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..
Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
Authors: Santosh Vempala, Andre Wibisono
NeurIPS 2019 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove a convergence guarantee in Kullback Leibler (KL) divergence assuming satisfies log-Sobolev inequality and f has bounded Hessian. Notably, we do not assume convexity or bounds on higher derivatives. We also prove convergence guarantees in Rényi divergence of order q > 1 assuming the limit of ULA satisfies either log-Sobolev or Poincaré inequality. |
| Researcher Affiliation | Academia | Santosh S. Vempala College of Computing Georgia Institute of Technology Atlanta, GA 30332 EMAIL Andre Wibisono College of Computing Georgia Institute of Technology Atlanta, GA 30332 EMAIL |
| Pseudocode | No | The paper describes the ULA algorithm by formula (xk+1 = xk rf(xk) + 2 zk) but does not present it in a formal pseudocode block or algorithm listing. |
| Open Source Code | No | The paper does not contain any statements about making source code publicly available or provide links to code repositories. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments involving datasets for training. It discusses probability distributions conceptually but does not use them as empirical datasets. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical validation on datasets, therefore no validation splits are mentioned. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup that would require hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe any experimental setup that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical proofs and analysis rather than empirical experiments, thus it does not include details on an experimental setup or hyperparameters. |