Stable Semantics in Large Language Models: A Geometric Perspective on Inference and Reasoning

This paper presents a structural and geometric analysis of semantic instability and hallucination behavior in large language models (LLMs). Rather than treating hallucination as a factual error or post-hoc failure, this work frames it as a dynamical phenomenon: a loss of semantic stability arising from the geometry of inference trajectories in high-dimensional representation space. Hallucination is analyzed as a state transition in which contraction properties break down and semantic trajectories escape stable basins. The paper builds on earlier works but is distinct in scope and audience. While the earlier series focused on general computational and physical convergence principles, specifically targets LLM architectures and the conditions under which coherent dialogue becomes unstable. This manuscript is currently under review at the Journal of Machine Learning Research (JMLR). The version archived here is provided as a public preprint to facilitate discussion, citation, and cross-disciplinary exchange.