Fluctuation distributions of energy minima in complex landscapes
Uložené v:
| Názov: | Fluctuation distributions of energy minima in complex landscapes |
|---|---|
| Autori: | Boltz, Horst-Holger, Kurchan, Jorge, Liu, Andrea, J |
| Prispievatelia: | 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 |
| Zdroj: | ISSN: 2643-1564. |
| Informácie o vydavateľovi: | CCSD American Physical Society |
| Rok vydania: | 2021 |
| Predmety: | 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] |
| Popis: | 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. |
| Druh dokumentu: | article in journal/newspaper |
| Jazyk: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/1911.08943; ARXIV: 1911.08943 |
| DOI: | 10.1103/physrevresearch.3.013061 |
| Dostupnosť: | 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 |
| Prístupové číslo: | edsbas.9631C9A8 |
| Databáza: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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 |