Learning Symmetrization for Equivariance with Orbit Distance Minimization

Dat Tien Nguyen, Jinwoo Kim, Hongseok Yang, Seunghoon Hong

Submission Track: Extended Abstract

Keywords: Equivariance, Symmetrization, Rotation Equivariance, Lorentz Equivariance

TL;DR: We propose orbit distance minimization, a method for symmetrization based equivariance for a wide range of groups including Lorentz.

Abstract: We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and improve them by replacing their conversion of neural features into group representations, with an optimization whose loss intuitively measures the distance between group orbits. This change makes our approach applicable to a broader range of matrix groups, such as the Lorentz group O(1, 3), than these two proposals. We experimentally show our method’s competitiveness on the SO(2) image classification task, and also its increased generality on the task with O(1, 3). Our implementation will be made accessible at https://github.com/tiendatnguyen-vision/Orbit-symmetrize.

Submission Number: 60