用可学习的曲率自适应调整图神经网络深度，提升信息传播效率。
Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature
- 基于Bakry-Émery曲率设计可学习的图结构感知机制
- 高曲率节点少层传播，低曲率节点深传，理论支持有效性能提升
- 适用于复杂图任务，尤其适合需要精准信息流控制的场景
图神经网络在图任务中表现出强大的表征能力。近期工作利用几何特性如曲率来建模复杂的连接模式与信息流动，以增强表征能力。然而，多数方法仅关注离散图拓扑，忽视了扩散动态和任务相关的依赖关系。为此，我们引入能同时捕捉结构与任务驱动特性的Bakry-Émery曲率，提出一种高效的可学习近似策略，使曲率计算在大规模图上可扩展。此外，我们设计了一种自适应深度机制，根据每个顶点的曲率动态调整消息传递层数，确保高效传播。理论分析表明，曲率与特征区分度相关：高曲率节点需较少层数，低曲率节点则受益于更深传播。在基准数据集上的大量实验验证了该方法的有效性，在多种图学习任务中均取得一致性能提升。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) have demonstrated strong representation learning capabilities for graph-based tasks. Recent advances on GNNs leverage geometric properties, such as curvature, to enhance its representation capabilities by modeling complex connectivity patterns and information flow within graphs. However, most existing approaches focus solely on discrete graph topology, overlooking diffusion dynamics and task-specific dependencies essential for effective learning. To address this, we propose integrating Bakry-Émery curvature, which captures both structural and task-driven aspects of information propagation. We develop an efficient, learnable approximation strategy, making curvature computation scalable for large graphs. Furthermore, we introduce an adaptive depth mechanism that dynamically adjusts message-passing layers per vertex based on its curvature, ensuring efficient propagation. Our theoretical analysis establishes a link between curvature and feature distinctiveness, showing that high-curvature vertices require fewer layers, while low-curvature ones benefit from deeper propagation. Extensive experiments on benchmark datasets validate the effectiveness of our approach, showing consistent performance improvements across diverse graph learning tasks.
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