Empirical Investigation of Latent Representational Dynamics in Large Language Models: A Manifold Evolution Perspective
This provides a unified framework for interpreting and guiding LLM behavior, offering insights into the interplay between internal dynamics and text generation quality, but it is incremental as it builds on existing phenomenological approaches without introducing new methods.
The paper tackled the problem of understanding how large language models generate text by modeling it as a trajectory on a low-dimensional semantic manifold, introducing metrics that link smoother trajectories to greater fluency and richer topological organization to enhanced coherence. Empirical analyses across Transformer architectures showed consistent relationships between these latent dynamics and text quality, with decoding parameters like temperature shaping trajectories in predictable ways.
This paper introduces the Dynamical Manifold Evolution Theory (DMET), a conceptual framework that models large language model (LLM) generation as a continuous trajectory evolving on a low-dimensional semantic manifold. The theory characterizes latent dynamics through three interpretable metrics-state continuity ($C$), attractor compactness ($Q$), and topological persistence ($P$)-which jointly capture the smoothness, stability, and structure of representation evolution. Empirical analyses across multiple Transformer architectures reveal consistent links between these latent dynamics and text quality: smoother trajectories correspond to greater fluency, and richer topological organization correlates with enhanced coherence. Different models exhibit distinct dynamical regimes, reflecting diverse strategies of semantic organization in latent space. Moreover, decoding parameters such as temperature and top-$p$ shape these trajectories in predictable ways, defining a balanced region that harmonizes fluency and creativity. As a phenomenological rather than first-principles framework, DMET provides a unified and testable perspective for interpreting, monitoring, and guiding LLM behavior, offering new insights into the interplay between internal representation dynamics and external text generation quality.