I've seen a bunch of tutorials on Neural Networks in Python, but I've never found any of them to be particularly good. They're either riddled with errors or use simple, single-example training with basic arrays. I've always wanted something a little more robust than the simple C-ish implementation and something less mathematically terse than the average neural network paper. I made this implementation in the hopes that it will explain how neural networks work and how you'd use a matrix library to train multiple examples at the same time. It's not optimized (since you can save your activation values and re-use them), but it should be easy to tune.
Here's the source:
And here are some visualized examples as the different activation functions try to learn f(x) = sin(x).