An Optimization and Generalization Analysis for Max-Pooling Networks

• URL: http://arxiv.org/abs/2002.09781v4
• Date: Thu, 4 Mar 2021 11:45:12 GMT
• Title: An Optimization and Generalization Analysis for Max-Pooling Networks
• Authors: Alon Brutzkus, Amir Globerson
• Abstract summary: Max-Pooling operations are a core component of deep learning architectures. We perform a theoretical analysis of a convolutional max-pooling architecture. We empirically validate that CNNs significantly outperform fully connected networks in our setting.
• Score: 34.58092926599547
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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