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Implicit regularization makes overparameterized asymmetric matrix sensing robust to perturbations
1Faculty of Mathematics and Natural Sciences, Department of Mathematics, University of Oslo , Oslo, Norway.
Summary
This study introduces perturbed gradient flow to analyze overparameterized learning models. It demonstrates improved robustness and efficiency for matrix sensing problems, even with imperfect data and moderate initializations.
Area of Science:
- Machine Learning
- Optimization
- Artificial Intelligence
Background:
- Overparameterized learning models present challenges in understanding generalization.
- Matrix sensing is a key problem for studying gradient descent in these models.
- Previous methods required extremely small initializations for factorized gradient descent.
Purpose of the Study:
- To develop a more robust and efficient method for solving matrix sensing problems.
- To analyze the behavior of gradient descent with perturbations and moderate initializations.
- To improve sample and time complexity analyses for overparameterized models.
Main Methods:
- Introduced a general formulation called perturbed gradient flow.
- Analyzed factorized gradient descent's robustness to perturbations.
- Extended the analysis to mini-batch stochastic gradient descent.
Main Results:
- Perturbed gradient flow offers sharper sample and time complexities.
- The method is robust to imperfect measurements and moderate initializations.
- Mini-batch stochastic gradient descent shows improved sample complexity.
Conclusions:
- Perturbed gradient flow provides a more tractable and robust framework for analyzing overparameterized models.
- This approach advances the understanding of generalization in machine learning.
- The findings have implications for safe, secure, and robust AI in critical systems.
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