Ollivier-Ricci Curvature

Latest papers

9 papers1 paper in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Distilling Graph Geometry: Knowledge Gap from GNNs to MLPs
Oct 7, 2026Zhewei Chen, Hao Zhu, Jiaojiao Jiang +1Ollivier-Ricci Curvature Knowledge Distillation
Australian National University · Data61, CSIRO · University of New South Wales
A Unified Geometric Framework for Developmental Analysis of Spatial Transcriptomic Data
Aug 15, 2026Mary Chriselda Antony Oliver, Kaitlyn Hohmeier, Tuyen Tran +3Ollivier-Ricci Curvature Spatial Transcriptomics
Department of Applied Mathematics and Theoretical Physics, University of Cambridge · Department of Mathematics, University of North Carolina at Chapel Hill · Department of Mathematics and Statistics, Loyola University Chicago +2
Discrete Ricci Curvature on Protein Contact Graphs for Lightweight Fold Classification
Jul 17, 2026Jianru ShenOllivier-Ricci Curvature
University of Montana Missoula, MT, USA
System-Prompt Conditioning and Hidden-State Geometry in Four Open-Weight Models: Corrections and What Survives
Jul 10, 2026Jorge Castillo Sepúlveda, Marco Torres Yévenes, Juan Carlos LanasTransformer Interpretability Ollivier-Ricci Curvature
Axis Dynamics SpA, Santiago, Chile
GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations
May 12, 2026Lake Yang, Junwei Su, Jingfeng Zeng +5Ollivier-Ricci Curvature
Imperial College London · University of Science and Technology of China · MaxQuant +2
A Residual-Shell-Based Lower Bound for Ollivier-Ricci Curvature
Apr 14, 2026Xiang Gu, Huichun Zhang, Jian SunOllivier-Ricci Curvature Approximation Algorithms
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China · School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, Guangdong, China
Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks
Apr 6, 2026Eleanor P WieslerOllivier-Ricci Curvature Riemannian Geometry
The Department of Mathematics Harvard University Cambridge, Massachusetts
Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning
Mar 20, 2026Haifang Cao, Yu Wang, Timing Li +2Ollivier-Ricci Curvature Graph Representation Learning
College of Intelligence and Computing, Tianjin University, Tianjin, China
Auditing Cascading Risks in Multi-Agent Systems via Semantic-Geometric Co-evolution
Mar 4, 2026Zixun Luo, Yuhang Fan, Hengyu Lin +2Ollivier-Ricci Curvature Multi-Agent LLM Systems
Huazhong University of Science and Technology · Lingnan University · Tsinghua University +1

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Distilling Graph Geometry: Knowledge Gap from GNNs to MLPs

Zhewei Chen, Hao Zhu, Jiaojiao Jiang, Ahad N. Zehmakan

Australian National University · Data61, CSIRO · University of New South Wales

Ollivier-Ricci Curvature Knowledge Distillation Cross-Architecture Knowledge Distillation Feature-Based Knowledge Distillation

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GNN-to-MLP distillation aims to retain the predictive accuracy of a message-passing teacher while deploying a graph-free MLP at inference. Existing methods mainly transfer node-wise predictions or use confidence-based reweighting, but they do not specify where the student should preserve the teacher's graph-induced geometry. We show that this omission leads to two spectral failure modes in the student's representation space. On sparse graphs, the student suffers from spectral underfit, missing high-energy teacher directions concentrated near boundary regions. On dense graphs, it suffers from spectral overfit, retaining spurious directions that the teacher has collapsed through aggregation. Motivated by an energy-weighted teacher-student alignment objective, we propose Graph Geometry-aware MLP (G^2MLP), a training-time distillation framework guided by Ollivier-Ricci curvature. Curvature identifies where the two spectral errors concentrate and is used to allocate supervision between prediction-level and representation-level alignment. The deployed model remains a standard MLP and requires no graph access at inference. Across node-classification benchmarks, G^2MLP consistently improves over graph-free distillation baselines, reduces the teacher-student rank gap in both regimes, and transfers without architectural changes to Graph Transformer teachers and link prediction.