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 [1].
Fast Convergence of Langevin Dynamics on Manifold: Geodesics meet Log-Sobolev
Authors: Xiao Wang, Qi Lei, Ioannis Panageas
NeurIPS 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our work generalizes the results of Vempala and Wibisono [2019] where f is defined on a manifold M rather than Rn. From technical point of view, we show that KL decreases in a geometric rate whenever the distribution e f satisfies a log-Sobolev inequality on M. Our main technical contributions are: A non-asymptotic convergence guarantee for Geodesic Langevin algorithm on closed manifold is provided, with the help of log-Sobolev inequality. |
| Researcher Affiliation | Academia | Xiao Wang SUTD EMAIL Qi Lei Princeton EMAIL Ioannis Panageas UC Irvine EMAIL |
| Pseudocode | No | The paper describes the steps of the Geodesic Langevin Algorithm, but it does not present them in a formally structured pseudocode block or labeled 'Algorithm'. |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that open-source code for the described methodology is provided. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments on datasets, thus no information on publicly available training datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments that would involve dataset validation splits. |
| Hardware Specification | No | The paper does not mention any specific hardware used for experiments, as it is a theoretical work. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers, as it is a theoretical work. |
| Experiment Setup | No | The paper is theoretical and does not provide specific experimental setup details such as hyperparameters or training configurations for empirical evaluation. |