Originally, I was attempting to create this neural network from scratch using a class Unit that would contain the units value, next & prev layers and the weights from the previous nodes. Doing so made the process way more convoluted than if I were to use matrices and vectors.
I found a tutorial online which really helped me understand why matrices are so important for neural networks.
After following the guide and making some adjustments to the network to make it my own, I have a successful XOR network! My goal now is to make it work with two output nodes, one representing 1 and the other 0. Then, I can apply the same concepts used here for my next deep learning exercise; a neural network w/ out machine learning libraries that works on the MNIST data set.
Since I've started looking at this problem from a linear algebra perspective it's much more intuitive, and I was able to get the network working with two outputs! Now it's time to move onto the MNIST dataset.