We analyze two geometric aspects of meaning-sensitive behavior in next-token models. First, high-dimensional geometry permits exponentially many nearly orthogonal feature directions at a fixed tolerance, although their residual overlaps limit simultaneous readout. Second, polysemy requires us to distinguish classical convex mixtures of sense vectors, context-dependent occurrence vectors, quantum coherence, and an optional shared-projector incidence construction over sense-labelled bases. For ordinary transformers, the quantum comparisons are structural and deliberately limited.
We analyze two geometric aspects of meaning-sensitive behavior in next-token models. First, high-dimensional geometry permits exponentially many nearly orthogonal feature directions at a fixed tolerance, although their residual overlaps limit simultaneous readout. Second, polysemy requires us to distinguish classical convex mixtures of sense vectors, context-dependent occurrence vectors, quantum coherence, and an optional shared-projector incidence construction over sense-labelled bases. For ordinary transformers, the quantum comparisons are structural and deliberately limited.
A composite system of N local q-level factors has dimension D=q^N. Although at most D vectors can be exactly orthogonal, a fixed squared-overlap tolerance \eps permits M_\eps(D)\gtrsim\exp(c_\eps D) mutually quasi-orthogonal directions. Consequently M_\eps(q^N)\gtrsim\exp(c_\eps q^N): the dimension grows exponentially in N, but its quasi-orthogonal capacity grows doubly exponentially. Lévy's lemma explains the accompanying concentration of regular observables, and Johnson--Lindenstrauss scaling gives the complementary finite-set account of exponential capacity. For Haar-random pure states the sharper exact law is \mathbb P(|\langleφ|ψ\rangle|^2\geq\eps)=(1-\eps)^{D-1}, while typical Fubini--Study angles lie within O(D^{-1/2}) of π/2: capacity explodes as angular structure homogenizes. We turn these facts into simultaneous overlap and trace-distance bounds for finite decoherence branch families, including mixed environments and collective weak coherences. The results are conditional on typical relative environmental dynamics. They neither select a pointer basis nor identify coherence suppression with readable or redundant records.
Abstract Language is not fixed. It is entangled, probabilistic, and observer-dependent. This paper introduces a new paradigm in linguistic theory named "Quantum Linguistics," inspired by the principles of Quantum Physics. Quantum physics and Linguistics have long been regarded as unrelated disciplines,describing nature at the inanimate microlevel on the one hand and language and its scientific study on the other hand. Over the past decades the linguistics has succeeded in providing ever more and refined explanations of generative grammar. Since quantum physics and linguistics deal with the symbolic, rule-governed structure of human language and the non-classical, probabilistic behaviour of subatomic particles, respectively, they have historically been seen as two separate disciplines. This framework allows modeling of polysemy, ambiguity, free word order, and argument structure in a unified, mathematically rigorous manner.To operationalize the model, we implement a Quantum Syntax-Semantics Integration (QSSI) pipeline, which encodes sentences into vector states, applies quantum operations for compositional syntax and semantics, and produces contextually resolved meanings through measurement. Two variants of the pipeline are considered: a classical simulation for experimental validation and a quantum-simulated version for future hardware implementation. The linguistic theory with quantum principles such as superposition, entanglement, and measurement, our model provides a novel probabilistic and context-dependent approach to understand language, explore new insights into human cognitive-linguistic processes, semantic ambiguity observation, and advanced natural language processing applications.
A lexeme can be represented as a vector in a Hilbert space. Each element of the vector represents the weight of a semantic relation with a second vector: the context of a second lexeme. Two query operators are defined in a way that they attribute the value +1 to the component of the state that corresponds to the word meaning we are interested in, and -1 in the orthogonal direction. Entangled states have been used to detect semantic relationships in Information Retrieval (IR). In particular, since the first operator corresponds to negation and the conditional gate corresponds to an implication in classical logic, they can represent two basic semantic relationships : hyponymy (e.g. genus-species) and antonymy (e.g. masculine-feminine). In fact, according to Semantics, if A and B are antonymic terms, then A is an hyponym of (i.e. implies) not-B as in the Gremias semiotic square. We underline how the relations of a given semantic universe, and the corresponding result of our operators, depends only on the considered text. Among others, this analogy suggests the application of quantum-based models to language and IR.
Large Language Models (LLMs) encode semantic relationships in high-dimensional vector embeddings. This paper explores the analogy between LLM embedding spaces and quantum mechanics, positing that LLMs operate within a quantized semantic space where words and phrases behave as quantum states. To capture nuanced semantic interference effects, we extend the standard realvalued embedding space to the complex domain, drawing parallels to the double-slit experiment. We introduce a ”semantic wave function” to formalize this quantum-derived representation and utilize potential landscapes, such as the double-well potential, to model semantic ambiguity. Furthermore, we propose a complex-valued similarity measure that incorporates both magnitude and phase information, enabling a more sensitive comparison of semantic representations. We develop a path integral formalism, based on a nonlinear Schro¨dinger equation with a gauge field and Mexican hat potential, to model the dynamic evolution of LLM behavior. This interdisciplinary approach offers a new theoretical framework for understanding and potentially manipulating LLMs, with the goal of advancing both artificial and natural language understanding
In alignment with the distributional hypothesis of language, the work “Quantum Projections on Conceptual Subspaces” (Martínez-Mingo A, Jorge-Botana G, Martinez-Huertas JÁ, et al. Quantum projections on conceptual subspaces. Cogn Syst Res 2023; 82: 101154) proposed a methodology for generating conceptual subspaces from textual information based on previous work (Martinez-Mingo A, Jorge-Botana G and Olmos R. Quantum approach for similarity evaluation in LSA vector space models. 2020). These subspaces enable the utilization of the quantum model of similarity put forth by Pothos and Busemeyer (Pothos E, Busemeyer J. A quantum probability explanation for violations of symmetry in similarity judgments. In Proceedings of the annual meeting of the cognitive science society, 2011, Vol. 33, No. 33), allowing for the empirical examination of the violations of assumptions concerning symmetry and triangular inequality (Tversky A. Features of similarity. Psychol Rev 1977; 84: 327–352; Yearsley JM, Barque-Duran A, Scerrati E, et al. The triangle inequality constraint in similarity judgments. Prog Biophys Mol Biol 2017; 130: 26–32), as well as the diagnosticity effect (Tversky A. Features of similarity. Psychol Rev 1977; 84: 327–352; Yearsley JM, Pothos EM, Barque-Duran A, et al. Context effects in similarity judgments. J Exp Psychol Gen 2022; 151: 711–717), within a data-driven environment. These psychological biases, deeply studied by authors such as Tversky and Kahneman, inform us about the limitations of modeling psychological similarity measures using tools from classical geometry. This commentary aims to offer methodological clarifications, discuss theoretical and practical implications, and speculate on future directions in this field of research. Concretely, it aims to propose the use of different contours (conceptual or contextual) to generate the subspaces, which lead to subspaces of terms or contexts. Once these contours are defined, a differentiation is proposed between Aggregated Terms Subspaces (ATSs), Aggregated Contexts Subspaces (ACSs), and Aggregated Features Subspaces (AFSs) depending on whether we define the subspaces by grouping the terms or contexts within the contour, or from the latent dimensions of the semantic space obtained in the contour window. Finally, new data is provided on the violation of the triangular inequality assumption through the application of the quantum similarity model to ATSs.
Question-order effects in human survey data have been reported to approximately satisfy the QQ (quantum question) equality, a parameter-free prediction of the standard projective quantum question-order model. We develop this equality into an audit framework for sequential binary judgments of autoregressive large language models (LLMs). Theoretically, we characterize mechanism families that satisfy QQ robustly, show that classical repetition can reproduce the equality exactly, and combine QQ with the rank-2 Contextuality-by-Default criterion through ∣qQQ∣≤OSS. This separates order sensitivity, QQ imbalance, and residual contextuality rather than treating them as interchangeable signatures. Methodologically, we introduce a committed multi-turn forced-branch protocol that reconstructs order-conditioned joint distributions from next-token log-probabilities under counterbalanced label mappings and pre-specified health gates. A first-signal pilot on an open-weight instruction-tuned model reveals the central measurement problem. Although all pre-specified health gates passed, the binary-conditioned distributions were near-deterministic for 17 of 18 item pairs under the direct-evaluation framing and 7 of 8 under the persona framing. Label assignment materially changed several mapping-specific QQ verdicts, and no item was certified as residually contextual. Thus, under the tested conditions, the observed QQ outcomes did not uniquely identify a response mechanism in the presence of a saturated and label-sensitive measurement interface. The main implication is methodological: next-token probabilities should not be interpreted as survey-response distributions without first establishing adequate dispersion. We therefore argue that saturation screening and label counterbalancing should precede structural interpretation in distribution-level audits of LLM judgments.