Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set—the intrinsic dimension (I_{d...

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Autores principales:	T. Mendes-Santos, X. Turkeshi, M. Dalmonte, Alex Rodriguez
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/022d2f65518840b0bedc492738de178e
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spelling	oai:doaj.org-article:022d2f65518840b0bedc492738de178e2021-12-02T16:22:43ZUnsupervised Learning Universal Critical Behavior via the Intrinsic Dimension10.1103/PhysRevX.11.0110402160-3308https://doaj.org/article/022d2f65518840b0bedc492738de178e2021-02-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.011040http://doi.org/10.1103/PhysRevX.11.011040https://doaj.org/toc/2160-3308The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set—the intrinsic dimension (I_{d})—behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based I_{d} estimators to compute the I_{d} of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the I_{d} uniquely characterizes the transition regime. The finite-size analysis of the I_{d} allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent ν in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.T. Mendes-SantosX. TurkeshiM. DalmonteAlex RodriguezAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 1, p 011040 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 T. Mendes-Santos X. Turkeshi M. Dalmonte Alex Rodriguez Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension
description	The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set—the intrinsic dimension (I_{d})—behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based I_{d} estimators to compute the I_{d} of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the I_{d} uniquely characterizes the transition regime. The finite-size analysis of the I_{d} allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent ν in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.
format	article
author	T. Mendes-Santos X. Turkeshi M. Dalmonte Alex Rodriguez
author_facet	T. Mendes-Santos X. Turkeshi M. Dalmonte Alex Rodriguez
author_sort	T. Mendes-Santos
title	Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension
title_short	Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension
title_full	Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension
title_fullStr	Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension
title_full_unstemmed	Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension
title_sort	unsupervised learning universal critical behavior via the intrinsic dimension
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/022d2f65518840b0bedc492738de178e
work_keys_str_mv	AT tmendessantos unsupervisedlearninguniversalcriticalbehaviorviatheintrinsicdimension AT xturkeshi unsupervisedlearninguniversalcriticalbehaviorviatheintrinsicdimension AT mdalmonte unsupervisedlearninguniversalcriticalbehaviorviatheintrinsicdimension AT alexrodriguez unsupervisedlearninguniversalcriticalbehaviorviatheintrinsicdimension
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Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

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