simple 2-layered xor perceptron

a numpy implementation of a simple neural network solving the xor problem with documented code

overview

this small neural net is implemented without using any deep learning frameworks like pytorch or tensorflow to classify the 4 xor samples. xor refers to an exclusive-or boolean expression where this OR that is true but this and that is not. If we take true as 1 and false as 0, then we can generate samples and labels. the xor problem is non-linearly separable (which becomes more clear if you plot the xor samples shown below), requiring a hidden layer and non-linear activation functions to solve

implementation details

• built using only numpy for computations and matplotlib for visualization
• custom implementation of:
  • feed-forward logic
  • backpropagation algorithm
  • sigmoid activation function
  • loss calculation
• total trainable parameters: 9
• modular design for clear separation of components

results

training progression:

initial predictions:

final predictions:

how to use

requirements:

• numpy
• matplotlib

usage:

open model.py and run

note: due to random weight initialization, you might need to run the model multiple times to avoid local minima.

the model classifies the following xor truth table:

(0,0) -> 0
(1,0) -> 1
(0,1) -> 1
(1,1) -> 0