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Computer Science > Machine Learning

arXiv:2108.07406 (cs)
[Submitted on 17 Aug 2021 (v1), last revised 22 Jan 2022 (this version, v4)]

Title:From the Greene--Wu Convolution to Gradient Estimation over Riemannian Manifolds

Authors:Tianyu Wang, Yifeng Huang, Didong Li
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Abstract:Over a complete Riemannian manifold of finite dimension, Greene and Wu introduced a convolution, known as Greene-Wu (GW) convolution. In this paper, we study properties of the GW convolution and apply it to non-Euclidean machine learning problems. In particular, we derive a new formula for how the curvature of the space would affect the curvature of the function through the GW convolution. Also, following the study of the GW convolution, a new method for gradient estimation over Riemannian manifolds is introduced.
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Optimization and Control (math.OC)
Cite as: arXiv:2108.07406 [cs.LG]
  (or arXiv:2108.07406v4 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2108.07406

Submission history

From: Didong Li [view email]
[v1] Tue, 17 Aug 2021 02:16:15 UTC (2,757 KB)
[v2] Mon, 13 Sep 2021 18:26:35 UTC (3,021 KB)
[v3] Sat, 16 Oct 2021 01:26:50 UTC (3,482 KB)
[v4] Sat, 22 Jan 2022 20:29:33 UTC (3,466 KB)
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