Understanding Deep Convolutional Networks

TL;DR

This paper reviews the architecture and mathematical properties of deep convolutional networks, highlighting their effectiveness in high-dimensional classification and regression tasks through multiscale and hierarchical analysis.

Contribution

It introduces a mathematical framework for analyzing convolutional networks' properties, focusing on invariants, symmetries, and sparse separations.

Findings

Convolutional networks achieve state-of-the-art results in high-dimensional problems.

A new mathematical framework helps analyze their invariants and hierarchical structures.

Applications demonstrate the practical relevance of the theoretical insights.

Abstract

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.