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Manuela Girotti

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Neural Networks Efficiently Learn Low-Dimensional Representations with SGD
Alireza Mousavi-Hosseini
Sejun Park
Manuela Girotti
Ioannis Mitliagkas
Murat A Erdogdu
We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input …
2023-02-01
ICLR.cc/2023/Conference (notable)
doi.org
openreview.net
A Study of Condition Numbers for First-Order Optimization
Charles Guille-escuret
Baptiste Goujaud
Manuela Girotti
Ioannis Mitliagkas
2021-03-18
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics (publié)
proceedings.mlr.press
arxiv.org
A Study of Condition Numbers for First-Order Optimization
Charles Guille-escuret
Baptiste Goujaud
Manuela Girotti
Ioannis Mitliagkas
The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothnes… (voir plus)s and strong convexity. These metrics are used to tune the hyperparameters of FOA. We introduce a class of perturbations quantified via a new norm, called *-norm. We show that adding a small perturbation to the objective function has an equivalently small impact on the behavior of any FOA, which suggests that it should have a minor impact on the tuning of the algorithm. However, we show that smoothness and strong convexity can be heavily impacted by arbitrarily small perturbations, leading to excessively conservative tunings and convergence issues. In view of these observations, we propose a notion of continuity of the metrics, which is essential for a robust tuning strategy. Since smoothness and strong convexity are not continuous, we propose a comprehensive study of existing alternative metrics which we prove to be continuous. We describe their mutual relations and provide their guaranteed convergence rates for the Gradient Descent algorithm accordingly tuned. Finally we discuss how our work impacts the theoretical understanding of FOA and their performances.
2020-12-10
ArXiv (preprint)
arxiv.org
arxiv.org