Operational Characterization of LLM Fatigue and Output Stability Degradation

This paper provides a formal operational characterization of "LLM fatigue," a phenomenon where large language models exhibit declining output stability and increased hallucinations during extended or repeated inference. While these issues are often treated as random errors, this work utilizes the Semantic Function formalism of Cognitional Mechanics to demonstrate that fatigue is a deterministic consequence of operator-driven dynamics. By modeling the internal state of the LLM as a semantic function, the research defines fatigue as a cumulative drift away from the initial semantic state, measurable through a rigorous stability function. The framework further explains hallucinations as rare semantic transitions triggered when operator perturbations allow the system to bypass logical constraints, modeled here as potential barriers. Additionally, the paper analyzes the impact of context window saturation, formalizing memory degradation as a forced projection that results in quantifiable information loss. By providing concrete indicators such as mean semantic drift and cumulative stability loss, this study establishes a structured methodology for monitoring and mitigating reliability issues in LLMs, shifting the discourse from probabilistic guesswork to the deterministic physics of machine cognition.