Multi-Scale Probabilistic Generation Theory: A Unified Information-Theoretic Framework for Hierarchical Structure in Large Language Models

Abstract

Large Language Models (LLMs) exhibit remarkable emergent abilities but remain poorly understood at a mechanistic level. This paper introduces the Multi-Scale Probabilistic Generation Theory (MSPGT), a theoretical framework that models LLMs as Hierarchical Variational Information Bottleneck (H-VIB) systems. MSPGT posits that standard language modeling objectives implicitly optimize multi-scale information compression, leading to the spontaneous formation of three internal processing scales-Global, Intermediate, and Local. We formalize this principle, derive falsifiable predictions about boundary positions and architectural dependencies, and validate them through cross-model experiments combining multi-signal fusion and causal interventions. Results across Llama and Qwen families reveal consistent multi-scale organization but strong architecture-specific variations, partially supporting and refining the theory. MSPGT thus advances interpretability from descriptive observation toward predictive, information-theoretic understanding of how hierarchical structure emerges within large neural language models.