Inference Equivalence: A Decoder-Constrained Framework for Representation Sufficiency in Neural Population Codes

Inference Equivalence: A Decoder-Constrained Framework for Representation Sufficiency in Neural Population Codes | 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 Inference Equivalence: A Decoder-Constrained Framework for Representation Sufficiency in Neural Population Codes Cam H. Pham This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9684727/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 Neural population analyses commonly evaluate representation-preserving transformations by assessing whether selected response statistics—such as firing rates and covariance structure—are maintained. Yet preservation of descriptive statistics does not guarantee preservation of downstream computation, because achievable inference depends on the constraints imposed on biological readout. We introduce Inference Equivalence (IE), a decoder-constrained framework for assessing representation sufficiency in neural population codes. IE defines functional equivalence through invariance of achievable inference risk within a specified decoder family, interpreted as biologically plausible downstream cortical decoding under synaptic and computational constraints. Rather than comparing neural representations through statistical similarity alone, IE evaluates whether distinct representations support equivalent perceptual or decision-related inference after decoder re-optimization. Using controlled perturbations of neural population activity, we show that preservation of low-order response statistics is neither necessary nor sufficient to preserve achievable decoding performance. Conversely, representations with substantial statistical distortions can remain functionally equivalent after decoder adaptation. These results establish IE as a practical and falsifiable framework for assessing functional equivalence in neural population codes and clarify when statistical similarity does—or does not—support equivalent downstream computation. Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterials.zip 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-9684727","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":639605948,"identity":"5d936850-00aa-4843-b8b1-f1feb0fd9842","order_by":0,"name":"Cam H. 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