Equivariance With Learned Canonicalization Functions

Sékou-Oumar Kaba, Arnab Kumar Mondal, Yan Zhang, Yoshua Bengio, Siamak Ravanbakhsh

Keywords: deep learning, symmetry, equivariance, shape recognition, group theory, vision

TL;DR: Learning to produce canonical representation of data to make any neural network equivariant

Abstract: Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce a canonical representation of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform canonicalization is better than doing it using predefined heuristics. Our results show that learning the canonicalization function indeed leads to better results and that the approach achieves great performance in practice.