Unable to solve the XOR problem with just two hidden neurons in Python

Question

I have a small, 3 layer, neural network with two input neurons, two hidden neurons and one output neuron. I am trying to stick to the below format of using only 2 hidden neurons

Answer 1

It is an unsolvable equation system, that is why NN can not solve it either. While it may be an oversimplification, if we say the transfer function is linear, the expression becomes something like

z = (w1*x+w2*y)*w3 + (w4*x+w5*y)*w6

Then there are the 4 cases:

xy=00, z=0 = 0
xy=10, z=1 = w1*w3+w4*w6
xy=01, z=1 = w2*w3+w5*w6
xy=11, z=0 = (w1+w2)*w3 + (w4+w5)*w6

The problem is that

0 = (w1+w2)*w3 + (w4+w5)*w6 = w1*w3+w2*w3 + w4*w6+w5*w6            <-- xy=11 line
                            = w1*w3+w4*w6 + w2*w3+w5*w6 = 1+1 = 2  <-- xy=10 and xy=01 lines

So the seemingly 6 degrees of freedom are just not enough here, that is why you experience the need for adding something extra.