000011704 001__ 11704 000011704 005__ 20250218124801.0 000011704 02470 $$ahttps://doi.org/10.1103/physrevresearch.3.013061$$2doi 000011704 037__ $$aTEXTUAL 000011704 037__ $$bArticle 000011704 041__ $$aeng 000011704 245__ $$aFluctuation distributions of energy minima in complex landscapes 000011704 269__ $$a2021-01-19 000011704 336__ $$aArticle 000011704 520__ $$aWe discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin-glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and nontrivial finite-size scaling. Based on this, we propose a picture of gradient-descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for nonconvex complex landscapes, rationalizing the commonality that we find across models.Received 2 December 2019Accepted 18 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.3.013061Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBoolean satisfiability problemNP-hard problemsPhysical SystemsGlassesSpin glassesTechniquesBrownian dynamicsComputational complexityRandom matrix theoryStochastic differential equationsStatistical Physics 000011704 536__ $$oSimons Foundation$$c454943 000011704 536__ $$oSimons Foundation$$c454945 000011704 536__ $$oSimons Foundation$$c348126 000011704 536__ $$oSimons Foundation$$c327939 000011704 540__ $$a<p>Published by the American Physical Society under the terms of the <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a> license.</p> 000011704 542__ $$fCC BY 000011704 690__ $$aInstitutes & Centers 000011704 692__ $$aJames Franck Institute 000011704 7001_ $$1https://orcid.org/0000-0003-0013-5186$$2ORCID$$aBoltz, Horst-Holger$$uUniversity of Chicago 000011704 7001_ $$1https://orcid.org/0000-0001-5367-3688$$2ORCID$$aKurchan, Jorge$$uPSL Research University 000011704 7001_ $$1https://orcid.org/0000-0002-2295-2729$$2ORCID$$aLiu, Andrea J.$$uUniversity of Pennsylvania 000011704 773__ $$tPhysical Review Research 000011704 8564_ $$9db4cbea9-a31f-4790-86df-4009da9453b8$$ePublic$$s1505459$$uhttps://knowledge.uchicago.edu/record/11704/files/PhysRevResearch.3.013061.pdf 000011704 908__ $$aI agree 000011704 909CO $$ooai:uchicago.tind.io:11704$$pGLOBAL_SET 000011704 983__ $$aArticle