Comment by zump

The key to understanding is drilling the backpropagation algorithm and being able to visualize the application of the multivariate chain rule as a computational graph.

EDIT: You won't understand until you do this yourself using pen and paper. It's a pain.

EDIT2: This nuts and bolts tutorial will help

http://briandolhansky.com/blog/2013/9/27/artificial-neural-n...