The Minimum-Action Semantic Framework (MAF): A Variational Principle for Conversational Stability in Large Language Models
Lionis, Kon · Zenodo (CERN European Organization for Nuclear Research) · 2025
The Minimum-Action Semantic Framework (MAF) is a candidate variational framework for reasoning about conversational stability in large language models. It models dialogue as a trajectory through a semantic manifold and defines a composite action functional that penalizes semantic displacement, predictive uncertainty, and proximity to constraint boundaries. Within this formalism, structured interpretive frameworks are modeled as supporting lower-cost conversational trajectories, which are hypothesized to exhibit reduced semantic drift, lower entropy, and greater constraint compatibility than less structured alternatives. These predicted effects are presented as behavioral hypotheses suitable for empirical evaluation, not as established facts about real LLM behavior. MAF is intended as a phenomenological and mathematically tractable account of how conversational structure may shape stability over time. It does not claim that language models literally compute action integrals, gradients, or explicit variational objectives during inference. Rather, it offers a candidate modeling lens: a way to describe dialogue as if it followed lower-action paths under suitable structural assumptions, while leaving the question of real mechanistic correspondence open. This record also includes an ML-native translation of MAF that restates the framework in standard machine learning and systems language without changing its core formal structure, stated propositions, or limitations. The translation is intended to improve interpretability and technical accessibility for ML-oriented readers while preserving the same candidate, hypothesis-driven posture as the main paper. MAF forms part of the broader Recursive Equilibrium mathematical program alongside RBE, HBE, and TSC. Within that program, it contributes a variational account of conversational drift, coherence, and possible convergence behavior across architectures, while keeping the burden of proof on future empirical testing. Archival PDF versions are included in this record; no substantive content changes have been made.