Disentangling Hyperedges through the Lens of Category Theory

Yoonho Lee, Junseok Lee, Sangwoo Seo, Sungwon Kim, Yeongmin Kim, Chanyoung Park

Keywords: Graph Neural Network, Category Theory, Disentangled Representation Learning, Categorical Deep Learning, Hypergraph

TL;DR: We propose a novel criterion for hyperedge disentanglement. We analyze hypergraph MPNN and disentanglement through the lens of category theory, and derive the criterion.

Abstract:

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).

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 21808