arXiv:2409.12033cs.LGcs.AI2024-09被引 2

用Mamba模型处理单纯复形,实现高阶结构间直接通信。

Topological Deep Learning with State-Space Models: A Mamba Approach for Simplicial Complexes

  • 以邻域细胞序列表示节点,用Mamba模型替代传统消息传递
  • 在多个单纯复形数据集上达到顶尖性能,优于现有方法
  • 适合研究高阶关系的图神经网络开发者使用

基于消息传递机制的图神经网络是处理图结构数据的主流方法,但其仅能建模成对交互,难以显式捕捉具有n体关系系统的复杂性。为此,拓扑深度学习应运而生,通过单纯复形、细胞复形等拓扑域研究和建模高阶交互。尽管这些新域提供强大表示,却带来了如何有效建模高阶结构间交互的新挑战。结构化状态空间序列模型在序列建模中表现优异,并被近期用于图数据,通过将节点邻域编码为序列来规避消息传递机制。本文提出一种新架构,专为单纯复形设计,以Mamba状态空间模型为核心。该方法基于邻近单元生成节点序列,实现不同秩的高阶结构间的直接通信。我们在多个基准上进行充分验证,结果表明该模型性能与当前最优单纯复形模型相当。

原文摘要 · Abstract (English)

Graph Neural Networks based on the message-passing (MP) mechanism are a dominant approach for handling graph-structured data. However, they are inherently limited to modeling only pairwise interactions, making it difficult to explicitly capture the complexity of systems with $n$-body relations. To address this, topological deep learning has emerged as a promising field for studying and modeling higher-order interactions using various topological domains, such as simplicial and cellular complexes. While these new domains provide powerful representations, they introduce new challenges, such as effectively modeling the interactions among higher-order structures through higher-order MP. Meanwhile, structured state-space sequence models have proven to be effective for sequence modeling and have recently been adapted for graph data by encoding the neighborhood of a node as a sequence, thereby avoiding the MP mechanism. In this work, we propose a novel architecture designed to operate with simplicial complexes, utilizing the Mamba state-space model as its backbone. Our approach generates sequences for the nodes based on the neighboring cells, enabling direct communication between all higher-order structures, regardless of their rank. We extensively validate our model, demonstrating that it achieves competitive performance compared to state-of-the-art models developed for simplicial complexes.

拓扑学习Mamba单纯复形高阶关系

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