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..
Local Linear Convergence of Forward--Backward under Partial Smoothness
Authors: Jingwei Liang, Jalal Fadili, Gabriel Peyré
NeurIPS 2014 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Several experimental results on some of the problems discussed above are provided to support our theoretical findings. 4 Numerical experiments In this section, we describe some examples to demonstrate the applicability of our results. More precisely, we consider solving min x Rn 1 2||y Ax||2 + λJ(x) (4.1) |
| Researcher Affiliation | Academia | Jingwei Liang and Jalal M. Fadili GREYC, CNRS-ENSICAEN-Univ. Caen EMAIL Gabriel Peyré CEREMADE, CNRS-Univ. Paris-Dauphine EMAIL |
| Pseudocode | No | The paper describes the Forward Backward (FB) splitting algorithm using a mathematical update rule (1.2) but does not provide it in a structured pseudocode or algorithm block format. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | No | The paper describes generating synthetic data for its experiments (e.g., 'A Rm n is generated uniformly at random from the Gaussian ensemble', 'x0 is 8-sparse', 'rank(x0) = 5') rather than using publicly available datasets with concrete access information. |
| Dataset Splits | No | The paper describes the experimental settings for various problems but does not provide specific dataset split information (e.g., percentages or counts for training, validation, or test sets). |
| Hardware Specification | No | The paper does not provide any specific hardware details used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers. |
| Experiment Setup | Yes | The tested experimental settings are (a) ℓ1-norm m = 48 and n = 128, x0 is 8-sparse; (b) Total Variation m = 48 and n = 128, (DDIFx0) is 8-sparse; (c) ℓ∞-norm m = 123 and n = 128, x0 has 10 saturating entries; (d) ℓ1 ℓ2-norm m = 48 and n = 128, x0 has 2 non-zero blocks of size 4; (e) Nuclear norm m = 1425 and n = 2500, x0 R50 50 and rank(x0) = 5. The number of measurements is chosen sufficiently large, δ small enough and λ of the order of δ so that [27, Theorem 1] applies, yielding that the minimizer of (4.1) is unique and verifies the non-degeneracy and restricted strong convexity assumptions (3.1)-(3.2). |