TopoSRL: Topology preserving self-supervised Simplicial Representation Learning

In this paper, we introduce $\texttt{TopoSRL}$, a novel self-supervised learning (SSL) method for simplicial complexes to effectively capture higher-order interactions and preserve topology in the learned representations. $\texttt{TopoSRL}$ addresses the limitations of existing graph-based SSL methods that typically concentrate on pairwise relationships, neglecting long-range dependencies crucial to capture topological information. We propose a new simplicial augmentation technique that generates two views of the simplicial complex that enriches the representations while being efficient. Next, we propose a new simplicial contrastive loss function that contrasts the generated simplices to preserve local and global information present in the simplicial complexes. Extensive experimental results demonstrate the superior performance of $\texttt{TopoSRL}$ compared to state-of-the-art graph SSL techniques and supervised simplicial neural models across various datasets corroborating the efficacy of $\texttt{TopoSRL}$ in processing simplicial complex data in a self-supervised setting.