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..
Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization
Authors: Jialun Zhang, Salar Fattahi, Richard Y Zhang
NeurIPS 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our numerical experiments find that Prec GD works equally well in restoring the linear convergence of other variants of nonconvex matrix factorization in the over-parameterized regime. ... Finally, we numerically compare Prec GD on other matrix factorization problems that fall outside of the matrix sensing framework. |
| Researcher Affiliation | Academia | Gavin Zhang University of Illinois at Urbana Champaign EMAIL Salar Fattahi University of Michigan EMAIL Richard Y. Zhang University of Illinois at Urbana Champaign EMAIL |
| Pseudocode | No | The paper describes algorithms using mathematical equations, such as 'Xk+1 = Xk - α∇f(Xk)(XkT Xk + ηkIr)^-1', but does not provide a formal pseudocode block or algorithm box. |
| Open Source Code | No | The paper does not provide any statement or link regarding the open-sourcing of the code for the methodology described. |
| Open Datasets | Yes | The data matrices A1, . . . , Am were taken from [13, Example 12], the ground truth M = ZZT was constructed by sampling each column of Z Rn r from the standard Gaussian, and then rescaling the last column to achieve a desired condition number. |
| Dataset Splits | No | The paper discusses problem dimensions (n, r) and initial conditions but does not specify training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide any specific hardware specifications used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers used for the experiments. |
| Experiment Setup | Yes | For Scaled GD and Prec GD, we used a modified version of the Polyak step-size where αk = ∇f(Xk)p/∇f(Xk) P . For GD we use a decaying stepsize. ... using the same learning rate α = 2 * 10^-2. |