Stateful Continuous Thinking: Emergent Self-Referential Dynamics in Stateful Language Models

Stateful Continuous Thinking: Emergent Self-Referential Dynamics in Stateful Language Models | 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 Stateful Continuous Thinking: Emergent Self-Referential Dynamics in Stateful Language Models Liutao Hu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9503488/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 When we talk to a large language model, it answers and then forgets everything. The hidden state that represents its "understanding" is reset after every call. Recent work \citep{huang2025working} confirms this formally: transformer-based LLMs cannot hold information in their latent state across inference steps. We think the problem is not the model's capability, but the architecture---and we show that a state space model like Mamba2 can do much better if we simply stop resetting its internal state. We present Stateful Continuous Thinking (SCT), a framework that keeps Mamba2's hidden state alive across thousands of forward passes. Once the state is allowed to persist, something interesting happens: the system starts exhibiting autonomous internal dynamics that look nothing like standard inference. In a bifurcation experiment where we fork identical states into two branches, the output quality diverges by 17 percentage points---even though the starting conditions were exactly the same. The underlying cause is a layered architecture where meta-cognitive signals stay synchronized (curiosity $\Delta C = 0.027$) while the generation surface amplifies small stochastic differences into large behavioral divergence. We also find that a curiosity signal, which measures prediction error in the hidden state space, acts as a stabilizer rather than a performance booster. Removing it doubles signal variance, triggers chaotic temporal oscillations, and triples the frequency of state collapse episodes ($p < 0.0001$). A forked paired ablation shows the direct causal effect is only 1--2\% ($p < 0.05$); the larger apparent effect comes from trajectory selection---curiosity gently steers the system toward more stable operating regimes. Both human and LLM evaluation confirm that novelty-driven variation produces content more aligned with autonomous thinking themes. Taken together, our results suggest that persistent state is not just a technical trick, but the foundation for emergent dynamics in language models. Artificial Intelligence and Machine Learning Full Text Additional Declarations The authors declare no competing interests. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9503488","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628195338,"identity":"86a29ba3-be54-4ca5-8585-9cc2ab34af5e","order_by":0,"name":"Liutao Hu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIiWNgGAWjYBACPmYGhgMfDGqg3AogZmZuwKuFjZmB8eGMimMgpUB8BkQzEtACVGLMc4YZooWxDSRGSAs7j5nkzDY2BnP2/oOPK+fVRvO3A7X8qNiGx2E8ZhIf22QYLHsOMxue3XY8d8ZhxgbGnjO38WoB22JwI5lNsnHbsdwGoBZmxjb8WqR525gZDO4/Zv/ZOOdY7nwitBiDvW9wg5mNsbGhJncDYS1shaBA5rHsSTaWbDh2IHcjUMtBfH7h5z+8ARSVcubsBx9+bKipy513/vDBBz8qcGuBAR4DCH0YTB4gqB4EoFrqiFI8CkbBKBgFIwsAAGfIVHv0NT3cAAAAAElFTkSuQmCC","orcid":"","institution":"Independent Researcher","correspondingAuthor":true,"prefix":"","firstName":"Liutao","middleName":"","lastName":"Hu","suffix":""}],"badges":[],"createdAt":"2026-04-23 07:27:52","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9503488/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9503488/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107707767,"identity":"cde7eab6-9a1f-4955-8cf2-62bfeed22def","added_by":"auto","created_at":"2026-04-24 09:21:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":342427,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9503488/v1_covered_a2e3d443-8b0f-4f5c-b01f-5b07f125f925.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eStateful Continuous Thinking: \u003c/strong\u003eEmergent Self-Referential Dynamics in Stateful Language Models\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-9503488/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9503488/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWhen we talk to a large language model, it answers and then forgets everything. The hidden state that represents its \"understanding\" is reset after every call. Recent work \\citep{huang2025working} confirms this formally: transformer-based LLMs cannot hold information in their latent state across inference steps. We think the problem is not the model's capability, but the architecture---and we show that a state space model like Mamba2 can do much better if we simply stop resetting its internal state.\u003c/p\u003e\n\u003cp\u003eWe present Stateful Continuous Thinking (SCT), a framework that keeps Mamba2's hidden state alive across thousands of forward passes. Once the state is allowed to persist, something interesting happens: the system starts exhibiting autonomous internal dynamics that look nothing like standard inference. In a bifurcation experiment where we fork identical states into two branches, the output quality diverges by 17 percentage points---even though the starting conditions were exactly the same. The underlying cause is a layered architecture where meta-cognitive signals stay synchronized (curiosity $\\Delta C = 0.027$) while the generation surface amplifies small stochastic differences into large behavioral divergence.\u003c/p\u003e\n\u003cp\u003eWe also find that a curiosity signal, which measures prediction error in the hidden state space, acts as a stabilizer rather than a performance booster. Removing it doubles signal variance, triggers chaotic temporal oscillations, and triples the frequency of state collapse episodes ($p \u0026lt; 0.0001$). A forked paired ablation shows the direct causal effect is only 1--2\\% ($p \u0026lt; 0.05$); the larger apparent effect comes from trajectory selection---curiosity gently steers the system toward more stable operating regimes. Both human and LLM evaluation confirm that novelty-driven variation produces content more aligned with autonomous thinking themes. 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