A Dynamical Systems Equivalence Model of Brain and Transformer-Based Language Models

A Dynamical Systems Equivalence Model of Brain and Transformer-Based 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 A Dynamical Systems Equivalence Model of Brain and Transformer-Based Language Models Karthik Gokuladas Menon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9603032/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 In this study, a dynamical systems framework for biological neural systems and transformer-based large language models (LLMs) is presented along with a systematic empirical test of brain-transformer representational equivalence across five distinct model architectures. Both the brain and LLMs are formalised as high-dimensional nonlinear state-space dynamical systems, with structural mappings between neural population activity, EEG observables, transformer residual-stream activations, and output logits. Using the ZuCo naturalistic reading (Task-NR) EEG dataset, a layer-wise Representational Similarity Analysis (RSA) and linear encoding modelling are conducted on GPT-2, BERT-Large, Mistral-7B, DeepSeek-7B, and Qwen3.5-9B equipped with a Sparse Autoencoder (SAE). Dense model architectures produced peak RSA alignment of ρ ≈ 0.054-0.055 with EEG theta and alpha bands, and negative cross-validated encoding model R2, indicating a fundamental geometric mismatch between polysemantic dense representations and neural codes. In contrast, sparse, monosemantic SAE features extracted from Qwen3.5-9B yielded a peak RSA alignment of ρ = 0.221 at layer 0 of a 32-layer sweep, representing a 4.3x improvement in biological alignment and saturating the lower noise ceiling (ρ_half = 0.221, ρ_upper = 0.362). The SAE encoding model achieves positive cross-validated R2 (0.15-0.27 across EEG channels), confirming linearly decodable neural predictions. Partial RSA controlling for sentence length and word length yields ρ = 0.044 (p = 1.8 x 10^-26) with a suppressor effect, ruling out surface-level confounds. It is argued that this improvement reflects a deep convergence. Biological brains and SAE-disentangled transformers both implement sparse distributed codes over a high-dimensional state space, and this shared representational geometry underpins the observed equivalence. The results of this study could have implications for AI interpretability, the mechanistic basis of machine psychology, and the neuroscience of semantic processing. Computational Neuroscience Artificial Intelligence and Machine Learning Dynamical Systems Transformer Architecture Neural Dynamics Representational Similarity Analysis Sparse Autoencoders Interpretability 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-9603032","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":633762971,"identity":"b5dfd8a2-63e5-4d50-8371-fd77cd6f8e58","order_by":0,"name":"Karthik Gokuladas Menon","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIiWNgGAWjYBACCSBmZjBIgPGBDPYGIG1ggU8LYzOqFp4DIC0SBLQwIGuRSIBZjx1Itp99/rigIM1ubXvvwccFDEDGzOdXN/wokGDgb+9OwKZFmifdsHmGQU7ytjPnko1nMAAZt3PKbvYAHSZx5uwGbFrkGNIYm3kMKpLNbuSYSfMwABm3c9Ju8AC1GEjkYtfC/wyq5f4bqJabZ9Ju/sGjRVoCbEuOndkNHpAWEIP92G18tkjOeMY4m8cgLcHsTI6xMZTBdlvGQIIHl18kzqcxfOb5k2xvdvyM4WOeChDj+LObb/7YyPG392LVAgOJDWDKAMTgMQAxefApBwF7JAb7A0KqR8EoGAWjYGQBAJLJX+Z14xDMAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0001-5820-4474","institution":"Independent Researcher","correspondingAuthor":true,"prefix":"","firstName":"Karthik","middleName":"Gokuladas","lastName":"Menon","suffix":""}],"badges":[],"createdAt":"2026-05-04 00:48:12","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-9603032/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9603032/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108517812,"identity":"4bd81559-4ef0-40ad-b22f-3a49371052b0","added_by":"auto","created_at":"2026-05-05 13:49:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1753841,"visible":true,"origin":"","legend":"","description":"","filename":"BrainTransformersPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9603032/v1_covered_3d2478a7-f5f8-4785-baa1-eb7d1b0673ea.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Dynamical Systems Equivalence Model of Brain and Transformer-Based Language Models\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Independent Researcher","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":"Dynamical Systems, Transformer Architecture, Neural Dynamics, Representational Similarity Analysis, Sparse Autoencoders, Interpretability","lastPublishedDoi":"10.21203/rs.3.rs-9603032/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9603032/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eIn this study, a dynamical systems framework for biological neural systems and transformer-based large language models (LLMs) is presented along with a systematic empirical test of brain-transformer representational equivalence across five distinct model architectures. Both the brain and LLMs are formalised as high-dimensional nonlinear state-space dynamical systems, with structural mappings between neural population activity, EEG observables, transformer residual-stream activations, and output logits. Using the ZuCo naturalistic reading (Task-NR) EEG dataset, a layer-wise Representational Similarity Analysis (RSA) and linear encoding modelling are conducted on GPT-2, BERT-Large, Mistral-7B, DeepSeek-7B, and Qwen3.5-9B equipped with a Sparse Autoencoder (SAE). Dense model architectures produced peak RSA alignment of ρ ≈ 0.054-0.055 with EEG theta and alpha bands, and negative cross-validated encoding model R2, indicating a fundamental geometric mismatch between polysemantic dense representations and neural codes. In contrast, sparse, monosemantic SAE features extracted from Qwen3.5-9B yielded a peak RSA alignment of ρ = 0.221 at layer 0 of a 32-layer sweep, representing a 4.3x improvement in biological alignment and saturating the lower noise ceiling (ρ_half = 0.221, ρ_upper = 0.362). The SAE encoding model achieves positive cross-validated R2 (0.15-0.27 across EEG channels), confirming linearly decodable neural predictions. Partial RSA controlling for sentence length and word length yields ρ = 0.044 (p = 1.8 x 10^-26) with a suppressor effect, ruling out surface-level confounds. It is argued that this improvement reflects a deep convergence. Biological brains and SAE-disentangled transformers both implement sparse distributed codes over a high-dimensional state space, and this shared representational geometry underpins the observed equivalence. The results of this study could have implications for AI interpretability, the mechanistic basis of machine psychology, and the neuroscience of semantic processing.\u003c/em\u003e\u003c/p\u003e","manuscriptTitle":"A Dynamical Systems Equivalence Model of Brain and Transformer-Based Language Models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-05 13:49:01","doi":"10.21203/rs.3.rs-9603032/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":"c6878317-23c5-44c3-b13b-9451f18dad66","owner":[],"postedDate":"May 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":67448374,"name":"Computational Neuroscience"},{"id":67448375,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2026-05-05T13:49:01+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-05 13:49:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9603032","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9603032","identity":"rs-9603032","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}