Fast deep neural network with adaptive learning rate AdaGrad and AdaDec using gpuArray

This project was forked from Nicolas Le Roux's nnetLib which you can find on his website and MATLAB Central File Exchange.

The major improvements are porting to GPU and adding adaptive learning rate.

Training deep neural network on GPU is more than 10 times faster than on CPU. So we can experiment and tune algorithms with various parameter combinations in fast iterative cycles.

Adaptive learning rate scheduling policies set parameter wise learning rate based on the gradient histories of each parameter. AdaGrad uses 1 ./ sqrt(K + sum(gradient_histories .^ 2)). AdaDec extends AdaGrad by introduces forgetting factor to do exponential averaging of the sum of squared gradients. The denominator becomes sqrt(K + S_t(gradient_histories)) in which S_t = forgetting_factor * S_t-1 + sum_h=0^N(gradient_h .^ 2). In pratice forgetting_factor is set to 0.999 or some similar values. When forgetting_factor is set to 1 and exponential averaging window size N is 1, AdaDec falls back to AdaGrad. The biggest drawback of AdaDec is the memory requirements grows proportionally with the window size. In large deep network, there are millions to billions of parameters. So the value of N is bounded by the available GPU memory.