Exercise:Vectorization

In the previous problem set, we implemented a sparse autoencoder for patches taken from natural images. In this problem set, you will vectorize your code to make it run much faster, and further adapt your sparse autoencoder to work on images of handwritten digits.  Our network for learning from handwritten digits will be much larger than the one we'd trained on the natural images, and so using the original implementation would have been painfully slow.  But with a vectorized implementation of the autoencoder, you will be able to learn interesting features from the handwritten characeters.