mlsanityData to 14 Oct 2026

Effective Structural Encodings via Local Curvature Profiles

arXiv 2311.14864 ↗First posted 24 Nov 2023cs.LG stat.MLcited by 13

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Abstract (arXiv)

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 31 of its 53 references that are in the map. First posted on arXiv 24 Nov 2023.

Builds on

31 of 53 references.

References · 31

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
  4. 2018How Powerful are Graph Neural Networks?cited by 4,393
  5. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  6. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 976
  7. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 881
  8. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 728
  9. 2022Recipe for a General, Powerful, Scalable Graph Transformercited by 713
  10. 2020Benchmarking Graph Neural Networkscited by 680
  11. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  12. 2020Graph Neural Networks in Recommender Systems: A Surveycited by 494
19 more
  1. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 478
  2. 2021Rethinking Graph Transformers with Spectral Attentioncited by 473
  3. 2019Provably Powerful Graph Networkscited by 389
  4. 2021Graph Neural Networks with Learnable Structural and Positional Representationscited by 333
  5. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 313
  6. 2022Long Range Graph Benchmarkcited by 263
  7. 2018Modeling polypharmacy side effects with graph convolutional networkscited by 237
  8. 2019What graph neural networks cannot learn: depth vs widthcited by 201
  9. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 155
  10. 2021GraphiT: Encoding Graph Structure in Transformerscited by 147
  11. 2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 105
  12. 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 98
  13. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  14. 2022GRPE: Relative Positional Encoding for Graph Transformercited by 70
  15. 2019Community Detection on Networks with Ricci Flowcited by 62
  16. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 41
  17. 2016Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flowscited by 21
  18. 2023Curvature-based Clustering on Graphscited by 14
  19. 2019Neighborhood Growth Determines Geometric Priors for Relational Representation Learningcited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 7.

13 papers.

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  1. 2025Balancing Efficiency and Expressiveness: Subgraph GNNs with Walk-Based Centralitycited by 5
  2. 2025Performance Heterogeneity in Graph Neural Networks: Lessons for Architecture Design and Preprocessingcited by 2
  3. 2025Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvaturescited by 1
  4. 2025Enhancing the Utility of Higher-Order Information in Relational Learningcited by 0
  5. 2025A Geometric Perspective on the Difficulties of Learning GNN-based SAT Solverscited by 0
  6. 2025A roadmap for curvature-based geometric data analysis and learningcited by 0
  7. 2026Neural Algorithmic Reasoning for Approximate k-Coloring with Recursive Warm Startscited by 0
  8. 2026ASEHybrid: When Geometry Matters Beyond Homophily in Graph Neural Networkscited by 0
  9. 2026Sobolev--Ricci Curvaturecited by 0
  10. 2026Periodic Topological Deep Learning for Polymer Design and Discoverycited by 0
  11. 2026VeriDrive: Verifiable Counterfactual Supervision for Cost-Efficient Vision-Language Planningcited by 0
  12. 2026Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvaturecited by 0
1 more
  1. 2026Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learningcited by 0