From the Greene--Wu Convolution to Gradient Estimation over Riemannian Manifolds
Machine Learning
2022-01-25 v4 Numerical Analysis
Numerical Analysis
Optimization and Control
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.
Keywords
Cite
@article{arxiv.2108.07406,
title = {From the Greene--Wu Convolution to Gradient Estimation over Riemannian Manifolds},
author = {Tianyu Wang and Yifeng Huang and Didong Li},
journal= {arXiv preprint arXiv:2108.07406},
year = {2022}
}