General Low-rank Matrix Optimization: Geometric Analysis and Sharper Bounds
Authors: Haixiang Zhang, Yingjie Bi, Javad Lavaei
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper considers the global geometry of general low-rank minimization problems via the Burer-Monteiro factorization approach. For the rank-1 case, we prove that there is no spurious second-order critical point... For the arbitrary rank-r case, the same property is established... We design a counterexample... we prove that all second-order critical points have a positive correlation to the ground truth. Finally, the strict saddle property... is established for both the symmetric and asymmetric problems... |
| Researcher Affiliation | Academia | Haixiang Zhang Department of Mathematics University of California, Berkeley Berkeley, CA 94704 haixiang_zhang@berkeley.edu Yingjie Bi Department of IEOR University of California, Berkeley Berkeley, CA 94704 yingjiebi@berkeley.edu Javad Lavaei Department of IEOR University of California, Berkeley Berkeley, CA 94704 lavaei@berkeley.edu |
| Pseudocode | Yes | Algorithm 1 Singular Value Projection (SVP) Algorithm |
| Open Source Code | No | The paper does not provide any links or explicit statements about the availability of open-source code for the described methodology. |
| Open Datasets | No | This paper is theoretical and does not describe empirical experiments with datasets. It mentions applications like "matrix completion" and "phase retrieval" but does not use any specific dataset for training or evaluation. |
| Dataset Splits | No | This paper is theoretical and does not describe empirical experiments with data splits, so no validation split information is provided. |
| Hardware Specification | No | This paper is theoretical and does not describe empirical experiments; therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | This paper is theoretical and does not describe empirical experiments; therefore, no software dependencies with version numbers are listed. |
| Experiment Setup | No | This paper is theoretical and does not describe empirical experiments; therefore, no experimental setup details, hyperparameters, or training settings are provided. |