Binarized Simplicial Convolutional Neural Networks

TL;DR

The proposed Binarized Simplicial Convolutional Neural Networks achieves reduced model complexity compared to previous SSCN variants through binarization and normalization, also serving as intrinsic nonlinearities of Bi-SCNN to shorten the execution time without compromising prediction performance and makes Bi-SCNN less prone to over-smoothing.

Abstract

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.

Figures (9)

• Figure 1: A graph with $N_0 = 24$ nodes, $N_1 = 38$ edges, and $N_2 = 2$ triangles having signals on the edges.
• Figure 2: Decomposing the edges of the graph with $N_1 = 38$ edges in Figure \ref{['fig_edge_signal']} using the SFT in \ref{['eq_SFT']} and $k=1$.
• Figure 3: An illustration of simplicial filtering on an edge signal using \ref{['conv1']}.
• Figure 4: Decomposing a SCNN layer with $J=2$ in equation \ref{['eq_break']} into Simplicial Convolutions with $J = 1$.
• Figure 5: An illustration of one Bi-SCNN layer.