# Group Cross-Correlations with Faintly Constrained Filters

arXiv: https://arxiv.org/abs/2601.00045 · HTML: https://mlsanity.com/paper/2601.00045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 7 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 5 of 5)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)

## Abstract (arXiv)

Group convolutional layers with respect to some group G are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained filters and G a non-abelian group, any hidden layer of such a network requires as many nodes as vertices in a fine enough discretization of G. In order to reduce the necessary number of nodes, certain constraints on filters were proposed in the literature. We propose weaker constraints retaining this benefit while also resolving an incompatibility previous constraints have for group actions with non-compact stabilizers. Moreover, we generalize previous results to group actions that are not necessarily transitive, and we weaken the common assumption that G is unimodular.