  Graph Neural Networks have a limitation of solely processing features on
graph nodes, neglecting data on high-dimensional structures such as edges and
triangles. Simplicial Convolutional Neural Networks (SCNN) represent
higher-order structures using simplicial complexes to break this limitation
albeit still lacking time efficiency. In this paper, we propose a novel neural
network architecture on simplicial complexes named Binarized Simplicial
Convolutional Neural Networks (Bi-SCNN) based on the combination of simplicial
convolution with a binary-sign forward propagation strategy. The usage of the
Hodge Laplacian on a binary-sign forward propagation enables Bi-SCNN to
efficiently and effectively represent simplicial features that have
higher-order structures than traditional graph node representations. Compared
to the previous Simplicial Convolutional Neural Networks, the reduced model
complexity of Bi-SCNN shortens the execution time without sacrificing the
prediction performance and is less prone to the over-smoothing effect.
Experimenting with real-world citation and ocean-drifter data confirmed that
our proposed Bi-SCNN is efficient and accurate.
