Universal characteristics of deep neural network loss surfaces from random matrix theory. (arXiv:2205.08601v1 [math-ph])

This paper considers several aspects of random matrix universality in deep
neural networks. Motivated by recent experimental work, we use universal
properties of random matrices related to local statistics to derive practical
implications for deep neural networks based on a realistic model of their
Hessians. In particular we derive universal aspects of outliers in the spectra
of deep neural networks and demonstrate the important role of random matrix
local laws in popular pre-conditioning gradient descent algorithms. We also
present insights …

arxiv deep neural network loss math network neural network random theory