# A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNs

arXiv: https://arxiv.org/abs/2406.03946 · HTML: https://mlsanity.com/paper/2406.03946/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2024.

## Built on by (most cited first, 8 of 8)

- [Relaxed Equivariance via Multitask Learning](https://mlsanity.com/paper/2410.17878/) (2024)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [AtlasD: Automatic Local Symmetry Discovery](https://mlsanity.com/paper/2504.10777/) (2025)
- [Approximate Equivariance via Projection-based Regularisation](https://mlsanity.com/paper/2601.05028/) (2026)
- [Algebraic Priors for Approximately Equivariant Networks](https://mlsanity.com/paper/2506.08244/) (2025)
- [Recurrent Equivariant Constraint Modulation: Learning Per-Layer Symmetry Relaxation from Data](https://mlsanity.com/paper/2602.02853/) (2026)
- [Tunable Soft Equivariance with Guarantees](https://mlsanity.com/paper/2603.26657/) (2026)
- [Bayesian 3D Steerable CNNs: Enabling Equivariance and Uncertainty Quantification Simultaneously](https://mlsanity.com/paper/2606.15479/) (2026)

## Abstract (arXiv)

Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased performance. To address this, this paper introduces a probabilistic method to learn the degree of equivariance in SCNNs. We parameterise the degree of equivariance as a likelihood distribution over the transformation group using Fourier coefficients, offering the option to model layer-wise and shared equivariance. These likelihood distributions are regularised to ensure an interpretable degree of equivariance across the network. Advantages include the applicability to many types of equivariant networks through the flexible framework of SCNNs and the ability to learn equivariance with respect to any subgroup of any compact group without requiring additional layers. Our experiments reveal competitive performance on datasets with mixed symmetries, with learnt likelihood distributions that are representative of the underlying degree of equivariance.