The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing
Authors: Xingyu Xu, Yandi Shen, Yuejie Chi, Cong Ma
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conduct numerical experiments to demonstrate the efficacy of Scaled GD(λ) for solving overparameterized low-rank matrix sensing. |
| Researcher Affiliation | Academia | 1Carnegie Mellon University, Pittsburgh, United States 2University of Chicago, Chicago, United States. |
| Pseudocode | No | The paper provides mathematical update rules (e.g., equations 6, 7, 8) but does not include any clearly labeled "Pseudocode" or "Algorithm" blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | Yes | We set the ground truth matrix X = U Σ Rn r where U Rn r is a random orthogonal matrix and Σ Rr r is a diagonal matrix whose condition number is set to be κ. We set n = 150 and r = 3, and use random Gaussian measurements with m = 10nr . |
| Dataset Splits | No | No specific dataset splits (e.g., percentages, sample counts, or explicit references to standard splits) for training, validation, or testing are mentioned. The paper describes generating synthetic data for its experiments. |
| Hardware Specification | No | No specific hardware details (e.g., CPU, GPU models, memory, or cloud instances) are provided for running the experiments. |
| Software Dependencies | No | No specific software components with version numbers (e.g., Python 3.8, PyTorch 1.9) are mentioned. |
| Experiment Setup | Yes | We set n = 150 and r = 3, and use random Gaussian measurements with m = 10nr . The learning rate of GD has been fine-tuned to achieve fastest convergence for each κ, while that of Scaled GD(λ) is fixed to 0.3. The initialization scale α in each case has been fine-tuned so that the final accuracy is 10 9. |