Cognitive Activation and Chaotic Dynamics in Large Language Models: A Quasi-Lyapunov Analysis of Reasoning Mechanisms

The human-like reasoning capabilities exhibited by Large Language Models (LLMs) challenge the traditional neural network theory's understanding of the flexibility of fixed-parameter systems. This paper proposes the "Cognitive Activation" theory, revealing the essence of LLMs' reasoning mechanisms from the perspective of dynamic systems: the model's reasoning ability stems from a chaotic process of dynamic information extraction in the parameter space. By introducing the Quasi-Lyapunov Exponent (QLE), we quantitatively analyze the chaotic characteristics of the model at different layers. Experiments show that the model's information accumulation follows a nonlinear exponential law, and the Multilayer Perceptron (MLP) accounts for a higher proportion in the final output than the attention mechanism. Further experiments indicate that minor initial value perturbations will have a substantial impact on the model's reasoning ability, confirming the theoretical analysis that large language models are chaotic systems. This research provides a chaos theory framework for the interpretability of LLMs' reasoning and reveals potential pathways for balancing creativity and reliability in model design.