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..
Convergence of Alternating Gradient Descent for Matrix Factorization
Authors: Rachel Ward, Tamara Kolda
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments suggest that our proposed initialization is not merely of theoretical benefit, but rather significantly improves the convergence rate of gradient descent in practice. |
| Researcher Affiliation | Collaboration | Rachel Ward University of Texas Austin, TX EMAIL Tamara G. Kolda Math Sci.ai Dublin, CA EMAIL |
| Pseudocode | No | The paper describes the alternating gradient descent update rule in Assumption 1 but does not present it as a structured pseudocode or algorithm block. |
| Open Source Code | No | The paper does not provide an unambiguous statement or a direct link to a source-code repository for the methodology described in this paper. |
| Open Datasets | No | The paper uses a synthetic matrix constructed as A = UΣV with U and V random 100 × 5 orthonormal matrices, but does not provide access, exact reproduction instructions (e.g., random seed), or a link to this specific matrix. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | We factorize a rank-5 (r = 5) matrix of size 100 × 100. The matrix is constructed as A = UΣV with U and V random 100 × 5 orthonormal matrices, and singular value ratio σr(A)/σ1(A) = 0.9. ... In all experiments we use the defaults C = 4 and D = Cν/9 with ν = 1e-10 for computing the proposed initialization as well as the theoretical step size. ... Proposed: X0 = 1 ηd Cσ1 AΦ(n d) Y0 = ηDσ1 n Φ(n d) |