Quantum Hierarchy for Understanding LLM Representations by Modeling Linear Projections and Nonlinear Dynamics

Abstract

Timo Aukusti Laine

Large Language Models (LLMs) excel in natural language tasks, but their high-dimensional embedding spaces pose significant interpretability challenges. Current approaches often linearize these spaces, overlooking the complex dynamics inherent in Transformer architectures. This article proposes a quantum framework to analyze LLM representations, leveraging quantum mechanical tools to explore semantic relationships and contextual influences. We introduce a layered hierarchy of semantic spaces and demonstrate that a classical LLM embedding system has an exact quantum mechanical analogue. Using this analogue, we model phenomena such as the modulation of Semantic Noise, the emergence of hallucinations via quantum tunneling, and the formation of stable semantic representations as soliton solutions. Furthermore, we present a simple quantum circuit design, demonstrating the possibility of using quantum computers to probe, analyze and go beyond real-valued LLM embedding spaces, potentially revealing structural information and relationships not readily accessible through classical techniques. This perspective enhances our understanding of LLM representations, leading to improved methods for analyzing and controlling LLM behavior, and supporting research into more efficient, reliable, and trustworthy AI systems.

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