重访网络去噪：一种受里奇流启发的图扩散方法
Network Denoising Revisited: A Ricci-Flow-Inspired Graph Diffusion Method
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中文总结 AI 辅助
该研究针对现有网络去噪方法忽略图非欧几里得几何的问题，提出受里奇流启发的曲率引导图扩散方法Ricci-Diffusion，经实验验证其可提升结构恢复与下游性能。
中文摘要 AI 辅助
网络为实体间的关系提供了基础表示，但现实世界的网络常因测量误差和固有随机性受到噪声干扰，阻碍了对有意义结构的发现。大多数去噪方法依赖于基于相似度的扩散，却忽略了图的非欧几里得几何特性，而局部变化会引发异构信息传输，这促使我们从几何角度重新审视网络去噪问题。本研究提出了Ricci-Diffusion，一种受里奇流（Ricci flow）启发的曲率引导图扩散方法。具体而言，Ricci-Diffusion展现出类似里奇流的演化过程，其中边级相对曲率会调节扩散核中的局部传输，并引导边权重更新以形成更规则的图几何结构。我们进一步提供理论分析表明，曲率能够区分普通相似度驱动的扩散核无法分离的图结构，且曲率会在单步扩散更新中引入一阶校正。所得扩散过程明确刻画了局部几何间的传输异构性，并在理论上收敛至稳定的去噪网络。在现实世界和合成图上的结果显示，曲率引导的更新与曲率同质化提升了结构恢复效果及下游性能。
英文摘要
Networks provide a fundamental representation of relationships among entities. However, real-world networks are often corrupted by noise caused by measurement errors and inherent stochasticity, hindering the discovery of meaningful structure. Most denoising methods rely on similarity-driven diffusion and ignore the non-Euclidean geometry of graphs, where local variations induce heterogeneous information transport. This motivates a geometric revisit of network denoising. In this work, we propose Ricci-Diffusion, a curvature-guided graph diffusion method inspired by Ricci flow. Specifically, Ricci-Diffusion exhibits a Ricci-flow-like evolution, in which relative edge-level curvature modulates local transport in the diffusion kernel and guides edge-weight updates toward a more regular graph geometry. We further provide a theoretical analysis showing that curvature can distinguish graph structures that common similarity-driven diffusion kernels fail to separate, and that curvature induces first-order corrections in one-step diffusion updates. The resulting diffusion process explicitly characterizes transport heterogeneity across local geometries and admits theoretical convergence to a stable denoised network. Results on real-world and synthetic graphs show that curvature-guided updates and curvature homogenization improve structure recovery and downstream performance.
发表机构
- School of Mathematics, Sun Yat-sen University（中山大学数学学院）
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