Papers › On Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifolds
On Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifolds
Tianyu Wang
We study Hessian estimators for functions defined over an n-dimensional complete analytic Riemannian manifold. We introduce new stochastic zeroth-order Hessian estimators using O (1) function evaluations. We show that, for an analytic real-valued function f, our estimator achieves a bias bound of order O ( γδ² ), where γ depends on both the Levi-Civita connection and function f, and δ is the finite difference step size. To the best of our knowledge, our results provide the first bias bound for Hessian estimators that explicitly depends on the geometry of the underlying Riemannian manifold. We also study downstream computations based on our Hessian estimators. The supremacy of our method is evidenced by empirical evaluations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections