重新定义谱图神经网络，打破与消息传递模型的对立僵局。
Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs
- 基于特征基对称性给出谱图神经网络的精确定义
- 证明谱域与空间域模型在表达能力上基本等价
- 主张融合两种视角，构建统一理论框架
图神经网络（GNN）通常分为消息传递神经网络（MPNN）和谱图神经网络（spectral GNN），分别对应机器学习与信号处理两大研究传统。尽管MPNN有明确定义，但目前尚无广泛接受的谱图神经网络判定标准。多数现有工作将谱图神经网络限制在基于线性谱滤波的分层架构中。在此限制下，我们证明谱域与空间域的图神经网络具有大致相当的表达能力。为推动领域发展，我们提出一种基于特征基对称性的谱图神经网络精确定义，与通过邻域置换对称性定义的MPNN形成对比。我们进一步指出，两种视角各有优势：MPNN适合用逻辑与图同构工具分析离散结构与表达力；谱视角则提供理解平滑、瓶颈、稳定性与社区结构的严谨工具。总体而言，我们主张通过厘清两种视角的异同，迈向统一的理论框架，以加速图学习的进步。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing. While MPNNs have a precise definition, there is no widely accepted criterion for what makes a mapping a spectral GNN. Most existing work restricts spectral GNNs to layered architectures based on linear spectral filters. Under this restriction, we show that spectral and spatial GNNs have largely equivalent expressive power. To promote progress in the field, we propose a precise definition of spectral GNNs based on eigenbasis symmetries, in contrast to the definition of MPNNs via neighborhood permutation symmetries. We further argue that the two perspectives offer complementary strengths. MPNNs provide a natural language for discrete structure and expressivity analysis through tools from logic and graph isomorphism, while the spectral perspective offers principled tools for understanding smoothing, bottlenecks, stability, and community structure. Overall, we argue that progress in graph learning will be accelerated by clarifying the similarities and differences between these perspectives and by moving toward a unified theoretical framework.
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