[adityab]

You should watch Max Tegmark's talk "Connections between Physics and Deep Learning" if this interests you [1].

Additionally, a paper that has everyone excited about deep connections between the mathematical analysis of physical systems and the hierarchical feature learning paradigm speaks of the connection in terms of the Renormalization Group [2].

Regardless of it's practical utility, the philosophical implications do tickle the intellect. On a dreamy note, I wonder if it would be possible to draw Category-theoretic parallels between some physical theories and statistical learning theory. There is so much to learn, and I am trying my best to teach myself (on the side) the mathematics that they don't teach in my CS grad school. So much to learn, such little time. :)

[1] https://youtu.be/5MdSE-N0bxs

[2] http://arxiv.org/abs/1410.3831