Radial basis function network for XOR

RBFN_EG.ipynb

You can change points to use it for different logic gates
# points
x1 = np.array([....])
x2 = np.array([....])
ys = np.array([....])

and centers by changing
# centers
mu1 = np.array([..])
mu2 = np.array([..])

In the end_to_end function, first I calculated the similarity between the inputs and the peaks.
Then, to find w used the equation Aw= Y in matrix form.
Each row of A (shape: (4, 2)) consists of

• index[0]: similarity of point with peak1
• index[1]: similarity of point with peak2
• index[2]: Bias input (1)

Y: Output associated with the input (shape: (4, ))

W is calculated using the same equation we use to solve linear regression using a closed solution (normal equation).

This part is the same as using a neural network architecture of 2-2-1,

• 2 node input (x1, x2) (input layer)
• 2 node (each for one peak) (hidden layer)
• 1 node output (output layer)

To find the weights for the edges to the 1-output unit. Weights associated would be:

• edge joining 1st node (peak1 output) to the output node
• edge joining 2nd node (peak2 output) to the output node
• bias edge