quantum-structure-in-ai-language

name	quantum-structure-in-ai-language
description	Quantum-like structure in AI language: Bell inequality violation and Bose-Einstein statistics in LLMs. Use when analyzing non-classical probability in language models, quantum cognition applied to AI, conceptual combinations in LLMs, evolutionary convergence of human and artificial cognition, or quantum statistical patterns in text generation.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2511.21731","published":"2025-11-21","authors":"Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran, Suzette Geriente, Roberto Leporini, Massimiliano Sassoli de Bianchi, Sandro Sozzo","journal":"Entropy 28, 622, 2026","tags":["quantum","cognition","llm","probability","bell-inequality","bose-einstein","semantics"]}

Quantum Structure in AI Language

LLMs exhibit quantum-like organizational structures in their distributive semantic spaces, mirroring patterns found in human cognition.

Core Findings

Bell Inequality Violation: Cognitive tests on conceptual combinations using ChatGPT and Gemini show significant Bell inequality violations, indicating non-classical probability models where probabilities do not satisfy Kolmogorov's axioms.

Bose-Einstein Statistics: Large-size text word distributions follow Bose-Einstein rather than Maxwell-Boltzmann statistics, matching patterns previously found in human cognitive tests and information retrieval corpora.

Evolutionary Convergence: Systematic emergence of non-classical quantum-like structures in conceptual-linguistic domains occurs regardless of whether the cognitive agent is human or artificial. Meaning-bearing vector spaces in LLMs converge toward the same quantum organization established through biological evolution in human cognition.

Methodology

1. Design cognitive tests on conceptual combinations for LLM subjects
2. Test for Bell inequality violations → non-classical probability
3. Analyze word distribution statistics → Bose-Einstein vs Maxwell-Boltzmann
4. Compare results with human cognitive test baselines
5. Map findings to unifying framework of quantum organization of meaning

Skill Patterns

Pattern 1: Quantum Probability in LLM Outputs

• Test LLM responses to conceptual combination tasks
• Check if response distributions violate classical probability axioms
• Apply Bell inequality tests to LLM-generated concept associations
• Compare violation patterns with human subject baselines

Pattern 2: Bose-Einstein Word Distribution Analysis

• Analyze large corpora of LLM-generated text
• Count word frequency distributions in conceptual domains
• Fit to Bose-Einstein vs Maxwell-Boltzmann statistical models
• Determine which distribution better explains LLM output patterns

Pattern 3: Semantic Space Quantum Structure

• LLMs organize meaning in vector spaces that exhibit quantum-like properties
• Conceptual combinations show superposition-like behavior
• Context-dependent meaning shifts mirror quantum measurement effects
• The neural network architecture is secondary to the meaning-bearing semantic structure

Activation Keywords

quantum cognition LLM, Bell inequality language model, Bose-Einstein text statistics, non-classical probability AI, evolutionary convergence cognition, conceptual combination quantum, quantum semantic structure, Kolmogorov axiom violation LLM

References

• arXiv:2511.21731 — Identifying Quantum Structure in AI Language (Entropy 28, 622, 2026)
• Related: quantum-cognition, quantum-like-mental-markers, quantum-like-cognitive-modeling skills