Learning Stable Group Invariant Representations with Convolutional Networks

TL;DR

This paper explores how deep convolutional networks can learn stable, invariant representations by controlling the invariance group through architecture and filters, extending beyond traditional physical transformation groups.

Contribution

It demonstrates that deep CNNs can be understood as learning stable invariance groups, with architecture and filters shaping the invariance properties and enabling more abstract representations.

Findings

CNN architecture determines the invariance group

Trainable filters characterize the group action

Additional layers enable more abstract invariance

Abstract

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing mathematical properties, where convolutions, together with pooling operators, bring stability to additive and geometric perturbations of the input. Whereas physical transformation groups are ubiquitous in image and audio applications, they do not account for all the variability of complex signal classes. We show that the invariance properties built by deep convolutional networks can be cast as a form of stable group invariance. The network wiring architecture determines the invariance group, while the trainable filter coefficients characterize the group action. We give explanatory examples which illustrate how the network architecture controls the resulting invariance group. We also explore the principle by which additional convolutional layers induce a group factorization enabling more abstract, powerful invariant representations.