Do you know that convolution operation is implemented in deep learning systems via matrix multiplication?

Here is a detailed description of how it is done by chunking the data
http://petewarden.com/2015/04/20/why-gemm-is-at-the-heart-of-deep-learning/

Theano library, by the way, provides many possibilities for implementation of convolution, among which CPUCorrMM (this isn't the main way however)
http://deeplearning.net/software/theano/library/tensor/nnet/conv.html