# Disentangling Hyperedges through the Lens of Category Theory

arXiv: https://arxiv.org/abs/2510.16289 · HTML: https://mlsanity.com/paper/2510.16289/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 87 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Factorizable Graph Convolutional Networks](https://mlsanity.com/paper/2010.05421/) (2020)
- [Be More with Less: Hypergraph Attention Networks for Inductive Text Classification](https://mlsanity.com/paper/2011.00387/) (2020)
- [Graph Neural Networks are Dynamic Programmers](https://mlsanity.com/paper/2203.15544/) (2022)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Backprop as Functor: A compositional perspective on supervised learning](https://mlsanity.com/paper/1711.10455/) (2017)
- [Categorical Foundations of Gradient-Based Learning](https://mlsanity.com/paper/2103.01931/) (2021)
- [Independence Promoted Graph Disentangled Networks](https://mlsanity.com/paper/1911.11430/) (2019)
- [Disentanglement of Correlated Factors via Hausdorff Factorized Support](https://mlsanity.com/paper/2210.07347/) (2022)
- [On the Power of Foundation Models](https://mlsanity.com/paper/2211.16327/) (2022)
- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Natural Graph Networks](https://mlsanity.com/paper/2007.08349/) (2020)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [Exploring Edge Disentanglement for Node Classification](https://mlsanity.com/paper/2202.11245/) (2022)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [Asynchronous Algorithmic Alignment with Cocycles](https://mlsanity.com/paper/2306.15632/) (2023)
- [Lenses and Learners](https://mlsanity.com/paper/1903.03671/) (2019)
- [Compositional Deep Learning](https://mlsanity.com/paper/1907.08292/) (2019)
- [SHINE: SubHypergraph Inductive Neural nEtwork](https://mlsanity.com/paper/2210.07309/) (2022)
- [Categorical Representation Learning: Morphism is All You Need](https://mlsanity.com/paper/2103.14770/) (2021)

## Abstract (arXiv)

Despite the promising results of disentangled representation learning in discovering latent patterns in graph-structured data, few studies have explored disentanglement for hypergraph-structured data. Integrating hyperedge disentanglement into hypergraph neural networks enables models to leverage hidden hyperedge semantics, such as unannotated relations between nodes, that are associated with labels. This paper presents an analysis of hyperedge disentanglement from a category-theoretical perspective and proposes a novel criterion for disentanglement derived from the naturality condition. Our proof-of-concept model experimentally showed the potential of the proposed criterion by successfully capturing functional relations of genes (nodes) in genetic pathways (hyperedges).