# On the finite representation of group equivariant operators via permutant measures

arXiv: https://arxiv.org/abs/2008.06340 · HTML: https://mlsanity.com/paper/2008.06340/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2020.

## Built on by (most cited first, 7 of 7)

- [Generalized Permutants and Graph GENEOs](https://mlsanity.com/paper/2206.14798/) (2022)
- [GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection](https://mlsanity.com/paper/2202.00451/) (2022)
- [A novel approach to graph distinction through GENEOs and permutants](https://mlsanity.com/paper/2406.08045/) (2024)
- [On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators](https://mlsanity.com/paper/2103.02543/) (2021)
- [A topological model for partial equivariance in deep learning and data analysis](https://mlsanity.com/paper/2308.13357/) (2023)
- [GENEOnet: Statistical analysis supporting explainability and trustworthiness](https://mlsanity.com/paper/2503.09199/) (2025)
- [An Algebraic Representation Theorem for Linear GENEOs in Geometric Machine Learning](https://mlsanity.com/paper/2601.03910/) (2026)

## Abstract (arXiv)

The study of G-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear G-equivariant operator can be produced by a suitable permutant measure, provided that the group G transitively acts on a finite signal domain X. This result makes available a new method to build linear G-equivariant operators in the finite setting.