Simplicial Representation Learning with Neural $k$-Forms

arXiv:2312.08515v2 Announce Type: replace
Abstract: Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as the need for graph rewiring, ambiguity in interpreting data, and over-smoothing. In this paper, we take a different approach, focusing on leveraging geometric information from simplicial complexes embedded in $\mathbb{R}^n$ using node coordinates. We use differential k-forms in \mathbb{R}^n to …

abstract arxiv cs.lg data deep learning domains forms geometry graph graphs information limitations math.at paper representation representation learning topology type