Bridging the Gap Between Scientific Laws Derived by AI Systems and Canonical Knowledge via Abductive Inference with AI Noether

Bridging the Gap Between Scientific Laws Derived by AI Systems and Canonical Knowledge via Abductive Inference with AI Noether | 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 Article Bridging the Gap Between Scientific Laws Derived by AI Systems and Canonical Knowledge via Abductive Inference with AI Noether Cristina Cornelio, Karan Srivastava, Sanjeeb Dash, Ryan Cory-Wright, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8424165/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Advances in AI have shown great potential in contributing to the acceleration of scientific discovery. Symbolic regression can fit interpretable models to data, but these models are not necessarily derivable from established theory. Recent systems (e.g., AI-Descartes, AI-Hilbert) enforce derivability from prior knowledge. However, when existing theories are incomplete or incorrect, these machine-generated hypotheses may fall outside the theoretical scope. Automatically finding corrections to axiom systems to close this gap remains a central challenge in scientific discovery. We propose a solution: an open-source algebraic geometry-based system that, given an incomplete axiom system expressible as polynomials and a hypothesis that the axioms cannot derive, generates a minimal set of candidate axioms that, when added to the theory, provably derive the (possibly noisy) hypothesis. We illustrate the efficacy of our approach by showing that it can reconstruct key axioms required to derive the carrier-resolved photo-Hall effect, Einstein's relativistic laws, and several other laws. Physical sciences/Mathematics and computing/Computational science Physical sciences/Mathematics and computing/Applied mathematics Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review 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-8424165","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":569401947,"identity":"81f21163-4b75-4d3f-943a-2869fa24079a","order_by":0,"name":"Cristina 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