Structure Complexity Entropy: A Principle for Structural Intelligence in AI

Structure Complexity Entropy: A Principle for Structural Intelligence in AI | 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 Structure Complexity Entropy: A Principle for Structural Intelligence in AI Luan Zhirong, Shaobo Zheng, Yujun Lai, Haoran Ding, Lujuan Dang, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8609404/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 Human intelligence excels at decomposing complex information into meaningful hierarchical structures, yet this capability remains a fundamental challenge for artificial intelligence. Current approaches, from manual curation to automated clustering, lack a principled way to quantify and autonomously discover such structures, often resulting in rigid binaries or semantically incoherent groupings. Here, we introduce Structural Complexity Entropy (SCEntropy), a novel metric that quantifies the internal disorder of an information set by measuring the heterogeneity of all pairwise relationships. SCEntropy provides AI with a foundational principle: a low value signifies a coherent concept, whereas a high value signals the need for decomposition. Leveraging this, we develop SCEntropy-driven Hierarchical Clustering (SHC), an algorithm that uses a single complexity threshold to autonomously construct multi-branch, semantically coherent hierarchies from the bottom up. We validate this principle across two core domains. In visual concept discovery, SHC not only recovers known taxonomies in image datasets like CIFAR-100 but also discovers semantically coherent and human-aligned super-categories, demonstrating an ability for autonomous knowledge structuring. Conversely, in natural language generation, we show that SCEntropy-derived hierarchies serve as a scaffold for coherent reasoning. By structurally constraining large language models, we enhance thematic focus and logical flow in multi-turn dialogues, mitigating semantic drift. Our work establishes SCEntropy as a universal framework for structural machine intelligence, enabling AI to not only discover how the world is organized but also to discipline its own internal processes, paving the way for more autonomous and interpretable systems. Physical sciences/Mathematics and computing/Computer science Physical sciences/Physics/Information theory and computation Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementaryinformation.docx Supplementary Information for munuscript 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-8609404","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":575594629,"identity":"030d5222-1f67-4a13-8613-1b098f226c75","order_by":0,"name":"Luan 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