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

24 May 2025
Yukun Zhang
Qi Dong
    AI4CE
ArXiv (abs)PDFHTML
Main:7 Pages
11 Figures
Bibliography:3 Pages
2 Tables
Appendix:8 Pages
Abstract

We introduce Dynamic Manifold Evolution Theory (DMET),a unified framework that models large language model generation as a controlled dynamical system evolving on a low_dimensional semantic manifold. By casting latent_state updates as discrete time Euler approximations of continuous dynamics, we map intrinsic energy_driven flows and context_dependent 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 latent_trajectory 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.

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@article{zhang2025_2505.20340,
  title={ Dynamic Manifold Evolution Theory: Modeling and Stability Analysis of Latent Representations in Large Language Models },
  author={ Yukun Zhang and Qi Dong },
  journal={arXiv preprint arXiv:2505.20340},
  year={ 2025 }
}
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