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..
Finite-Time Analysis of Projected Langevin Monte Carlo
Authors: Sebastien Bubeck, Ronen Eldan, Joseph Lehec
NeurIPS 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We ran the volume algorithm with both H&R and LMC on the following set of convex bodies: K = [ 1, 1]n (referred to as the Box ) and K = [ 1, 1]n n 2 Bn (referred to as the Box and Ball ), where n = 10 k, k = 1, . . . , 10. The computed volume (normalized by 2n for the Box and by 0.2 2n for the Box and Ball ) as well as the clock time (in seconds) to terminate are reported in the figure above. From these experiments it seems that LMC and H&R roughly compute similar values for the volume (with H&R being slightly more accurate), and LMC is almost always a bit faster. |
| Researcher Affiliation | Collaboration | S ebastien Bubeck Microsoft Research EMAIL Ronen Eldan Weizmann Institute EMAIL Joseph Lehec Universit e Paris-Dauphine EMAIL |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. The algorithm (1) is presented as a mathematical formula. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | No | The 'datasets' used are geometric shapes (Box and Box and Ball) defined by mathematical expressions, not publicly available datasets with specific access information. The paper does not provide a link, DOI, or formal citation for accessing these geometric definitions as data. |
| Dataset Splits | No | The paper does not specify training, validation, or test dataset splits. The experiments involve computing the volume of geometric bodies, not training models with data splits. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models, or memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'Cousins and Vempala provide a Matlab implementation' but does not specify a version number for Matlab or any other software dependencies with versions. |
| Experiment Setup | Yes | We implemented the same procedure with LMC instead of H&R, and we choose the step-size η = 1/(βn2), where β is the smoothness parameter of the underlying log-concave distribution (in particular here β = 1/σ2 ℓ). |