"An artificial neural network (ANN), usually called "neural network" (NN), is a mathematical model or computational model that tries to simulate the structure and/or functional aspects of biological neural networks. It consists of an interconnected group of artificial neurons and processes information using a connectionist approach to computation. In most cases an ANN is an adaptive system that changes its structure based on external or internal information that flows through the network during the learning phase. Neural networks are non-linear statistical data modeling tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data." (Wikipedia)
So, repetition is the mother of all learning they say. You damn right it is. And you can do it in AS3 of course. Not the fastest choice out there but that's not the point. NN's are usually not that fast but they're useful in so many ways.
So, here is my implementation of a neural network multi-layer-perceptron made in AS3, set to learn a simple XOR problem. It uses 2 inputs neurons , 2 hidden layers, each having 2 neurons and one output neuron. It takes about 2 seconds to train it using 10.000 epochs, but then you can save a snapshot of the NN memory as a byteArray, save it to the server and load it back again in an instant without requiring a new training. I didn't take the time to thoroughly document the classes just yet but I'm sure you'll find them pretty easy to use.
Some reading material:
http://fbim.fh-regensburg.de/~saj39122/jfroehl/diplom/e-index.html (this is great)