aiqbench analysis
This paper introduces Ricci-Diffusion, a novel graph denoising technique that leverages geometric curvature principles inspired by Ricci flow to better handle non-Euclidean structures in noisy networks. Unlike standard similarity-driven methods, this approach modulates information transport based on local edge-level curvature, offering theoretical convergence guarantees and improved structure recovery for downstream tasks. The work represents significant progress in applying advanced differential geometry concepts to enhance the robustness of machine learning models operating on graph-structured data.
Network Denoising Revisited: A Ricci-Flow-Inspired Graph Diffusion Method
arXiv:2608.16923v1 Announce Type: cross Abstract: 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.
Abstract: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.
Social and Information Networks (cs.SI); Machine Learning (cs.LG)
arXiv:2608.16923 [cs.SI]
(or arXiv:2608.16923v1 [cs.SI] for this version)
https://doi.org/10.48550/arXiv.2608.16923 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 269 words
Related coverage
Ricci-Filtration: Boosting Retrieval-Augmented Generation Reranker to Query-Answer Tasks by Discrete Ricci Flow
arXiv · Jun 16, 2026
Efficient Graph Generation via Direct Prediction and Flow Matching
arXiv · Oct 6, 2026
J++ Lens: Jacobian Filtering Enables More Faithful Workspace Lenses
LessWrong · Oct 8, 2026
Rebuilding AUTOMATIC1111 with Gradio Workflow
Hugging Face · Sep 10, 2026