Mathematics of Neural Networks

In this paper I try to describe both the role of mathematics in shaping our understanding of how neural networks operate, and the curious new mathematical concepts generated by our attempts to capture neural networks in equations. My target reader being the non-expert, I will present a biased selection of relatively simple examples of neural network tasks, models and calculations, rather than try to give a full encyclopedic review-like account of the many mathematical developments in this �field

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.161.3556&rep=rep1&type=pdf