Semantic Wave Functions: Exploring Meaning in Large Language Models Through Quantum Formalism

• URL: http://arxiv.org/abs/2503.10664v1
• Date: Sun, 09 Mar 2025 08:23:31 GMT
• Title: Semantic Wave Functions: Exploring Meaning in Large Language Models Through Quantum Formalism
• Authors: Timo Aukusti Laine,
• Abstract summary: Large Language Models (LLMs) encode semantic relationships in high-dimensional vector embeddings.<n>This paper explores the analogy between LLM embedding spaces and quantum mechanics.<n>We introduce a "semantic wave function" to formalize this quantum-derived representation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 real-valued 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 Schr\"odinger 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.

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