用复数权重扩散提升图神经网络表达能力，解决过平滑和异质图难题
Complex-Weighted Convolutional Networks: Provable Expressiveness via Complex Diffusion
- 为边赋予复数权重，将随机游走拓展到复数域
- 理论上证明可解任意节点分类任务，稳态下实现高表达性
- 模型简单易用，无需额外超参数，适合各类图数据任务
图神经网络在众多应用中表现卓越，但受限于过平滑问题及在异质图上的性能不佳。为此，我们提出一种新框架，为图结构赋予复数权重，使每条边关联一个复数，驱动扩散过程将随机游走扩展至复数域。理论证明：在适当选择复数权重下，任意节点分类任务均可在复随机游走的稳态中求解。基于此，我们提出复数加权卷积网络（CWCN），从数据中直接学习合适的复数权重结构，同时引入可学习矩阵与非线性激活函数增强扩散能力。CWCN实现简单，除标准GNN超参数外无需额外调参，在基准数据集上表现竞争力。结果表明，复数加权扩散提供了一种兼具理论严谨性与实践有效性的通用机制，显著提升GNN表达能力。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) have achieved remarkable success across diverse applications, yet they remain limited by oversmoothing and poor performance on heterophilic graphs. To address these challenges, we introduce a novel framework that equips graphs with a complex-weighted structure, assigning each edge a complex number to drive a diffusion process that extends random walks into the complex domain. We prove that this diffusion is highly expressive: with appropriately chosen complex weights, any node-classification task can be solved in the steady state of a complex random walk. Building on this insight, we propose the Complex-Weighted Convolutional Network (CWCN), which learns suitable complex-weighted structures directly from data while enriching diffusion with learnable matrices and nonlinear activations. CWCN is simple to implement, requires no additional hyperparameters beyond those of standard GNNs, and achieves competitive performance on benchmark datasets. Our results demonstrate that complex-weighted diffusion provides a principled and general mechanism for enhancing GNN expressiveness, opening new avenues for models that are both theoretically grounded and practically effective.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。