Article (Scientific journals)
Gradient descent dynamics and the jamming transition in infinite dimensions
Manacorda, Alessandro; Zamponi, Francesco
2022In Journal of Physics. A, Mathematical and Theoretical
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Abstract :
[en] Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft repulsive particles in the limit of infinite spatial dimension d. The gradient descent dynamics then displays a jamming transition: at low density, it reaches zero-energy states in which particles' overlaps are fully eliminated, while at high density the energy remains finite and overlaps persist. At the transition, the dynamics becomes critical. In the d → ∞ limit, a set of self-consistent dynamical equations can be derived via mean field theory. We analyze these equations and we present some partial progress towards their solution. We also study the random Lorentz gas in a range of d = 2...22, and obtain a robust estimate for the jamming transition in d → ∞. The jamming transition is analogous to the capacity transition in supervised learning, and in the appendix we discuss this analogy in the case of a simple one-layer fully-connected perceptron.
Disciplines :
Physics
Author, co-author :
Manacorda, Alessandro  ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Zamponi, Francesco;  Centre National de la Recherche Scientifique - CNRS > Laboratoire de Physique de l'École Normale Supérieure
External co-authors :
yes
Language :
English
Title :
Gradient descent dynamics and the jamming transition in infinite dimensions
Publication date :
15 August 2022
Journal title :
Journal of Physics. A, Mathematical and Theoretical
ISSN :
1751-8121
Publisher :
Institute of Physics (IOP), Bristol, United Kingdom
Special issue title :
Random Landscapes and Dynamics in Evolution, Ecology and Beyond
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Physics and Materials Science
European Projects :
H2020 - 723955 - GlassUniversality - Universal explanation of low-temperature glass anomalies
Funders :
CE - Commission Européenne [BE]
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