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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
Alan Milligan
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 observe that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis in practice. 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 and find that they fall short in explaining Adam's behaviour across various rotation types. In contrast, we verify the orthogonality of the update as a promising indicator of Adam's basis sensitivity, suggesting it may be the key quantity for developing rotation-dependent theoretical frameworks that better explain its empirical success.
2025-09-17
NeurIPS.cc/2025/Conference (poster)
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
The recently developed average-case analysis of optimization methods allows a more fine-grained and representative convergence analysis than… (voir plus) usual worst-case results. In exchange, this analysis requires a more precise hypothesis over the data generating process, namely assuming knowledge of the expected spectral distribution (ESD) of the random matrix associated with the problem. This work shows that the concentration of eigenvalues near the edges of the ESD determines a problem's asymptotic average complexity. This a priori information on this concentration is a more grounded assumption than complete knowledge of the ESD. This approximate concentration is effectively a middle ground between the coarseness of the worst-case scenario convergence and the restrictive previous average-case analysis. We also introduce the Generalized Chebyshev method, asymptotically optimal under a hypothesis on this concentration and globally optimal when the ESD follows a Beta distribution. We compare its performance to classical optimization algorithms, such as gradient descent or Nesterov's scheme, and we show that, in the average-case context, Nesterov's method is universally nearly optimal asymptotically.
2022-06-27
Proceedings of the 39th International Conference on Machine Learning (publié)
doi.org
proceedings.mlr.press
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.
2020-06-02
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics (publié)
doi.org
proceedings.mlr.press