Binarized Simplicial Convolutional Neural Networks.

Graph Neural Networks have the limitation of processing features solely on graph nodes, neglecting data on high-dimensional structures such as edges and triangles. Simplicial Convolutional Neural Networks (SCNN) represent high-order structures using simplicial complexes to break this limitation but still lack time efficiency. In this paper, a novel neural network architecture named Binarized Simplicial Convolutional Neural Networks (Bi-SCNN) is proposed based on the combination of simplicial convolution with a weighted binary-sign forward propagation strategy. The utilization of the Hodge Laplacian on a weighted binary-sign forward propagation enables Bi-SCNN to efficiently and effectively represent simplicial features with higher-order structures, surpassing the capabilities of traditional graph node representations. The Bi-SCNN achieves reduced model complexity compared to previous SSCN variants through binarization and normalization, also serving as intrinsic nonlinearities of Bi-SCNN; this enables Bi-SCNN to shorten the execution time without compromising prediction performance and makes Bi-SCNN less prone to over-smoothing. Experimenting with real-world citation and ocean-drifter data confirmed that our proposed Bi-SCNN is efficient and accurate.