提出高阶方向性模型，让神经网络更好处理有向复杂结构数据
Higher-Order Topological Directionality and Directed Simplicial Neural Networks
- 基于有向单纯复形设计消息传递网络，捕捉高阶节点间非对称关系
- 理论上比有向图模型更擅长区分同构图，实验验证在有向数据上表现更优
- 适合处理社交网络、生物通路等具有方向性关系的复杂系统
拓扑深度学习（TDL）是一种处理定义在高阶组合拓扑空间（如单纯复形或细胞复形）上的信号的新范式。尽管许多复杂系统具有非对称关系结构，但现有TDL模型通常强制对称化这些关系。本文首次引入高阶方向性概念，并基于此构建有向单纯复形神经网络（Dir-SNN）。Dir-SNN是运行于有向单纯复形上的消息传递网络，可利用单纯形间的有向且可能非对称的交互。据我们所知，这是首个使用高阶方向性概念的TDL模型。理论与实证证明，当面对同构有向图时，Dir-SNN比其有向图对应模型更具表达能力。合成源定位任务实验表明，在底层结构为有向时，Dir-SNN优于无向SNN；当结构为无向时，性能相当。
原文摘要 · Abstract (English)
Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric relational structure, most TDL models forcibly symmetrize these relationships. In this paper, we first introduce a novel notion of higher-order directionality and we then design Directed Simplicial Neural Networks (Dir-SNNs) based on it. Dir-SNNs are message-passing networks operating on directed simplicial complexes able to leverage directed and possibly asymmetric interactions among the simplices. To our knowledge, this is the first TDL model using a notion of higher-order directionality. We theoretically and empirically prove that Dir-SNNs are more expressive than their directed graph counterpart in distinguishing isomorphic directed graphs. Experiments on a synthetic source localization task demonstrate that Dir-SNNs outperform undirected SNNs when the underlying complex is directed, and perform comparably when the underlying complex is undirected.
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