[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118010-en":3,"doc-seo-118010-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118010,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Machine learning phase transitions - Connections to the Fisher information","Machine-learning methods for detecting phase transitions from data often lack a clear theoretical rationale and known limitations. This work derives principled links between common ML indicators and information-theoretic quantities. Using information geometry, it proves that several ML-based phase-transition indicators provide lower bounds that approximate the square root of the system’s (quantum) Fisher information. Numerical demonstrations validate the bounds across classical and quantum phase transitions.","Machine learning phase transitions: Connections to the Fisher information  \narXiv :2311 . 10710v1 [ cond-mat .dis-nn] 17 Nov 2023  \nJulian Arnold, 1 Niels L¨orch, 1 Flemming Holtorf,2, 3 and Frank Sch¨afer3  \n1 Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland  \n2 Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  \n3 CSAIL, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (Dated: November 20, 2023)  \nDespite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential failure modes of these techniques by rooting popular machine-learning indicators of phase transitions in information-theoretic concepts. Using tools from information geometry, we prove that several machine-learning indicators of phase transitions approximate the square root of the system’s (quantum) Fisher information from below – a quantity that is known to indicate phase transitions but is often difficult to compute from data. We numerically demonstrate the quality of these bounds for phase transitions in classical and quantum systems.  \nIntroduction.—Traditionally, critical phenomena have been studied by relying on the Ginzburg-Landau-Wilson paradigm which is based on concepts such as symmetry breaking and local order parameters [1] . This framework fails to describe topological phase transitions [2, 3] for which there is no local order parameter. Moreover, identifying the proper order parameters of systems whose symmetry-breaking patterns are unknown is difficult. Information-theoretic quantities are particularly promising for studying phase transitions without relying on this traditional paradigm. Such quantities are universal and their computation does not require a detailed analysis of the system’s physics, such as its order parameters.  \nIn this context, the classical Fisher information (FI) [4] and its quantum counterpart [5] have been extensively studied as universal indicators of phase transitions, i.e. , as quantities whose maxima are signatures of critical points. The FI is a generalized susceptibility that measures the sensitivity of the system with respect to a tuning parameter. In the case of classical equilibrium systems, it measures fluctuations in the system’s collective variables and is proportional to well-known response functions, such as the magnetic susceptibility orthe heat capacity [6] . Similarly, the quantum FI reduces to the fidelity susceptibility [7–9], i.e., the leadingorder response of the fidelity between quantum states to parameter fluctuations. The fidelity susceptibility has been shown to detect symmetry-breaking [10, 11], topological [12–14], and Berezinskii-Kosterlitz-Thouless-type (BKT-type) [15, 16] quantum phase transitions. Moreover, the quantum FI has been used to investigate finitetemperature transitions as well as non-equilibrium phenomena, such as dissipative [17–19], dynamical [20, 21], or excited-state [22] phase transitions.  \nRecently, also machine learning (ML) has emerged as an alternative paradigm for studying phase transitions [23–25] . The appeal of ML methods is akin to the one of information-theoretic approaches: they are generic and can be used to characterize a system using minimal explicit knowledge of its underlying physics. A large class of ML methods are based on solving clas-  \nsification or regression tasks using predictive models such as neural networks (NNs) [26–30] . By analyzing the model predictions, indicators of phase transitions are computed whose local maxima mark critical points. This framework has been employed to investigate many systems, including symmetry-breaking [26– 39], topological [26, 27 , 29 , 30 , 32–35, 37 , 40 , 41], and non-equilibrium [27, 28 , 37 , 42–45] phase transitions in both the classical and quantu","cbCailNpfsxcoQjJ","https://ap.wps.com/l/cbCailNpfsxcoQjJ","pdf",811201,1,18,"English","en",105,"# Introduction\n## Fisher information as an indicator of phase transitions\n## Machine learning as an alternative paradigm\n# Detecting phase transitions from data","[{\"question\":\"What fundamental gap does the work address about ML phase-transition detection?\",\"answer\":\"It targets the lack of an explicit working principle and well-defined fundamental limits for machine-learning indicators derived from data.\"},{\"question\":\"How are ML indicators connected to Fisher information in this research?\",\"answer\":\"The paper proves that a broad class of ML indicators lower-bound and approximate the square root of the system’s (quantum) Fisher information with respect to the tuning parameter.\"},{\"question\":\"What do the numerical demonstrations cover?\",\"answer\":\"They assess the tightness and quality of the derived bounds for phase transitions in both classical and quantum systems.\"}]","Machine learning phase transitions - Connections to the Fisher information | PDF",1785680741,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-phase-transitions-connections-to-the-fisher-information","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-phase-transitions-connections-to-the-fisher-information/118010/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What fundamental gap does the work address about ML phase-transition detection?","Question",{"text":75,"@type":76},"It targets the lack of an explicit working principle and well-defined fundamental limits for machine-learning indicators derived from data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are ML indicators connected to Fisher information in this research?",{"text":80,"@type":76},"The paper proves that a broad class of ML indicators lower-bound and approximate the square root of the system’s (quantum) Fisher information with respect to the tuning parameter.",{"name":82,"@type":73,"acceptedAnswer":83},"What do the numerical demonstrations cover?",{"text":84,"@type":76},"They assess the tightness and quality of the derived bounds for phase transitions in both classical and quantum systems.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]