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

Large Language Models (LLMs) have emerged as transformative tools in natural language processing, demonstrating remarkable capabilities in tasks ranging from text generation and translation to question answering and code completion. At the heart of these models lies a sophisticated mechanism for representing text: high-dimensional vector embeddings. These embeddings map words, phrases, and even entire documents into a continuous semantic space, where geometric relationships reflect semantic similarities. For instance, words with related meanings are positioned closer together, while dissimilar concepts are further apart. While these embedding spaces are often treated as continuous for practical purposes, a fundamental aspect of LLMs hints at an underlying discreteness: their reliance on a finite vocabulary of tokens. This discrete foundation suggests that the seemingly continuous semantic space might, in fact, possess a quantized structure, analogous to the discrete energy levels observed in quantum systems. This inherent quantization prompts a compelling question: can we leverage the powerful theoretical frameworks of mathematical physics and tools of quantum mechanics to gain a deeper understanding of the organization and dynamics of these semantic spaces? Furthermore, if this quantization is valid, could quantum computing, for example, offer new approaches to training or exploiting these models, potentially unlocking significant performance gains?