Semantic Valued Schema Theory of Genetic Programming in Symbolic Regression

Semantic Valued Schema Theory of Genetic Programming in Symbolic Regression | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Semantic Valued Schema Theory of Genetic Programming in Symbolic Regression Yilin Liu, Zhengwen Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8316711/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Schema Theory offers a principled lens for analyzing the dynamics of Evolutionary Algorithms (EAs), yet its extension to Genetic Programming (GP) is obstructed by the nonlinear structure of GP trees and the irregular correspondence between syntax and semantics. These characteristics prevent classical, structure-based schema formulations from capturing the mechanisms that determine how information is preserved, disrupted, and propagated during GP evolution. Motivated by the significant role of semantics in GP, this study introduces Valued Schema Theory (VST), which characterizes a schema through both its semantic output and the quantity of effective genetic material it carries. Beyond providing a semantic definition of schemata, the proposed theory models the flow of value through GP populations. It describes schema dynamics through a pessimistic survival inequality that integrates selection pressure, crossover-induced structural disruption, and the differing robustness of significant meaning and zero-valued regions. This formulation yields a tractable account of how meaningful information spreads while non-informative regions function as protective buffers. Empirical evaluation across four representative benchmark tasks covering Boolean regression, numerical symbolic regression, and symbolic-regression-like classification shows that VST achieves consistently high accuracy in predicting schema-frequency transitions. These results indicate that VST captures the microscopic mechanisms through which semantic information is redistributed during GP evolution, providing a coherent account of GP’s underlying search dynamics. Schema Theory Genetic Programming Evolutionary Dynamics Symbolic Regression. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 31 Mar, 2026 Reviews received at journal 30 Mar, 2026 Reviews received at journal 19 Feb, 2026 Reviews received at journal 17 Jan, 2026 Reviewers agreed at journal 09 Jan, 2026 Reviewers agreed at journal 22 Dec, 2025 Reviewers agreed at journal 20 Dec, 2025 Reviewers invited by journal 19 Dec, 2025 Editor assigned by journal 09 Dec, 2025 Submission checks completed at journal 09 Dec, 2025 First submitted to journal 09 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8316711","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":564068875,"identity":"6fd38211-1f99-4cd5-bff1-7392fef3281b","order_by":0,"name":"Yilin Liu","email":"","orcid":"","institution":"Brunel University London","correspondingAuthor":false,"prefix":"","firstName":"Yilin","middleName":"","lastName":"Liu","suffix":""},{"id":564068876,"identity":"8dbf3ec6-7249-4ed5-a0c8-a31f94e1adbc","order_by":1,"name":"Zhengwen Huang","email":"data:image/png;base64,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","orcid":"","institution":"Brunel University London","correspondingAuthor":true,"prefix":"","firstName":"Zhengwen","middleName":"","lastName":"Huang","suffix":""}],"badges":[],"createdAt":"2025-12-09 10:53:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8316711/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8316711/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99309032,"identity":"6ec4b6da-0b72-4c19-a08f-977fa742af84","added_by":"auto","created_at":"2025-12-31 16:09:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":948852,"visible":true,"origin":"","legend":"","description":"","filename":"SemanticValuedSchemaTheoryforGeneticProgramminginSymbolicRegressionSubmitVer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8316711/v1_covered_5d7540d4-7a5a-4425-bf47-6b7a611fede1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Semantic Valued Schema Theory of Genetic Programming in Symbolic Regression","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"genetic-programming-and-evolvable-machines","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"genp","sideBox":"Learn more about [Genetic Programming and Evolvable Machines](http://link.springer.com/journal/10710)","snPcode":"10710","submissionUrl":"https://submission.nature.com/new-submission/10710/3","title":"Genetic Programming and Evolvable Machines","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Schema Theory, Genetic Programming, Evolutionary Dynamics, Symbolic Regression.","lastPublishedDoi":"10.21203/rs.3.rs-8316711/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8316711/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Schema Theory offers a principled lens for analyzing the dynamics of Evolutionary Algorithms (EAs), yet its extension to Genetic Programming (GP) is obstructed by the nonlinear structure of GP trees and the irregular correspondence between syntax and semantics. 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