# Learning Symmetrization for Equivariance with Orbit Distance Minimization

Source: [Learning Symmetrization for Equivariance with Orbit Distance Minimization](<https://www.sota2.com/research/paper/68fa712d1e209131cea4fbf0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:00:40.638Z

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

Published: 2023-11-13T08:14:29.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2311.07143>)

[PDF](<https://arxiv.org/pdf/2311.07143.pdf>)