Escaping the Inequality Attractor: Truncated Backpropagation, Top-Tail Taxation, and Pareto Calibration in a Differentiable Agent-Based Model

Escaping the Inequality Attractor: Truncated Backpropagation, Top-Tail Taxation, and Pareto Calibration in a Differentiable Agent-Based Model | 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 Escaping the Inequality Attractor: Truncated Backpropagation, Top-Tail Taxation, and Pareto Calibration in a Differentiable Agent-Based Model JUAN MOISES DE LA SERNA TUYA This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9320806/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Differentiable agent-based models enable gradient-based calibration against empirical targets, yet egalitarian economies — where Gini targets lie far below the model's natural attractor (~0.47–0.53) — present a fundamental gradient-vanishing problem. We present Civilization-ABM v5, addressing three interconnected limitations of its predecessor. First, a C∞-differentiable top-tail wealth tax targeting the wealthiest 10% via a sigmoid soft-threshold provides a high-magnitude gradient (∂L/∂τ ≈ −10.3) that escapes the attractor. Second, Truncated Backpropagation Through Time (TBPTT, K=10) provides locally stable gradient estimates without propagating through the full attractor horizon. Third, an epsilon-constraint Pareto-front calibrator traces the Gini–Palma trade-off surface, revealing structural tensions that scalar optimisers cannot resolve. Applied to five World Bank archetypes (Nordic, European, United States, Latin America, South Africa), v5 reduces Nordic ΔGini from 0.128 to 0.008 (17-fold improvement) and achieves ΔPalma=0.166 for South Africa. An ablation study on the Nordic archetype confirms that the top-tail tax is the primary attractor-escape mechanism (65.7% loss reduction), while TBPTT contributes secondary refinement. The Nordic Pareto analysis demonstrates that joint World Bank targets (Gini=0.270, Palma=0.90) are structurally unattainable in this model class. We propose a general recipe for gradient-based calibration of agent-based models with attractor dynamics. JEL Classification: C63 · D31 · C61 · E62 · C15 agent-based model differentiable simulation wealth inequality Palma ratio truncated backpropagation Pareto calibration Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-9320806","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":621515814,"identity":"6d7a07c3-bde8-45c6-97d3-48a2365fedcd","order_by":0,"name":"JUAN MOISES DE LA SERNA TUYA","email":"data:image/png;base64,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","orcid":"","institution":"Universidad Internacional De La Rioja","correspondingAuthor":true,"prefix":"","firstName":"JUAN","middleName":"MOISES DE LA SERNA","lastName":"TUYA","suffix":""}],"badges":[],"createdAt":"2026-04-04 13:25:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9320806/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9320806/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107482736,"identity":"8a3d428f-199d-4b50-a980-130794bc918b","added_by":"auto","created_at":"2026-04-22 02:24:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":353734,"visible":true,"origin":"","legend":"","description":"","filename":"jeicmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9320806/v1_covered_86c9072e-c7df-40d7-9f00-a525ebe74451.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Escaping the Inequality Attractor: Truncated Backpropagation, Top-Tail Taxation, and Pareto Calibration in a Differentiable Agent-Based Model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"agent-based model, differentiable simulation, wealth inequality, Palma ratio, truncated backpropagation, Pareto calibration","lastPublishedDoi":"10.21203/rs.3.rs-9320806/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9320806/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDifferentiable agent-based models enable gradient-based calibration against empirical targets, yet egalitarian economies — where Gini targets lie far below the model's natural attractor (~0.47–0.53) — present a fundamental gradient-vanishing problem. We present Civilization-ABM v5, addressing three interconnected limitations of its predecessor. First, a C∞-differentiable top-tail wealth tax targeting the wealthiest 10% via a sigmoid soft-threshold provides a high-magnitude gradient (∂L/∂τ ≈ −10.3) that escapes the attractor. Second, Truncated Backpropagation Through Time (TBPTT, K=10) provides locally stable gradient estimates without propagating through the full attractor horizon. Third, an epsilon-constraint Pareto-front calibrator traces the Gini–Palma trade-off surface, revealing structural tensions that scalar optimisers cannot resolve. Applied to five World Bank archetypes (Nordic, European, United States, Latin America, South Africa), v5 reduces Nordic ΔGini from 0.128 to 0.008 (17-fold improvement) and achieves ΔPalma=0.166 for South Africa. An ablation study on the Nordic archetype confirms that the top-tail tax is the primary attractor-escape mechanism (65.7% loss reduction), while TBPTT contributes secondary refinement. 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