Download the xornnetpy file from the course webpage and

Question

E27: Computer Vision - Spring 2016 - HOMEWORK 12

Backpropagation in a simple network

The binary XOR function is given by the following truth table:

y1	y2	y1 ⊗ y2
-1	-1	-1
-1	1	1
1	-1	1
1	1	-1

It can be computed by a simple two-layer network with the following structure:

Note that both the input and hidden layer of the network have bias nodes. The output is computed by

y₃ = f(x₃) = f(w₀₃ + w₁₃ y₁ + w₂₃ y₂)

y₄ = f(x₄) = f(w₀₄ + w₁₄ y₁ + w₂₄ y₂)

y₅ = f(x₅) = f(w₀₅ + w₃₅ y₃ + w₄₅ y₄)

where w_ij is the weight from node i to node j and w_0j is the weight from a bias node.

Download the xor_nnet.py file from the course webpage and complete the steps marked # TODO to implement the back-propagation algorithm described in the class handout for this simple network. If you keep the α parameter and tolerance specified in the file, your implementation should converge in 61 iterations.

Attachment:- xor_nnet.py.rar