libfann/fann
A C library implementing multilayer artificial neural networks with backpropagation training support.

FANN is a free open-source neural network library written in C that implements multilayer artificial neural networks with support for both fully connected and sparsely connected networks. It provides multiple training algorithms including RPROP, Quickprop, Batch, and Incremental backpropagation, along with a framework for handling training datasets. The library supports cross-platform execution with both fixed and floating point operations and includes bindings to over 15 programming languages.