Variational Self-Supervised Learning on Simplicial Complexes

Graphs effectively model pairwise interactions but are in-adequate for capturing the complex multi-entity interactions common in fields like biochemistry, social networks, and trade dynamics. To address this limitation, simplicial complexes extend graphs by incorporating higher-order interactions, enabling more comprehensive system modeling. This paper focuses on the challenge of limited data learning in simplicial complexes, where the scarcity of labeled data hampers the performance of Simplicial Neural Networks (SNNs). We propose VarRepSC, a variational self-supervised learning framework that generates task-agnostic variational embeddings for simplicial complexes while preserving essential topological features. By employing a variational encoder trained with a self-supervised loss-comprising evidence lower bound (ELBO), Hodge decomposition, and view divergence-VarRepSC effectively captures higher-order interactions and demonstrates robustness to minor perturbations. Experimental results on node, simplex, and simplicial complex classification tasks reveal significant performance gains over baseline models, particularly in limited data settings. Additionally, Var-RepSC incorporates uncertainty modeling in embeddings, enabling active learning strategies to optimize sample labeling. This work advances self-supervised learning for simplicial complexes by offering a probabilistic framework for complex data representation.