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Thesis explores Ollivier-Ricci curvature for graphs and machine learning

By PulseAugur Editorial · [1 sources] ·

This thesis explores the Ollivier-Ricci curvature of metric spaces, building upon the work of Yann Ollivier and optimal transport theory. It details major results connecting this curvature to classical Ricci curvature in Riemannian manifolds, including extensions of theorems like Bonnet-Myers and Lévy-Gromov. The work also covers Lin-Lu-Yau's extension of Ollivier-Ricci curvature to graphs and Jost-Liu's combinatorial bounds, concluding with novel proofs for directed graphs and applications in network science and graph machine learning. AI

IMPACT Extends theoretical frameworks for graph analysis, potentially improving graph neural network performance and network science algorithms.

RANK_REASON The item is an academic paper published on arXiv detailing theoretical research. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Thesis explores Ollivier-Ricci curvature for graphs and machine learning

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The item is an academic paper published on arXiv detailing theoretical research. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Eleanor P Wiesler ·

    Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks

    arXiv:2604.14211v2 Announce Type: replace-cross Abstract: This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserstein Distance and optimal transport theory. We present some of the major results an…

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