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.
|Number of pages||11|
|State||Published - 2021|
|Event||37th Conference on Uncertainty in Artificial Intelligence, UAI 2021 - Virtual, Online|
Duration: 27 Jul 2021 → 30 Jul 2021
|Conference||37th Conference on Uncertainty in Artificial Intelligence, UAI 2021|
|Period||27/07/21 → 30/07/21|