Semantic Wave Functions: Exploring Meaning in Large Language Models Through Quantum Formalism
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909585489526784 |
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| author | Laine, Timo Aukusti |
| author_facet | Laine, Timo Aukusti |
| contents | 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semantic Wave Functions: Exploring Meaning in Large Language Models Through Quantum Formalism Laine, Timo Aukusti Computation and Language Machine Learning Quantum Physics 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 Schrödinger 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. |
| title | Semantic Wave Functions: Exploring Meaning in Large Language Models Through Quantum Formalism |
| topic | Computation and Language Machine Learning Quantum Physics |
| url | https://arxiv.org/abs/2503.10664 |