  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 create representations of simplices, offering interpretability
and geometric consistency without message passing. This approach also enables
us to apply differential geometry tools and achieve universal approximation.
Our method is efficient, versatile, and applicable to various input complexes,
including graphs, simplicial complexes, and cell complexes. It outperforms
existing message passing neural networks in harnessing information from
geometrical graphs with node features serving as coordinates.
