How would you implement a neural network on a web application?

I would do it on the back-end using what technology is most applicable to the problem you are trying to solve.  A specialized back-end server that supplies a RESTFul service as an interface to the UI.  Good luck using JavaScript on the browser for something like this.

Why do you want to do that? If you want to build a website that uses some neural network based machine learning, you can just write it as server code in whatever language you want, and take advantage of the many machine learning libraries in C++, python, etc. I don't really see any use case for implementing a neural network on the client side aside from a toy program on a website that teaches neural networks. If that's what you want to do, the simplest solution (but certainly not the most elegant) would probably be a Java applet. A pure javascript implementation with an HTML5 UI is certainly a possibility but that would be some significant work and the result would likely be slow. (Or would it? I don't know so much about modern Web tech and I know that javascript interpreters made huge progress in the last years, but still, backpropagation training on large many-dimensional sets demands significant computing power) A javascript/HTML5 interface interacting with an efficient server side implementation would probably be a better idea.

Someone's already done this in JavaScript: check out https://github.com/harthur/brain on Github. The client-side version is at https://github.com/harthur/brain/blob/gh-pages/brain-0.6.3.js As the author of the project notes, "Training is computationally expensive, so you should try to train the network offline (or on a Worker)." So you're going to either be doing this as a part of an offline HTML5 application or using it on a Web Worker. The brain.js library then provides a 'toFunction' method which allows you to turn the trained network into a normal JavaScript function. There's also a toJSON() method if you want to use that to serialise the neural network and save it for later. This is a pretty basic example of the brain.js library, for guesstimating colour contrast: [code js] var net = new brain.NeuralNetwork(); net.train([{input: { r: 0.03, g: 0.7, b: 0.5 }, output: { black: 1 }},           {input: { r: 0.16, g: 0.09, b: 0.2 }, output: { white: 1 }},           {input: { r: 0.5, g: 0.5, b: 1.0 }, output: { white: 1 }}]); var output = net.run({ r: 1, g: 0.4, b: 0 });  // { white: 0.99, black: 0.002 }[/code]

I vote for do ann on the backend answer. :) But, if you are insisting on doing it in web up front, you can try crowding ann learning to several mobiles / desktops, borrowing their computing power, basically like a combi of what cluster computing, distributed computing, and crowdsourcing do. I just don't know the real life situation perfect for this project though. And also sorry, I forgot which project actually had done this (If I am not mistaken, it is mentioned in Tanenbaum Book of Operating System)

IMO, Training process should be handled in "backend" with power server, then trained ANN could be used in frontend by js