I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets".

Most of the papers/books that are often quoted in papers/online as references are not written in a very math-friendly manner. I am specifically referring to the fact that this field is highly interdisciplinary, and the language used (e.g. 'levels', 'stacking networks') are not standard mathematical terminology, but rather very specialized terms.

So I am writing this post to find out if there exists a book or review article written for pure mathematicians about the core mathematical ideas of the whole deep-learning thing.

My hope is that is there is a reference that follows (sort of ) the theorem-lemma-proof format or at least tries to where ever possible, or at least gives some rigorous definitions so that I can make sense of the terminology.

Thank you.