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

论文探讨图和机器学习的Ollivier-Ricci曲率

作者 PulseAugur 编辑部 · [1 个来源] ·

本论文基于Yann Ollivier的工作和最优传输理论，探讨了度量空间的Ollivier-Ricci曲率。论文详细介绍了该曲率与黎曼流形中经典Ricci曲率的联系的主要结果，包括Bonnet-Myers和Lévy-Gromov等定理的推广。研究还涵盖了Lin-Lu-Yau将Ollivier-Ricci曲率推广到图上的工作，以及Jost-Liu的组合界限，最后通过对有向图的新证明及其在网络科学和图机器学习中的应用进行了总结。 AI

影响 扩展了图分析的理论框架，可能提高图神经网络性能和网络科学算法。

排序理由 该条目是一篇在arXiv上发表的学术论文，详细介绍了理论研究。[lever_c_demoted from research: ic=1 ai=1.0]

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论文探讨图和机器学习的Ollivier-Ricci曲率

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该条目是一篇在arXiv上发表的学术论文，详细介绍了理论研究。[lever_c_demoted from research: ic=1 ai=1.0]
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报道来源 [1]

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

    黎曼流形和有向图的Ollivier-Ricci曲率及其在图神经网络中的应用

    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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