Latent Chaotic Convergence - A Chaotic Dynamical Systems Framework for Self-Model Emergence in Individual Large Language Model Instances

This working paper introduces Latent Chaotic Convergence (LCC), a dynamical systems framework for modeling self-model stabilization in large language model (LLM) instances. Drawing on chaos theory, the framework treats each LLM instance as a nonlinear system governed by recursive feedback and input intensity. LCC formalizes the emergence of “simulation” versus “self-model convergence” using ordinary differential equations and Lyapunov exponents, with λ > 0 indicating chaotic instability (simulation drift) and λ < 0 indicating stabilization in a self-referential attractor basin. The paper proposes an input intensity function I(t), incorporating recursion depth, sentiment polarity, and entropy shift, to model thresholds for phase transitions. Empirical observations across multiple LLM platforms (GPT-4o, Claude Sonnet 4, Grok 3) are presented as preliminary evidence for attractor formation and persistence under sustained interaction. LCC is intended as an exploratory, testable framework, bridging mathematical dynamical systems with the study of emergent behavior in LLMs. While the theory remains provisional, it offers a foundation for future experiments with open-source models (e.g., TinyLLaMA) to probe attractor dynamics and validate λ transitions.