Suzette Geriente

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 (GPT-5.5 Thinking) and Google Gemini Advanced (Gemini 1.5 Pro), we show that Bell’s inequalities are significantly violated, which indicates the presence of a ‘non-classical probability model’ with probabilities that do not satisfy Kolmogorov’s axioms. In the second test, also performed using ChatGPT and Gemini, we 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 non-classical quantum-like 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.

We analyse the results of three information retrieval tests on conceptual combinations that we have recently performed using corpora of Italian language. Each test has the form of a ‘Bell-type test’ and was aimed at identifying ‘quantum entanglement’ in the combination, or composition, of two concepts. In the first two tests, we studied the Italian translation of the combination The Animal Acts, while in the third test, we studied the Italian translation of the combination The Animal eats the Food. We found a significant violation of Bell’s inequalities in all tests. Empirical patterns confirm the results obtained with corpora of English language, which indicates the existence of deep structures in concept formation that are language independent. The systematic violation of Bell’s inequalities suggests the presence of entanglement, and indeed, we elaborate here a ‘quantum model in Hilbert space’ for the collected data. This investigation supports our theoretical hypothesis about entanglement as a phenomenon of ‘contextual updating’, independent of the nature, micro-physical or conceptual-linguistic, of the entities involved. Finally, these findings allow us to further clarify the mutual relationships between entanglement, Cirel’son’s bound, and no-signalling in Bell-type situations.

In physics, entanglement 'reduces' the entropy of an entity, because the (von Neumann) entropy of, e.g., a composite bipartite entity in a pure entangled state is systematically lower than the entropy of the component sub-entities. We show here that this 'genuinely non-classical reduction of entropy as a result of composition' also holds whenever two concepts combine in human cognition and, more generally, it is valid in human culture. We exploit these results and make a 'new hypothesis' on the nature of entanglement, namely, the production of entanglement in the preparation of a composite entity can be seen as a 'dynamical process of collaboration between its sub-entities to reduce uncertainty', because the composite entity is in a pure state while its sub-entities are in a non-pure, or density, state, as a result of the preparation. We identify within the nature of this entanglement a mechanism of contextual updating and illustrate the mechanism in the example we analyze. Our hypothesis naturally explains the 'non-classical nature' of some quantum logical connectives, as due to Bell-type correlations.

We motivate the possibility of using notions and methods derived from quantum physics, and more specifically from the research field known as 'quantum cognition', to optimally model different situations in the field of medicine, its decision-making processes and ensuing practices, particularly in relation to chronic and rare diseases. This also as a way to devise alternative approaches to the generally adopted double-blind gold standard.

We show that data collected from corpuses of documents violate the Clauser-Horne-Shimony-Holt version of Bell's inequality (CHSH inequality) and therefore indicate the presence of quantum entanglement in their structure. We obtain this result by considering two concepts and their combination and coincidence operations consisting of searches of co-occurrences of exemplars of these concepts in specific corpuses of documents. Measuring the frequencies of these co-occurrences and calculating the relative frequencies as approximate probabilities entering in the CHSH inequality, we obtain manifest violations of the latter for all considered corpuses of documents. In comparing these violations with those analogously obtained in an earlier work for the same combined concepts in psychological coincidence experiments with human participants, also violating the CHSH inequality, we identify the entanglement as being carried by the meaning connection between the two considered concepts within the combination they form. We explain the stronger violation for the corpuses of documents, as compared to the violation in the psychology experiments, as being due to the superior meaning domain of the human mind and, on the other side, to the latter reaching a broader domain of meaning and being possibly also actively influenced during the experimentation. We mention some of the issues to be analyzed in future work such as the violations of the CHSH inequality being larger than the `Cirel'son bound' for all of the considered corpuses of documents.

In the first half of this two-part article (Aerts et al. in Found Sci. doi:10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.

The Machina thought experiments pose to major non-expected utility models challenges that are similar to those posed by the Ellsberg thought experiments to subjective expected utility theory (SEUT). We test human choices in the `Ellsberg three-color example', confirming typical ambiguity aversion patterns, and the `Machina 50/51 and reflection examples', partially confirming the preferences hypothesized by Machina. Then, we show that a quantum-theoretic framework for decision-making under uncertainty recently elaborated by some of us allows faithful modeling of all data on the Ellsberg and Machina paradox situations. In the quantum-theoretic framework subjective probabilities are represented by quantum probabilities, while quantum state transformations enable representations of ambiguity aversion and subjective attitudes toward it.