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

Tianyu Wang; Yifeng Huang; Didong Li

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arXiv · 2108.07406

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

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.

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Tianyu Wang, Yifeng Huang, Didong Li. 2021-08-17. From the Greene--Wu Convolution to Gradient Estimation over Riemannian Manifolds. https://arxiv.org/abs/2108.07406

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