用量子力学框架解释大模型语义表示，揭示词义的波动与干涉特性。
Semantic Wave Functions: Exploring Meaning in Large Language Models Through Quantum Formalism
- 将语言嵌入扩展为复数域，构建语义波函数模拟词义叠加态。
- 引入相位与幅度联合相似度，提升对细微语义差异的感知能力。
- 适合对理论建模、语义动态演化感兴趣的学者参考。
大型语言模型（LLMs）在高维向量空间中编码语义关系。本文探索了LLM嵌入空间与量子力学之间的类比，提出LLMs运行于一种量化的语义空间中，词语和短语可视为量子态。为捕捉复杂的语义干涉效应，我们把标准实值嵌入空间扩展到复数域，借鉴双缝实验思想。引入“语义波函数”以形式化这一量子衍生表示，并利用势能景观（如双阱势）建模语义模糊性。此外，我们提出一种包含幅度与相位信息的复值相似度度量，实现更敏感的语义表征比较。基于非线性薛定谔方程与规范场及墨西哥帽势能，我们构建路径积分形式化框架，用于建模LLM行为的动态演化。该跨学科方法为理解并可能操控LLM提供了新的理论框架，旨在推进人工与自然语言理解。
原文摘要 · Abstract (English)
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.
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