Now that we've had a quick refresher on Neural Networks, I thought that perhaps a good starting point, code-wise, would be for us to write a very simple neural network. We're not going to go crazy; we'll just lay the basic framework for a few functions so that you can get a good idea of what is behind the scenes of many of the APIs that you'll use. From start to finish, we'll develop this network application so that you are familiar with all the basic components that are contained in a neural network. This implementation is not perfect or all-encompassing, nor is it meant to be. As I mentioned, this will merely provide a framework for us to use in the rest of the book. This is a very basic neural network with the added functionality of being able to save and load networks and data. In any event, you will have a foundation from which to write your own neural network and change the world, should you so desire.

In this chapter, we are going to cover the following topics:

• Neural network training
• Terminology
• Synapses
• Neurons
• Forward propagation
• Sigmoid function
• Back propagation
• Error calculations