Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
Abstract
We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao norm --- that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of the new capacity measure, through which we establish norm-comparison inequalities and further show that the new measure serves as an umbrella for several existing norm-based complexity measures. We discuss upper bounds on the generalization error induced by the proposed measure. Extensive numerical experiments on CIFAR-10 support our theoretical findings. Our theoretical analysis rests on a key structural lemma about partial derivatives of multi-layer rectifier networks.
Keywords
Cite
@article{arxiv.1711.01530,
title = {Fisher-Rao Metric, Geometry, and Complexity of Neural Networks},
author = {Tengyuan Liang and Tomaso Poggio and Alexander Rakhlin and James Stokes},
journal= {arXiv preprint arXiv:1711.01530},
year = {2020}
}
Comments
To appear in the proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019