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.

本文提出了一种基于几何传递的方法，以端到端的方式将一个单纯复形嵌入到一个通用嵌入空间中，从而实现单纯复形级别的表示学习，并在公开可用的网格数据集上进行了验证。这是学习单纯复形级别表示的第一种方法。