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Damien Scieur

Visiteur de recherche indépendant - Samsung SAIT
Superviseur⋅e principal⋅e
Simon Lacoste-Julien
Sujets de recherche
Optimisation
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Publications

Understanding Adam Requires Better Rotation Dependent Assumptions
Lucas Maes
Tianyue H. Zhang
Alexia Jolicoeur-Martineau
Ioannis Mitliagkas
Damien Scieur
Simon Lacoste-Julien
Charles Guille-escuret
Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This… (voir plus) paper investigates Adam's sensitivity to rotations of the parameter space. We demonstrate that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature, evaluating their adequacy in explaining Adam's behavior across various rotation types. This work highlights the need for new, rotation-dependent theoretical frameworks to fully understand Adam's empirical success in modern machine learning tasks.
2024-10-25
ArXiv (prépublication)
doi.org
arxiv.org
Understanding Adam Requires Better Rotation Dependent Assumptions
Lucas Maes
Tianyue H. Zhang
Alexia Jolicoeur-Martineau
Ioannis Mitliagkas
Damien Scieur
Simon Lacoste-Julien
Charles Guille-escuret
Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This… (voir plus) paper investigates Adam's sensitivity to rotations of the parameter space. We demonstrate that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature, evaluating their adequacy in explaining Adam's behavior across various rotation types. This work highlights the need for new, rotation-dependent theoretical frameworks to fully understand Adam's empirical success in modern machine learning tasks.
2024-10-10
NeurIPS.cc/2024/Workshop/OPT (publié)
doi.org
openreview.net
Only tails matter: Average-Case Universality and Robustness in the Convex Regime
Leonardo Cunha
Gauthier Gidel
Fabian Pedregosa
Damien Scieur
Courtney Paquette
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
doi.org
openreview.net
Only Tails Matter: Average-Case Universality and Robustness in the Convex Regime
Leonardo Cunha
Gauthier Gidel
Fabian Pedregosa
Damien Scieur
Courtney Paquette
2022-06-20
ArXiv (prépublication)
doi.org
openreview.net
Accelerating Smooth Games by Manipulating Spectral Shapes
Waïss Azizian
Damien Scieur
Ioannis Mitliagkas
Simon Lacoste-Julien
Gauthier Gidel
2020-06-03
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics (publié)
proceedings.mlr.press
arxiv.org
Accelerating Smooth Games by Manipulating Spectral Shapes
Waïss Azizian
Damien Scieur
Ioannis Mitliagkas
Simon Lacoste-Julien
Gauthier Gidel
We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set co… (voir plus)ntaining all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes restricted to the real line represent well-understood classes of problems, like minimization. Shapes spanning the complex plane capture the added numerical challenges in solving smooth games. In this framework, we describe gradient-based methods, such as extragradient, as transformations on the spectral shape. Using this perspective, we propose an optimal algorithm for bilinear games. For smooth and strongly monotone operators, we identify a continuum between convex minimization, where acceleration is possible using Polyak's momentum, and the worst case where gradient descent is optimal. Finally, going beyond first-order methods, we propose an accelerated version of consensus optimization.
2020-01-02
ArXiv (preprint)
arxiv.org
arxiv.org