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..
Polynomial time guarantees for the Burer-Monteiro method
Authors: Diego Cifuentes, Ankur Moitra
NeurIPS 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6 Experiments We present some experimental results to complement our theorems. We rely on the library NLopt [24] (MIT license) to solve the nonlinear problem (BM). Concretely, we use the augmented Lagrangian method (ALM) implemented in NLopt (which is based on [8]), and we use the preconditioned truncated Newton method as the subroutine. We also rely on the commercial solver Mosek for SDPs. Figure 1 shows the percentage of experiments solved correctly for each value of r and p. |
| Researcher Affiliation | Academia | Diego Cifuentes School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332 EMAIL Ankur Moitra Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139 EMAIL |
| Pseudocode | No | The paper refers to algorithms (e.g., 'Theorem 4 below we show that AFAC points can be computed in polynomial time'), but it does not provide explicit pseudocode or an algorithm block for any method. |
| Open Source Code | Yes | Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] In supplementary material |
| Open Datasets | No | For our first experiment we consider a random SDP with a planted solution. More precisely, we take a matrix X0 S50, X0 0 of rank r {4, 7, 12}, and generate a random SDP for which X0 is an optimal solution. To do so, we generate m := τ(r) random constraints that are satisfied at X0, and then find a cost matrix C in the normal cone of X0. We generate 100 random SDPs for each r. We use random data for the experiments. |
| Dataset Splits | No | The paper states 'N/A' for specifying 'training details (e.g., data splits, hyperparameters, how they were chosen)' in the ethics review guidelines. |
| Hardware Specification | No | The paper states 'N/A' for 'total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)' in the ethics review guidelines, indicating no specific hardware details. |
| Software Dependencies | No | The paper mentions 'NLopt [24]' and 'Mosek' as software used, but it does not specify version numbers for these components. |
| Experiment Setup | No | The paper states 'N/A' for specifying 'training details (e.g., data splits, hyperparameters, how they were chosen)' in the ethics review guidelines. |