S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning

S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning | 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 S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning said slaoui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9251795/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 This article introduces S-AI-Recursive, a bio-inspired Sparse Artificial Intelligence architecture in which reasoning is operationalized as a hormonal closed-loop iteration rather than a single feed-forward pass. Building upon the S-AI foundational framework [1], the hormonal–probabilistic unification doctrine [2], and the formal mathematical methodology established in S-AI-IoT [3], the present work formalizes the Recursive Reasoning Cycle (RRC) as a dynamical system governed by two novel hormones — Clarifine , a convergence signal, and Confusionin , an uncertainty detector — whose antagonistic regulation drives iterative state refinement toward a stable cognitive equilibrium. The complete mathematical framework is developed: recursive state dynamics, Lyapunov stability proof, entropic contraction theorem, hormonal stopping criterion with finite-time termination guarantee, Euler–Maruyama discretization with projection, primal-dual agent-selection under iteration budget, and recursive engram memory with warm-start acceleration. Experimental validation on the SAI-UT+ testbench demonstrates that S-AI-Recursive achieves competitive reasoning performance on abstract and symbolic benchmarks with fewer than ten million parameters, confirming the central principle of temporal parsimony : iterative cognitive depth substitutes for architectural width. Artificial Intelligence and Machine Learning Sparse Artificial Intelligence Recursive Reasoning Hormonal Orchestration Clarifine Confusionin Lyapunov Stability Entropic Contraction Temporal Parsimony Iterative Cognitive Equilibrium Bio-Inspired Modular AI 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-9251795","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":613702735,"identity":"d8f1dd70-a81d-44a5-a2ef-e4a70e60f911","order_by":0,"name":"said slaoui","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYHACxgNAgoefgYH9A9F6wFokGxjYiLcGpIXB4ACxWuQb2B8c+FFxWMb4Rnba4woGO3kGscMP8GoxOMBjcLDnzGEesxu52w3PMCQbNkinGeDXwsDDcIC3DaxlA9A/zAkM0gn4tYAcdvAvUIvxDLCWeqCWdAIhd4DB4DDIFgOJ3G1ALYeBWnIIOAyo+LDMmXQeiTNvNxs2GBw3bJPOKcDvsPb2hw/fVFjb87fnbnzYUFEtzy+dvgG/w5hRLWUgJUJHwSgYBaNgFOACABX1QgIXA026AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0001-6900-8102","institution":"Mohammed V university","correspondingAuthor":true,"prefix":"","firstName":"said","middleName":"","lastName":"slaoui","suffix":""}],"badges":[],"createdAt":"2026-03-28 10:13:06","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-9251795/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9251795/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105904584,"identity":"93722ede-a768-4900-9c4f-ca2ea2c2d85f","added_by":"auto","created_at":"2026-04-01 10:09:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":837178,"visible":true,"origin":"","legend":"","description":"","filename":"SlaouiSAIRecursive.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9251795/v1_covered_7750e441-4b3d-49e5-824d-9a94344a471e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eS-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning\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":true,"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":"Sparse Artificial Intelligence, Recursive Reasoning, Hormonal Orchestration, Clarifine, Confusionin, Lyapunov Stability, Entropic Contraction, Temporal Parsimony, Iterative Cognitive Equilibrium, Bio-Inspired Modular AI","lastPublishedDoi":"10.21203/rs.3.rs-9251795/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9251795/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article introduces S-AI-Recursive, a bio-inspired Sparse Artificial Intelligence architecture in which reasoning is operationalized as a hormonal closed-loop iteration rather than a single feed-forward pass. Building upon the S-AI foundational framework [1], the hormonal–probabilistic unification doctrine [2], and the formal mathematical methodology established in S-AI-IoT [3], the present work formalizes the Recursive Reasoning Cycle (RRC) as a dynamical system governed by two novel hormones — \u003cstrong\u003eClarifine\u003c/strong\u003e, a convergence signal, and \u003cstrong\u003eConfusionin\u003c/strong\u003e, an uncertainty detector — whose antagonistic regulation drives iterative state refinement toward a stable cognitive equilibrium. The complete mathematical framework is developed: recursive state dynamics, Lyapunov stability proof, entropic contraction theorem, hormonal stopping criterion with finite-time termination guarantee, Euler–Maruyama discretization with projection, primal-dual agent-selection under iteration budget, and recursive engram memory with warm-start acceleration. Experimental validation on the SAI-UT+ testbench demonstrates that S-AI-Recursive achieves competitive reasoning performance on abstract and symbolic benchmarks with fewer than ten million parameters, confirming the central principle of \u003cstrong\u003etemporal parsimony\u003c/strong\u003e: iterative cognitive depth substitutes for architectural width.\u003c/p\u003e","manuscriptTitle":"S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-31 04:10:44","doi":"10.21203/rs.3.rs-9251795/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"64f237b6-8e0a-4edd-8691-c34f542ec658","owner":[],"postedDate":"March 31st, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65304929,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2026-03-31T04:10:44+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-31 04:10:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9251795","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9251795","identity":"rs-9251795","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}