拓扑深度学习与状态空间模型:简约复合物的曼巴方法

Marco Montagna, Simone Scardapane, Lev Telyatnikov
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引用次数: 0

摘要

基于消息传递(MP)机制的图神经网络是处理图结构数据的主要方法。然而,它们本身仅限于建模成对的相互作用,因此难以明确捕捉具有 $n$ 体关系的系统的复杂性。为了解决这个问题,拓扑深度学习应运而生,成为利用各种拓扑域(如单纯形和细胞复合物)研究和建模高阶相互作用的一个前景广阔的领域。虽然这些新领域提供了强大的表征,但也带来了新的挑战,例如通过高阶 MP 有效地建模高阶结构之间的相互作用。与此同时,结构化状态空间序列模型已被证明能有效地进行序列建模,最近又通过将节点的邻域编码为序列,从而避免了 MP 机制,使其适用于图数据。在这项工作中,我们提出了一种新颖的架构,旨在利用 Mamba 状态空间模型作为骨干,对简单复合物进行操作。我们的方法根据相邻单元为节点生成序列,从而实现了所有高阶结构之间的直接通信,而不管它们的阶数如何。我们对我们的模型进行了广泛验证,证明与针对简单复合物开发的最先进模型相比,我们的模型具有极强的性能竞争力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Topological Deep Learning with State-Space Models: A Mamba Approach for Simplicial Complexes
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.
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