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 Shift Toward Open and Reproducible AI Research," Under Review, 2026. doi: 10.48550/arXiv.2606.16974..
Efficient Sampling on Riemannian Manifolds via Langevin MCMC
Authors: Xiang Cheng, Jingzhao Zhang, Suvrit Sra
NeurIPS 2022 | Venue PDF | LLM Run Details | Input Tokens: 19,320 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 4,210 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study the task of efficiently sampling from a Gibbs distribution dĪ = e hdvolg over a Riemannian manifold M via (geometric) Langevin MCMC; this algorithm involves computing exponential maps in random Gaussian directions and is efficiently implementable in practice. The key to our analysis of Langevin MCMC is a bound on the discretization error of the geometric Euler-Murayama scheme, assuming h is Lipschitz and M has bounded sectional curvature. Our error bound matches the error of Euclidean Euler-Murayama in terms of its stepsize dependence. Combined with a contraction guarantee for the geometric Langevin Diffusion under Kendall-Cranston coupling, we prove that the Langevin MCMC iterates lie within Îĩ-Wasserstein distance of Ī after O(Îĩ 2) steps, which matches the iteration complexity for Euclidean Langevin MCMC. |
| Researcher Affiliation | Academia | Xiang Cheng Massachusetts Institute of Technology EMAIL Jingzhao Zhang Tsinghua University EMAIL Suvrit Sra Massachusetts Institute of Technology EMAIL |
| Pseudocode | No | The paper describes mathematical models and processes but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statement about open-source code release or a link to a code repository. |
| Open Datasets | No | This is a theoretical paper and does not involve experimental evaluation on datasets. Therefore, no information about publicly available datasets is provided. |
| Dataset Splits | No | This is a theoretical paper and does not involve experimental evaluation on datasets, so there are no training/validation/test splits mentioned. |
| Hardware Specification | No | The paper is theoretical and does not describe computational experiments, so no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not specify software dependencies with version numbers for experimental reproducibility. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup, hyperparameters, or system-level training settings. |