Disentangling Hyperedges through the Lens of Category Theory

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 categorytheoretical 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). Our implementation is available at https://github.com/Yoonho-Lee-AI4Science/Natural-HNN. (a) Natural Transformation in HNN (b) Natural Transformation in HNN, factor perspective DLRep PISet Entangled Disentangled en dis en en dis Entangled Disentangled fc× f d <fc, f d > <fc, f d > fc× f d f f fc× f d fc × f d dis dis 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 PISet. 'c' and 'd' denotes factors. entangled and disentangled representations. Figure 3 (b) is equivalent to Figure 3 (a), but only the components related to the factor 'c' are shown (explanations are in Appendix A .6). Note that α X,c " α X o 9 p c where p c : X dis Ñ X dis c . If factor 'c' is relevant to the morphism between node set V and hyperedge E, the naturality condition must hold for the perspective of factor 'c'. Thus, factor 'c' representation of a hyperedge (i.e., H dis c ) must be the same (or similar) regardless of applying f en o 9 α H,c (i.e., message passing on entangled representation first, and then disentangling factors) or α X,c o 9 f dis c (i.e., disentangling factors first, and then message passing on disentangled representation). In other words, the factor representation must be consistent regardless of the sequence of operations if that factor is relevant to the interaction context of a hyperedge. We use this property as a guidance for disentanglement, since it must hold for any kind of hypergraph message passing neural networks, and must work regardless of data characteristics.