# Testing for Geometric Invariance and Equivariance

arXiv: https://arxiv.org/abs/2205.15280 · HTML: https://mlsanity.com/paper/2205.15280/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 10 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 3 of 3)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [On the Benefits of Invariance in Neural Networks](https://mlsanity.com/paper/2005.00178/) (2020)
- [Provably Strict Generalisation Benefit for Invariance in Kernel Methods](https://mlsanity.com/paper/2106.02346/) (2021)

## Built on by (most cited first, 1 of 1)

- [Non-parametric Hypothesis Tests for Distributional Group Symmetry](https://mlsanity.com/paper/2307.15834/) (2023)

## Abstract (arXiv)

Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions f : X rightarrow ℝ). These models perform better (with respect to L2 loss) and are increasingly being used in practice, but encounter problems when the symmetry is falsely assumed. In this paper we present a framework for testing for G-equivariance for any semi-group G. This will give confidence to the use of such models when the symmetry is not known a priori. These tests are independent of the model and are computationally quick, so can be easily used before model fitting to test their validity.