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Fluctuation distributions of energy minima in complex landscapes

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Title: Fluctuation distributions of energy minima in complex landscapes
Authors: Boltz, Horst-Holger, Kurchan, Jorge, Liu, Andrea, J
Contributors: James Franck Institute, University of Chicago, Laboratoire de Physique Statistique de l'ENS (LPS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Systèmes Classiques ou Quantiques en Interaction, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL), University of Pennsylvania
Source: ISSN: 2643-1564.
Publisher Information: CCSD
American Physical Society
Publication Year: 2021
Subject Terms: Boolean satisfiability problem, NP-hard problems, Glasses, Spin glasses, Brownian dynamics, Computational complexity, Random matrix theory, Stochastic differential equations, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Description: International audience ; We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin-glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and nontrivial finite-size scaling. Based on this, we propose a picture of gradient-descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for nonconvex complex landscapes, rationalizing the commonality that we find across models.
Document Type: article in journal/newspaper
Language: English
Relation: info:eu-repo/semantics/altIdentifier/arxiv/1911.08943; ARXIV: 1911.08943
DOI: 10.1103/physrevresearch.3.013061
Availability: https://hal.science/hal-04990843
https://hal.science/hal-04990843v1/document
https://hal.science/hal-04990843v1/file/PhysRevResearch.3.013061.pdf
https://doi.org/10.1103/physrevresearch.3.013061
Rights: http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.9631C9A8
Database: BASE
Description
Abstract:International audience ; We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin-glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and nontrivial finite-size scaling. Based on this, we propose a picture of gradient-descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for nonconvex complex landscapes, rationalizing the commonality that we find across models.
DOI:10.1103/physrevresearch.3.013061