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.

翻译：图神经网络存在仅处理图节点特征而忽略边、三角形等高维结构数据的局限性。单纯复形卷积神经网络（SCNN）通过使用单纯复形表征高阶结构突破了这一局限，但该模型仍缺乏时间效率。本文基于单纯卷积与二值符号前向传播策略的结合，提出了一种名为二值化单纯复形卷积神经网络（Bi-SCNN）的新型单纯复形架构。通过在二值符号前向传播中应用霍奇拉普拉斯算子，Bi-SCNN能够高效且有效地表征具有比传统图节点表示更高阶结构的单纯特征。相较于现有单纯复形卷积神经网络，Bi-SCNN的模型复杂度降低缩短了执行时间，且更不易产生过平滑效应，同时保持预测性能不降。基于真实引用数据集和海洋漂流数据集的实验证实，本文提出的Bi-SCNN兼具高效性与准确性。