# Max filtering with reflection groups

arXiv: https://arxiv.org/abs/2212.05104 · HTML: https://mlsanity.com/paper/2212.05104/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2022.

## Built on by (most cited first, 4 of 4)

- [Quantitative Bounds for Sorting-Based Permutation-Invariant Embeddings](https://mlsanity.com/paper/2510.22186/) (2025)
- [Quantitative Approximation Rates for Group Equivariant Learning](https://mlsanity.com/paper/2602.20370/) (2026)
- [If you can distinguish, you can express: Galois theory, Stone--Weierstrass, machine learning, and linguistics](https://mlsanity.com/paper/2510.09902/) (2025)
- [Transversal Pooling Neural Networks](https://mlsanity.com/paper/2609.36237/) (2026)

## Abstract (arXiv)

Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the setting where G is a reflection group. Our analysis involves an interplay between Coxeter's classification and semidefinite programming.