# MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothing

arXiv: https://arxiv.org/abs/2506.15571 · HTML: https://mlsanity.com/paper/2506.15571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Builds on (most cited first, 8 of 8)

- [SJTU-TMQA: A quality assessment database for static mesh with texture map](https://mlsanity.com/paper/2309.15675/) (2023)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks](https://mlsanity.com/paper/2504.04052/) (2025)
- [Learning Discretized Neural Networks under Ricci Flow](https://mlsanity.com/paper/2302.03390/) (2023)
- [Deep Learning as Ricci Flow](https://mlsanity.com/paper/2404.14265/) (2024)
- [Ricci flow-based brain surface covariance descriptors for diagnosing Alzheimer's disease](https://mlsanity.com/paper/2403.06645/) (2024)
- [Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces](https://mlsanity.com/paper/2311.01788/) (2023)
- [Geometry matters: insights from Ollivier Ricci Curvature and Ricci Flow into representational alignment through Ollivier-Ricci Curvature and Ricci Flow](https://mlsanity.com/paper/2501.00919/) (2025)

## Abstract (arXiv)

Real-time mesh smoothing at scale remains a formidable challenge: classical Ricci-flow solvers demand costly global updates, while greedy heuristics suffer from slow convergence or brittle tuning. We present MicroRicci, the first truly self-tuning, local Ricci-flow solver that borrows ideas from coding theory and packs them into just 1K + 200 parameters. Its primary core is a greedy syndrome-decoding step that pinpoints and corrects the largest curvature error in O(E) time, augmented by two tiny neural modules that adaptively choose vertices and step sizes on the fly. On a diverse set of 110 SJTU-TMQA meshes, MicroRicci slashes iteration counts from 950+=140 to 400+=80 (2.4x speedup), tightens curvature spread from 0.19 to 0.185, and achieves a remarkable UV-distortion-to-MOS correlation of r = -0.93. It adds only 0.25 ms per iteration (0.80 to 1.05 ms), yielding an end-to-end 1.8x runtime acceleration over state-of-the-art methods. MicroRicci's combination of linear-time updates, automatic hyperparameter adaptation, and high-quality geometric and perceptual results makes it well suited for real-time, resource-limited applications in graphics, simulation, and related fields.