I am looking for an open source neural network library. So far, I have looked at FANN, WEKA, and OpenNN. Are the others that I should look at? The criteria, of course, is documentation, examples, and ease of use.
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Netlab is a commonly used Matlab library. (free and open source)
Last update: 2019/01/07 (I will update this answer from time to time...)
Simple Implementations of Neural Networks
Deep Learning
Because neural networks are quite popular at the moment ("deep learning") there are many research libraries available. Most of them are kind of easy to set up, integrate, and use. Although not as easy as the libraries mentioned above. They provide leading edge functionality and high performance (with GPUs etc.). Most of these libraries also have automatic differentiation. You can easily specify new architectures, loss functions etc. and don't have to specify the backpropagation manually.
A performance comparison for GPU-accelerated libraries can be found here (a bit outdated unfortunately). A comparison of GPUs and library versions can be found here.
Inactive:
If you want flexibility in defining network configurations, like sharing parameters or creating different types of convolutional architectures, then you should look at the family of Torch libraries: http://www.torch.ch/.
I haven't gone through the documentation for Torch 7 yet, but documentation for the other versions was pretty decent and the code is very readable (in Lua and C++).
You can use accord.net framework. http://accord-framework.net/
It contains Neural learning algorithms such as Levenberg-Marquardt, Parallel Resilient Backpropagation, the Nguyen-Widrow initialization algorithm, Deep Belief Networks and Restrictured Boltzmann Machines, and many other neural network related items.