TopoSRL: Topology preserving self-supervised Simplicial Representation Learning

In this paper, we introduce TopoSRL , a novel self-supervised learning (SSL) method for simplicial complexes to effectively capture higher-order interactions and preserve topology in the learned representations. TopoSRL addresses the limitations of existing graph-based SSL methods that typically concentrate on pairwise relationships, neglecting long-range dependencies crucial to capturing 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 TopoSRL compared to state-of-the-art graph SSL techniques and supervised simplicial neural models across various datasets corroborating the efficacy of TopoSRL in processing simplicial complex data in a self-supervised setting.