Emergent Non-Classical Probabilistic Structure in Large Language Models Under Contextual Modulations

Emergent Non-Classical Probabilistic Structure in Large Language Models Under Contextual Modulations | 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 Emergent Non-Classical Probabilistic Structure in Large Language Models Under Contextual Modulations Jyotiranjan Beuria This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9326649/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract Classical probability theory provides the standard foundation for rational inference, yet human probability judgments are known to systematically violate Kolmogorovian axioms through phenomena such as conjunction fallacies and question-order effects. Whether large language models (LLMs) exhibit structurally analogous departures from classical probability remains an important empirical question with broad implications for AI evaluation and cognitive science. Here, we report a controlled experimental investigation of the probabilistic structure of LLM responses under systematically varied contextual prompts, treating model outputs as behavioral observables of a high-dimensional inference system. Using paradigms drawn from cognitive decision research, we evaluated multiple LLMs across tasks, including ambiguity judgments, belief revision, order effects, conjunction fallacies, and base-rate reasoning. Our experiments reveal systematic violations of the law of total probability accompanied by pronounced order-dependent effects across all models. Critically, these deviations are not random: they exhibit a structured interference form characterized by a phase-dependent term and a non-trivial upper bound, and the observed scaling relation demonstrates that the resulting probability assignments cannot be embedded within any single Kolmogorov probability space. These findings are consistent with a constrained non-commutative probabilistic structure, formally analogous to quantum probability models previously proposed for human cognition, without implying that neural networks implement quantum-physical processes. Our results establish non-commutative probability as a principled descriptive framework for contextual inference in large-scale artificial systems, and highlight the need for structural, beyond accuracy-based evaluation of probabilistic reasoning in modern AI. Physical sciences/Mathematics and computing Physical sciences/Physics Biological sciences/Psychology Social science/Psychology Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 12 May, 2026 Reviews received at journal 05 May, 2026 Reviews received at journal 21 Apr, 2026 Reviewers agreed at journal 10 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers invited by journal 09 Apr, 2026 Editor invited by journal 09 Apr, 2026 Editor assigned by journal 07 Apr, 2026 Submission checks completed at journal 07 Apr, 2026 First submitted to journal 05 Apr, 2026 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. 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