Summary of Convergence Of Gradient Descent with Small Initialization For Unregularized Matrix Completion, by Jianhao Ma et al.
Convergence of Gradient Descent with Small Initialization for Unregularized Matrix Completion
by Jianhao Ma, Salar Fattahi
First submitted to arxiv on: 9 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Machine Learning (stat.ML)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper tackles symmetric matrix completion, aiming to reconstruct a positive semidefinite matrix from partially observed entries. It demonstrates that vanilla gradient descent (GD) with small initialization converges to the ground truth without requiring explicit regularization, even in over-parameterized scenarios where the true rank is unknown. The results improve upon existing methods by not relying on accurate initial points or exact knowledge of the true rank. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper studies how to fill in missing pieces of a special kind of matrix called symmetric matrices. It shows that using a simple method, gradient descent with small starting values, can accurately complete these matrices even when only some parts are known. This is useful because often we don’t have all the information and need to make educated guesses. |
Keywords
* Artificial intelligence * Gradient descent * Regularization
