[论文解读] Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks

Mathilde Papillon, Sophia Sanborn+2 more|arXiv (Cornell University)|Apr 20, 2023

Gene Regulatory Network Analysis被引用 15

一句话总结

一份全面综述，介绍拓扑深度学习并统一跨超图、单纯复形和细胞复形，以及组合复形等领域的广泛消息传递拓扑神经网络（TNNs）。它提供统一的记号、图形张量图以及对挑战与机遇的讨论。

ABSTRACT

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature for relational systems has also led to a lack of unification in notation and language across message-passing Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying message-passing TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL for relational systems, and compare the recently published message-passing TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.

研究动机与目标

• 为关系系统提供对拓扑深度学习（TDL）的易于理解的简介。
• 使用统一的数学和图形记号统一并比较已发表的消息传递拓扑神经网络（TNNs）。
• 分析 TNN 的体系结构、应用及实际考量。
• 确定当前挑战与未来在 TDL 发展中的机会。

提出的方法

• 给出离散域（图、超图、单纯复形、细胞复形、组合复形）及其秩和单元的数据。
• 定义边界关系和入射矩阵以编码邻域结构。
• 将消息传递分解为四个步骤（消息、邻域内聚合、邻域之间聚合、更新）并描述特征在各层中的更新方式。
• 使用张量图来直观表示消息传递方案并比较体系结构。
• 按域和消息传递类型对 TNN 架构进行分类和评审，并在其记号中给出统一的方程。

Figure 1: Topological Neural Network : Data associated with a complex system are features defined on a data domain , which is preprocessed into a computational domain that encodes interactions between the system’s components with neighborhoods . The TNN’s layers use message passing to successively u

实验结果

研究问题

• RQ1 在不同拓扑域中，拓扑神经网络的消息传递常见架构有哪些？
• RQ2 统一记号如何帮助比较 TNN 在超图、单纯复形、细胞复形和组合复形中的应用？
• RQ3 针对各种关系数据任务，TNN 的主要优势与局限性是什么？
• RQ4 仍存在哪些挑战以及拓扑深度学习未来发展的机会有哪些？

主要发现

• 拓扑深度学习超越图的范畴，扩展到超图、单纯复形和细胞复形等域，从而对高阶关系进行更丰富的建模。
• 统一的四步消息传递框架（消息、邻域内聚合、邻域之间聚合、更新）有助于在不同域之间对 TNN 架构进行系统比较。
• 张量图提供对消息在拓扑域和层中传播的直观图形表示。
• TNN 架构因域而异，并且在使用标准、注意力或通用消息传递方面也有所不同，每个模型使用多种邻域结构。
• 综述强调在学习过程中保持拓扑结构通常能带来更强的表达力和性能，尽管存在领域特定的限制和实际考量。

Figure 2: Domains: Nodes in blue, (hyper)edges in pink, and faces in dark red. Figure adapted from [ 11 ] .