Empirical Investigation of Latent Representational Dynamics in Large Language Models: A Manifold Evolution Perspective

TL;DR

DMET reframes LLM generation as a continuous trajectory on a low-dimensional semantic manifold, addressing the opacity of latent dynamics. It introduces three quantitative metrics—$C$ (state continuity), $Q$ (attractor clustering quality), and $P$ (topological persistence)—and links them to fluency, consistency, and coherence, with a mapping to Transformer components. Across three Transformer architectures, prompts, and decoding settings, DMET demonstrates robust correlations between the dynamical metrics and text quality, revealing model-specific dynamical regimes and a golden zone for decoding. The framework provides a theory-grounded, testable basis to monitor, interpret, and steer LLM behavior, offering principled guidance to reduce semantic drift, enhance coherence, and tailor generation to application needs.

Abstract

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.

Figures (9)

• Figure 1: Overview of the DMET framework: latent trajectories evolve on a low-dimensional semantic manifold under intrinsic energy gradients and context-driven forces, with discrete Transformer layers implementing Euler steps of this continuous dynamics.
• Figure 2: Latent representations reside on a low-dimensional semantic manifold rather than occupying the full ambient space.
• Figure 3: Fluency–Coherence trade-off under varying $\tau$ and $p$ (DeepSeek-R1); a "golden zone" achieves optimal fluency, diversity, and structure.
• Figure 4: PCA projection of hidden-state dynamics under varying decoding; semantic attractors and directional convergence validate DMET predictions.
• Figure 5: Representative hidden-state trajectory evolution under varying $\tau$; higher temperatures increase spread and delay convergence.