[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84541-en":3,"doc-seo-84541-105":29,"detail-sidebar-cat-0-en-105":90},{"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":13,"seo_description":14,"update_tm":27,"read_time":28},84541,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Validating Causal Abstraction Metrics on Simulated Complex Systems","Science requires explanations that connect high-level causal accounts to the behavior produced by lower-level mechanisms. No shared method exists for judging whether a proposed high-level explanation is valid. This work introduces a benchmark of ten simulated complex systems, covering discrete/continuous states and static/dynamical regimes, each with ground-truth causal explanations and invalid contrastive conditions. It evaluates more than thirty candidate metrics and shows that only causal-family metrics with faithfulness testing over unmapped variables reliably distinguish valid from invalid abstractions.","arXiv :2607 .00267v1 [ cs .LG] 30 Jun 2026  \nValidating Causal Abstraction Metrics on Simulated Complex Systems  \nMaxime Méloux 1 Tiago Pimentel2 François Portet 1 Maxime Peyrard 1  \n1Université Grenoble Alpes, CNRS, Grenoble INP, LIG 2ETH Zürich  \n{melouxm, portetf, [peyrardm}@univ-grenoble-alpes.fr](peyrardm}@univ-grenoble-alpes.fr)[ ](peyrardm}@univ-grenoble-alpes.fr)[tiago.pimentel@inf.ethz.ch](tiago.pimentel@inf.ethz.ch)  \nAbstract  \nA central goal of science is to produce valid explanations of complex systems: high-level causal accounts that faithfully reflect the behavior of lower-level mechanisms. Yet no consensus exists on how to measure whether a proposed high-level explanation is actually valid. We introduce a benchmark of ten complex systems spanning both discrete and continuous state spaces, as well as static and dynamical regimes, each equipped with consensual ground-truth causal explanations and invalid contrastive conditions. Within a unified causal abstraction framework, we systematically evaluate over thirty candidate metrics drawn from observational, functional, information-theoretic, and causal families. Our results show that only the latter reliably discriminates valid from invalid abstractions, and only when incorporating faithfulness testing over unmapped variables. Building on these findings, we introduce the Causal Abstraction Error (CAE), a continuous validity metric with an explicit faithfulness test, which passes all discrimination tests across every system and can converge with as few as 30 sampled interventions. We offer it as a general-purpose metric for the discovery and validation of high-level explanations.  \n1 Introduction  \nA central goal of science is to produce explanations: not merely descriptions or predictions, but accounts of why phenomena occur [Hempel, 1965, Woodward, 2004] . While the philosophy of science has long debated what explanations are, a working consensus has emerged around a few core desiderata: good scientific explanations should be causally informative [Woodward, 2004, Pearl, 2009, Salmon, 1984], parsimonious [Kitcher, 1989, Batterman and Rice, 2014], and appropriately scoped to the context and level of description at which the target phenomenon is best characterized [Lombrozo, 2006, Potochnik, 2017] . Finding good explanations is particularly difficult when the system under study exhibits what Warren Weaver famously called organized complexity [Weaver, 1991]: systems with many interacting parts that are neither so disordered as to yield to statistical averaging, nor so simple as to admit direct analytic treatment. The appropriate high-level variables for explanation must be discovered, and the class of functions that legitimately aggregate low-level quantities into those variables is itself a subject of inquiry [Hoel et al., 2013, Potochnik, 2017] .  \nThis raises a fundamental challenge: what are useful high-level variables, and how should they be defined from lower-level quantities? Different fields studying different classes of complex systems have developed their own candidate answers, such as firing rates and population codes in systems neuroscience [Cunningham and Yu, 2014], or species abundance and trophic levels in ecology [Loreau, 2010] . However, a unified cross-disciplinary methodology for evaluating high-level explanations of complex systems remains elusive. A sobering illustration of why comes from Jonas and Kording [2017], who applied the standard causal and statistical toolkit of neuroscience to a fully observable microprocessor: a relatively simple system engineered for modular, hierarchical organization. In doing so, they failed to recover meaningful high-level properties of this system. The recent success of  \nPreprint.  \nartificial intelligence (AI) offers a similar account. Similarly to microprocessors, modern AI systems are structurally complex, yet they are fully observable and perfectly manipulable, a rare property in the natural sciences. This pr","cbCaie1RMaR5Pb7e","https://ap.wps.com/l/cbCaie1RMaR5Pb7e","pdf",1443216,1,40,"English","en",105,"# Introduction\n## Evaluating high-level explanations\n## Causal abstraction framework\n## Benchmarking candidate validity metrics","[{\"question\":\"What problem does the work address about causal abstraction?\",\"answer\":\"It addresses the lack of a consensus method to measure whether a high-level causal explanation faithfully reflects lower-level mechanisms in complex systems.\"},{\"question\":\"What does the benchmark include?\",\"answer\":\"The benchmark contains ten simulated complex systems spanning discrete/continuous state spaces and static/dynamical regimes, each with consensual ground-truth causal explanations plus invalid contrastive conditions.\"},{\"question\":\"How do the authors validate which metrics work best?\",\"answer\":\"They systematically evaluate over thirty candidate metrics across observational, functional, information-theoretic, and causal families, and show that only causal-family metrics with faithfulness testing over unmapped variables reliably discriminate valid from invalid abstractions.\"}]",1784196528,101,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"validating-causal-abstraction-metrics-on-simulated-complex-systems","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/validating-causal-abstraction-metrics-on-simulated-complex-systems/84541/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does the work address about causal abstraction?","Question",{"text":74,"@type":75},"It addresses the lack of a consensus method to measure whether a high-level causal explanation faithfully reflects lower-level mechanisms in complex systems.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What does the benchmark include?",{"text":79,"@type":75},"The benchmark contains ten simulated complex systems spanning discrete/continuous state spaces and static/dynamical regimes, each with consensual ground-truth causal explanations plus invalid contrastive conditions.",{"name":81,"@type":72,"acceptedAnswer":82},"How do the authors validate which metrics work best?",{"text":83,"@type":75},"They systematically evaluate over thirty candidate metrics across observational, functional, information-theoretic, and causal families, and show that only causal-family metrics with faithfulness testing over unmapped variables reliably discriminate valid from invalid abstractions.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,118,121,126,129,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":21,"slug":117},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":119,"slug":120},30,"research-report",{"id":122,"doc_module":4,"doc_module_name":45,"category_name":123,"show_sort_weight":124,"slug":125},9,"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]