An Optimization and Generalization Analysis for Max-Pooling Networks
Abstract
Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However, these architectures are not well understood from a theoretical perspective. For example, we do not understand when they can be globally optimized, and what is the effect of over-parameterization on generalization. Here we perform a theoretical analysis of a convolutional max-pooling architecture, proving that it can be globally optimized, and can generalize well even for highly over-parameterized models. Our analysis focuses on a data generating distribution inspired by pattern detection problem, where a "discriminative" pattern needs to be detected among "spurious" patterns. We empirically validate that CNNs significantly outperform fully connected networks in our setting, as predicted by our theoretical results.
Cite
@article{arxiv.2002.09781,
title = {An Optimization and Generalization Analysis for Max-Pooling Networks},
author = {Alon Brutzkus and Amir Globerson},
journal= {arXiv preprint arXiv:2002.09781},
year = {2021}
}