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

• URL: http://arxiv.org/abs/2505.20340v2
• Date: Mon, 13 Oct 2025 15:56:25 GMT
• Title: Empirical Investigation of Latent Representational Dynamics in Large Language Models: A Manifold Evolution Perspective
• Authors: Yukun Zhang, Qi Dong,
• Abstract summary: 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.<n>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.
• Score: 4.935224714809964
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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