Simplicial Complex Representation Learning

Abstract: Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d simplicial complexes, has witnessed a great attention in recent years. However, there has not been enough effort to extend representation learning to higher dimensional simplicial objects due to the additional complexity these objects hold, especially when it comes to entire-simplicial complex representation learning. In this work, we propose a method for simplicial complex-level representation learning that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved. Our method uses our novel geometric message passing schemes to learn an entire simplicial complex representation in an end-to-end fashion. We demonstrate the proposed model on publicly available mesh dataset. To the best of our knowledge, this work presents the first method for learning simplicial complex-level representation.