Multi-Scale Probabilistic Generation Theory: A Hierarchical Framework for Interpreting Large Language Models

Large Transformer based language models achieve remarkable performance but remain opaque in how they plan, structure, and realize text. We introduce MultiScale Probabilistic Generation Theory (MSPGT), a hierarchical framework that factorizes generation into three semantic scalesglobal context, intermediate structure, and local word choices and aligns each scale with specific layer ranges in Transformer architectures. To identify scale boundaries, we propose two complementary metrics: attention span thresholds and inter layer mutual information peaks. Across four representative models (GPT-2, BERT, RoBERTa, and T5), these metrics yield stable local/intermediate/global partitions, corroborated by probing tasks and causal interventions. We find that decoderₒnly models allocate more layers to intermediate and global processing while encoderₒnly models emphasize local feature extraction. Through targeted interventions, we demonstrate that local scale manipulations primarily influence lexical diversity, intermediate-scale modifications affect sentence structure and length, and globalₛcale perturbations impact discourse coherence all with statistically significant effects. MSPGT thus offers a unified, architecture-agnostic method for interpreting, diagnosing, and controlling large language models, bridging the gap between mechanistic interpretability and emergent capabilities.