Neural Networks Explained: Solving the XOR Logic Gate with Backpropagation

The XOR logic gate is an excellent example of a neural network that can be trained and utilized to solve complex problems. A non-linear decision boundary is needed as the XOR logic gate is not linearly separable. This means that a multi-layer neural network is needed. Backpropagation will be used to train the network, and how this is done will be shown with an architecture diagram and with the equations. A numerical example will be provided to show how the equations are solved. To train the network, 40,000 epochs are run to optimize the weights and biases. The network was trained using both stochastic and batch gradient descent, which resulted in similar solutions. Adding noise to the input points in conjunction with adding a hidden layer made it so the resulting decision boundary plot was very close to the ideal case.