mlsanityData to 7 Oct 2026

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

arXiv 2108.07406 ↗First posted 17 Aug 2021cs.LG cs.NA math.NAcited by 6

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 13 of its 41 references that are in the map. First posted on arXiv 17 Aug 2021.

Builds on

13 of 41 references.

References · 13

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2017Image reconstruction by domain transform manifold learningcited by 231
  3. 2013Optimal rates for zero-order convex optimization: the power of two function evaluationscited by 190
  4. 2016First-order Methods for Geodesically Convex Optimizationcited by 92
  5. 2016Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifoldscited by 64
  6. 2015Multi-scale exploration of convex functions and bandit convex optimizationcited by 20
  7. 2018Projection-Free Bandit Convex Optimizationcited by 17
  8. 2019Improved Regret Bounds for Projection-free Bandit Convex Optimizationcited by 16
  9. 2017Efficient Manifold and Subspace Approximations with Sphereletscited by 11
  10. 2020Regret Bounds without Lipschitz Continuity: Online Learning with Relative-Lipschitz Lossescited by 11
  11. 2015Bandit Convex Optimization: sqrt{T} Regret in One Dimensioncited by 10
  12. 2019Geodesic Distance Estimation with Sphereletscited by 9
1 more
  1. 2019Classification via local manifold approximationcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 1; 2024: 0; 2025: 1; 2026: 1.

6 papers.

  1. 2022Stochastic Zeroth Order Gradient and Hessian Estimators: Variance Reduction and Refined Bias Boundscited by 7
  2. 2023Zeroth-order Riemannian Averaging Stochastic Approximation Algorithmscited by 7
  3. 2022On Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifoldscited by 4
  4. 2022Convergence Rates of Stochastic Zeroth-order Gradient Descent for L ojasiewicz Functionscited by 1
  5. 2025Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approachcited by 1
  6. 2026Riemannian Zeroth-Order Gradient Estimation with Structure-Preserving Metrics for Geodesically Incomplete Manifoldscited by 0