Universal characteristics of deep neural network loss surfaces from random matrix theory
This work provides foundational insights into neural network optimization for researchers, though it is incremental in applying existing random matrix tools.
The paper tackles the problem of understanding deep neural network loss surfaces by applying random matrix theory to model Hessians, deriving universal characteristics of spectral outliers and demonstrating their role in pre-conditioning gradient descent algorithms.
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 into deep neural network loss surfaces from quite general arguments based on tools from statistical physics and random matrix theory.