04/2025

Language Models as Quantum Systems: Exploring Semantic Embeddings with Quantum Mechanics

A quantum-inspired model offers a new perspective on Large Language Models (LLMs) by suggesting their semantic spaces exhibit quantized properties analogous to quantum systems. This perspective shifts from treating LLM embeddings as purely continuous to recognizing an underlying discreteness rooted in the finite vocabulary of tokens. LLMs rely on high-dimensional vector embeddings to represent text, but their reliance on a finite vocabulary suggests an underlying discreteness, motivating the exploration of quantum mechanics as a framework.


The model rests on six core principles:

1. Completeness of Vocabulary: The LLM's vocabulary forms a complete basis for representing semantic information.
2. Semantic Space as a Complex Hilbert Space: The semantic space is defined as a complex Hilbert space, allowing for modeling of interference and superposition.
3. Discretization of Semantic States: Semantic states are discrete and correspond to the LLM's token vocabulary.
4. Linear Schrödinger-like Equation: Semantic representation evolution is initially approximated by a linear Schrödinger-like equation.
5. Nonlinear Semantic Wave Propagation: A more advanced model incorporates nonlinear effects through a Nonlinear Schrödinger Equation and nonlinear potential functions.
6. Semantic Charge and Gauge Interaction: Words possess a "semantic charge," and their interactions are mediated by a gauge field.

The model uses these principles to explain observed LLM behaviors, such as probabilistic outputs, semantic ambiguity, and long-range dependencies. This approach is valuable; by establishing a link between quantum mechanics and LLMs, it potentially unlocks new insights into their inner workings. It provides a theoretical framework for explaining the behavior of these "black box" systems, offering a more interpretable understanding of their internal representations and dynamics. Furthermore, it opens the door to leveraging quantum algorithms and computing techniques to model LLMs, potentially leading to faster, larger, and more accurate models in the future. While acknowledging the model's inherent limitations as an analogy and the need for empirical validation, the work suggests future research directions, including quantum computing for LLMs, path integral formalisms for analysis, and harnessing the inherent probabilistic nature of LLMs for creative applications.


References:

1. T.A.Laine, OA J Applied Sci Technol, 3(1), 01-22 (2025).
2. T.A.Laine, OA J Applied Sci Technol, 3(2), 01-13 (2025).

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