# Dynamic Graph Structure Learning via Resistance Curvature Flow

arXiv: https://arxiv.org/abs/2601.08149 · HTML: https://mlsanity.com/paper/2601.08149/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Graph-Revised Convolutional Network](https://mlsanity.com/paper/1911.07123/) (2019)
- [Attention-driven Graph Clustering Network](https://mlsanity.com/paper/2108.05499/) (2021)
- [In Defense of the Triplet Loss Again: Learning Robust Person Re-Identification with Fast Approximated Triplet Loss and Label Distillation](https://mlsanity.com/paper/1912.07863/) (2019)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Deep Metric Learning with Spherical Embedding](https://mlsanity.com/paper/2011.02785/) (2020)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Network Alignment by Discrete Ollivier-Ricci Flow](https://mlsanity.com/paper/1809.00320/) (2018)
- [Curvature-aware Manifold Learning](https://mlsanity.com/paper/1706.07167/) (2017)
- [An efficient alternative to Ollivier-Ricci curvature based on the Jaccard metric](https://mlsanity.com/paper/1710.01724/) (2017)
- [Efficient Curvature-aware Graph Network](https://mlsanity.com/paper/2511.01443/) (2025)

## Built on by (most cited first, 1 of 1)

- [Scalable Subgraph Sampling via Resistance Curvature](https://mlsanity.com/paper/2609.27209/) (2026)

## Abstract (arXiv)

Geometric Representation Learning (GRL) aims to approximate the non-Euclidean topology of high-dimensional data through discrete graph structures, grounded in the manifold hypothesis. However, traditional static graph construction methods based on Euclidean distance often fail to capture the intrinsic curvature characteristics of the data manifold. Although Ollivier-Ricci Curvature Flow (OCF) has proven to be a powerful tool for dynamic topological optimization, its core reliance on Optimal Transport (Wasserstein distance) leads to prohibitive computational complexity, severely limiting its application in large-scale datasets and deep learning frameworks. To break this bottleneck, this paper proposes a novel geometric evolution framework: Resistance Curvature Flow (RCF). Leveraging the concept of effective resistance from circuit physics, RCF transforms expensive curvature optimization into efficient matrix operations. This approach achieves over 100x computational acceleration while maintaining geometric optimization capabilities comparable to OCF. We provide an in-depth exploration of the theoretical foundations and dynamical principles of RCF, elucidating how it guides the redistribution of edge weights via curvature gradients to eliminate topological noise and strengthen local cluster structures. Furthermore, we provide a mechanistic explanation of RCF's role in manifold enhancement and noise suppression, as well as its compatibility with deep learning models. We design a graph optimization algorithm, DGSL-RCF, based on this framework. Experimental results across deep metric learning, manifold learning, and graph structure learning demonstrate that DGSL-RCF significantly improves representation quality and downstream task performance.