation:
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
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb9da028-c1e8-4fb4-9df2-7f4287e8030e%2F5d2cf0a4-850b-4c99-884a-cad0ce831eb4%2Frq32dd8_processed.jpeg&w=3840&q=75)
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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