Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds
Authors: Yunrui Guan, Krishnakumar Balasubramanian, Shiqian Ma
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We establish high-accuracy sampling guarantees for the Riemannian Proximal Sampler, showing that generating samples with ε-accuracy requires O(log(1/ε)) iterations in Kullback-Leibler divergence assuming access to exact oracles and O(log2(1/ε)) iterations in the total variation metric assuming access to sufficiently accurate inexact oracles. Furthermore, we present practical implementations of these oracles by leveraging heat-kernel truncation and Varadhan s asymptotics. ... Our work is theoretical and includes some toy examples. |
| Researcher Affiliation | Academia | Yunrui Guan Department of Computational Applied Mathematics and Operations Research Rice University Houston, TX 77005 EMAIL Krishnakumar Balasubramanian Department of Statistics University of California, Davis Davis, CA 95616 EMAIL Shiqian Ma Department of Computational Applied Mathematics and Operations Research Rice University Houston, TX 77005 EMAIL |
| Pseudocode | Yes | Algorithm 1 Riemannian proximal sampler... Algorithm 2 RHK through rejection sampling... Algorithm 3 MBI through rejection sampling... Algorithm 4 Inexact manifold proximal sampler with Varadhan s asymptotics |
| Open Source Code | Yes | Codes were provided in supplementary material. |
| Open Datasets | No | In this experiment, we test the performance of Algorithms 2 and 3 for sampling from the von Mises Fisher distribution on hyperspheres and compare it with the Riemannian LMC method. ... Our work is theoretical and includes some toy examples. The paper uses theoretical distributions on manifolds for numerical experiments and does not specify any publicly available empirical datasets. |
| Dataset Splits | No | The paper describes numerical experiments for sampling from distributions on hyperspheres and positive definite matrices, which are theoretical constructs, not empirical datasets. No dataset split information is provided as there are no traditional datasets used. |
| Hardware Specification | Yes | The toy examples are run on a personal laptop using Matlab, and only CPU (AMD Ryzen 7 PRO 5850U). |
| Software Dependencies | No | The toy examples are run on a personal laptop using Matlab, and only CPU (AMD Ryzen 7 PRO 5850U). No specific version for Matlab is mentioned, and no other software or library versions are provided. |
| Experiment Setup | Yes | We demonstrate the performance of our Algorithm on S2 R3 with µ = (10, 0.1, 2)T and κ = 10, and on S5 with µ = (5, 0.1, 2, 1, 1, 1)T and κ = 10. For both algorithms, we use uniform distribution on the hypersphere as initialization. ... We test the performance of Algorithm 4 when the potential function f(X) = 1 2σ2 d(X, Im)4, m = 3, σ = 0.03... For both algorithms we initialize the algorithm at X0 = 2I3. ... We choose η = 0.0001, and compute the average number of iterations executed by rejection sampling. |