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.
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