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Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran, Suzette Geriente, Roberto Leporini, Massimiliano Sassoli de Bianchi, Sandro Sozzo

TL;DR

The paper investigates whether AI language systems exhibit quantum-like structure in meaning and linguistic data by performing Bell-inequality tests on LLM outputs and analyzing word-frequency statistics through Bose–Einstein distributions. It finds that LLMs can produce CHSH violations up to the maximal quantum bound, mirroring entanglement-like correlations observed in human cognition, and that story texts generated by LLMs exhibit BE-type word clustering not captured by classical MB statistics. The authors introduce a cogniton-energy framework and an Einsteinian-unification perspective, arguing that structured vector spaces and coherence underpin meaning across humans, AI, and physical phenomena. These results suggest a universal, substrate-independent organization of meaning and offer a lens for AI safety and advances in semantic modeling beyond traditional neural-network descriptions.

Abstract

We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell's inequalities are significantly violated, which indicates the presence of 'quantum entanglement' in the tested concepts. In the second test, also performed using ChatGPT and Gemini, we instead identify the presence of 'Bose-Einstein statistics', rather than the intuitively expected 'Maxwell-Boltzmann statistics', in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the 'systematic emergence of quantum structures in conceptual-linguistic domains', regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.

Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition

TL;DR

The paper investigates whether AI language systems exhibit quantum-like structure in meaning and linguistic data by performing Bell-inequality tests on LLM outputs and analyzing word-frequency statistics through Bose–Einstein distributions. It finds that LLMs can produce CHSH violations up to the maximal quantum bound, mirroring entanglement-like correlations observed in human cognition, and that story texts generated by LLMs exhibit BE-type word clustering not captured by classical MB statistics. The authors introduce a cogniton-energy framework and an Einsteinian-unification perspective, arguing that structured vector spaces and coherence underpin meaning across humans, AI, and physical phenomena. These results suggest a universal, substrate-independent organization of meaning and offer a lens for AI safety and advances in semantic modeling beyond traditional neural-network descriptions.

Abstract

We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell's inequalities are significantly violated, which indicates the presence of 'quantum entanglement' in the tested concepts. In the second test, also performed using ChatGPT and Gemini, we instead identify the presence of 'Bose-Einstein statistics', rather than the intuitively expected 'Maxwell-Boltzmann statistics', in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the 'systematic emergence of quantum structures in conceptual-linguistic domains', regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.

Paper Structure

This paper contains 7 sections, 14 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. LLMs that violate Bell's inequalities
  3. The non-classical statistics of stories written by LLMs
  4. Einsteinian Unification
  5. Conclusion
  6. Appendix: Conversation with ChatGPT on CHSH Inequalities
  7. Appendix: Pooh's Peculiar Predicament and the Whispering Wind

Figures (2)

  • Figure 1: In the left graph, we represent the 'numbers of appearances' $N(E_i)$ of words in Gemini's Winnie the Pooh story (Appendix \ref{['appendixb']}) ranked from the lowest energy level, corresponding to the most frequently appearing word, to the highest energy level, corresponding to the least frequently appearing word, as listed in Table \ref{['TableGeminiWinnie']}. The blue line represents the data, i.e. the numbers of appearances deduced from the story (fourth column of Table \ref{['TableGeminiWinnie']}), the red line represents these numbers of appearances predicted by the BE distribution model (fifth column), and same for the green line but for the MB distribution model (sixth column). In the right graph, we represent the the same data as in the left graph, but using a log-log plot (both axes on a logarithmic scale). The red and blue line coincide almost completely in both graphs, whereas the green line does not coincide at all. This shows that the BE distribution is a good model for the numbers of appearances, while the MB distribution is not.
  • Figure 2: The energy $E(E_i)$ radiated per energy level of Gemini’s Winnie the Pooh story (Appendix \ref{['appendixb']}) as a function of the energy levels $E_i$. The blue line represents the data (seventh column of Table \ref{['TableGeminiWinnie']}), the red line represents the values predicted by the BE model (eighth column), and same for the green line but for the MB model (ninth column).