Theoretical Exploration Report on the Unified Quantum Semantic Model

Claudio Garola, Jarosław Pykacz, Sandro Sozzo

Konstantin Dubenko

Pranay M. Mahendrakar

Life of Research AbstractThis paper introduces a novel theoretical framework for understanding semantic processing in Large LanguageModels through the lens of sheaf theory and quantum contextuality. We propose that the semantic structure ofLLM-generated text can be rigorously modeled as a sheaf over the topological space of prompt contexts, wherelocal semantic sections may fail to glue into globally consistent interpretations. This mathematical formalizationreveals a deep structural parallel between LLM behavior and quantum mechanical systems exhibitingcontextuality, as characterized by the Kochen-Specker theorem. Our central thesis posits that hallucinationphenomena in LLMs arise fundamentally from cohomological obstructions to the existence of global semanticsections, analogous to how quantum systems exhibit measurement outcomes that cannot be explained by preexisting hidden variables. We develop a complete categorical framework using topos-theoretic methods, introduceformal definitions of semantic presheaves and their associated Grothendieck topologies, and demonstrate howCech cohomology groups can quantify the degree of semantic inconsistency in model outputs. This work bridgesabstract mathematics with practical AI interpretability, offering new diagnostic tools for understanding when andwhy language models produce incoherent or factually inconsistent outputs.

Financial Physics Lab, Finland, Timo Aukusti Laine

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

Marco Aurelio De Cunha

Alеxander Raikov