# Stochastic Neural Network Symmetrisation in Markov Categories

arXiv: https://arxiv.org/abs/2406.11814 · HTML: https://mlsanity.com/paper/2406.11814/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2024.

## Built on by (most cited first, 5 of 5)

- [Revisiting Random Walks for Learning on Graphs](https://mlsanity.com/paper/2407.01214/) (2024)
- [SigmaDock: Untwisting Molecular Docking With Fragment-Based SE(3) Diffusion](https://mlsanity.com/paper/2511.04854/) (2025)
- [Inverting Data Transformations via Diffusion Sampling](https://mlsanity.com/paper/2602.08267/) (2026)
- [SymDiff: Equivariant Diffusion via Stochastic Symmetrisation](https://mlsanity.com/paper/2410.06262/) (2024)
- [A Diagrammatic Approach to Improve Computational Efficiency in Group Equivariant Neural Networks](https://mlsanity.com/paper/2412.10837/) (2024)

## Abstract (arXiv)

We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism varphi : H → G, we would like a procedure that converts H-equivariant neural networks to G-equivariant ones. We formulate this in terms of Markov categories, which allows us to consider neural networks whose outputs may be stochastic, but with measure-theoretic details abstracted away. We obtain a flexible and compositional framework for symmetrisation that relies on minimal assumptions about the structure of the group and the underlying neural network architecture. Our approach recovers existing canonicalisation and averaging techniques for symmetrising deterministic models, and extends to provide a novel methodology for symmetrising stochastic models also. Beyond this, our findings also demonstrate the utility of Markov categories for addressing complex problems in machine learning in a conceptually clear yet mathematically precise way.