基于连续时间量子游走的图神经网络
Continuous-Time Quantum Walks based Graph Neural Network
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中文总结 AI 辅助
针对图神经网络在异质性图性能差及过平滑问题，提出基于连续时间量子游走的CTQW-GNN，结合三类互补聚合模块，通过理论分析为游走时间选择提供原则性规则。
中文摘要 AI 辅助
图神经网络（GNN）广泛应用于图结构数据，但多数存在两个关键缺陷：其一，在同质性假设下消息传递表现为低通滤波器，导致在异质性图上性能较差；其二，堆叠层会使节点特征趋近于常数，引发过平滑问题。现有方法通常分别解决这些问题，而少数联合方案大多依赖经验启发式方法，且许多过平滑补救措施会牺牲模型表达能力。我们提出CTQW-GNN，一种基于连续时间量子游走（CTQW）的图神经网络，以理论依据解决上述两个问题。其设计利用了CTQW传播子$e^{-iHt}$的两个特性：第一，它是幺正的，且特征值位于单位圆上，因此无频率分量被衰减，抵消了低通偏差；第二，幺正性保留特征范数，防止狄利克雷能量随深度指数衰减，从而缓解过平滑。CTQW-GNN结合了三个互补的聚合模块：基于CTQW的聚合通过幺正传播子演化节点特征，为异质性图保留中高频信号，同时防止狄利克雷能量崩溃；CTQW注意力聚合从CTQW振幅构建多跳邻居图，并在其上应用注意力，使模型能访问单跳聚合遗漏的远距离同质性节点；LF聚合使用标准低通GAT分支，以在同质性图上保持强性能，纯CTQW聚合在该场景下可能表现不佳。我们还提供了谱间隙分析以解释能量保留，并给出类似Lieb-Robinson的边界，为选择游走时间$t$提供了原则性规则。
英文摘要
Graph Neural Networks (GNNs) are widely used on graph-structured data, but most suffer from two key weaknesses. First, message passing behaves as a low-pass filter under the homophily assumption, leading to poor performance on heterophilic graphs. Second, stacking layers drives node features toward constants, causing over-smoothing. Existing methods usually address these issues separately, while the few joint solutions rely largely on empirical heuristics, and many over-smoothing remedies sacrifice model expressiveness. We propose \textbf{CTQW-GNN}, a GNN based on Continuous-Time Quantum Walks (CTQW), to address both issues with theoretical justification. Its design exploits two properties of the CTQW propagator $e^{-\mathrm{i}Ht}$. First, it is unitary and has eigenvalues on the unit circle, so no frequency component is damped, counteracting the low-pass bias. Second, unitarity preserves feature norms and prevents the Dirichlet energy from decaying exponentially with depth, thereby mitigating over-smoothing. CTQW-GNN combines three complementary aggregation modules. \textit{CTQW-based Aggregation} evolves node features through the unitary propagator, preserving mid- and high-frequency signals for heterophilic graphs while preventing Dirichlet-energy collapse. \textit{CTQW-Attention Aggregation} constructs a multi-hop neighbor graph from CTQW amplitudes and applies attention over it, enabling access to distant homophilic nodes missed by single-hop aggregation. \textit{LF Aggregation} uses a standard low-pass GAT branch to retain strong performance on homophilic graphs, where pure CTQW aggregation can be suboptimal. We further provide a spectral-gap analysis explaining energy preservation and a Lieb--Robinson-type bound that gives a principled rule for selecting the walk time $t$.
发表机构
- Renmin University of China（中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。
