Disentangling Hyperedges through the Lens of Category Theory

TL;DR

This work targets hyperedge-level disentanglement in hypergraph neural networks by deriving a category-theoretic criterion from the naturality condition. The authors introduce Natural-HNN, a two-branch, factor-aware architecture that enforces consistency between entangled and disentangled representations to reveal hyperedge contextual factors. Empirical evaluation on cancer subtype classification and pathway-context analyses shows that Natural-HNN outperforms baselines and better preserves functional semantics of pathways, suggesting robust discovery of hidden hyperedge semantics. The approach offers a principled, generalizable framework for disentangling group interactions with potential impact on biology and other domains with complex hypergraph structures.

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).

Figures (22)

• Figure 1: The factor representation consistency criterion assigns a high relevance score when the factor representation learned by two different routes is similar (i.e., consistent factor representation).
• Figure 2: Compositional structure in hypergraph representation learning.
• Figure 3: Naturality condition in disentangled representation learning to capture group interaction mechanism related factors. $X$ denotes a set of node representations and $H$ denotes hyperedge representation. $V$ and $E$ denote nodes and hyperedge in $\mathbf{PISet}$. '$c$' and '$d$' denotes factors.
• Figure 4: Architecture of proof-of-concept model Natural-HNN. It calculates the relevance of factor $k$ ($\alpha_{i}^{k}$) and performs weighted message passing for each factor.
• Figure 5: Captured interaction context. Captured patterns are shown in red boxes and not captured patterns are shown with orange boxes. Weakly captured cases are marked as dotted red block.