Dynamic Manifold Evolution Theory: Modeling and Stability Analysis of Latent Representations in Large Language Models

We introduce Dynamic Manifold Evolution Theory (DMET), a unified framework that models large language model generation as a controlled dynamical system evolving on a lowdimensional semantic manifold. By casting latentₛtate updates as discrete time Euler approximations of continuous dynamics, we map intrinsic energydriven flows and contextdependent forces onto Transformer components (residual connections, attention, feed-forward networks). Leveraging Lyapunov stability theory We define three empirical metrics (state continuity, clustering quality, topological persistence) that quantitatively link latentₜrajectory properties to text fluency, grammaticality, and semantic coherence. Extensive experiments across decoding parameters validate DMET's predictions and yield principled guidelines for balancing creativity and consistency in text generation.