Emergent Causal-Geometric Dynamics Across Depth in Large Language Models

Abstract

Geometric analyses of large language model (LLM) representations reveal structured variation across depth but remain fundamentally correlational with respect to token prediction formation. Meanwhile, causal interventions expose depth-dependent efficacy profiles without a unifying account of their representational dynamics. A complete account of LLM function requires explaining how representational structure evolves across depth to causally produce predictions. We synthesize these perspectives by combining geometric analysis with mechanistic interventions, explicitly centralizing depth-wise dynamics as the organizing axis for interpreting LLM function. In decoder-only LLMs, we identify a sharp transition from context-processing to prediction-forming computation, accompanied by a more gradual reorganization of representational geometry across layers. This synthesis reveals a late-layer geometric code in which angular structure parameterizes next-token distributional similarity and enables selective causal control over predictions, while representation norms encode information largely decoupled from prediction. Together, our results provide a synthesis of causal and geometric perspectives, yielding a mechanistic account of how control-relevant geometric dynamics across depth transform context into prediction in language models. This perspective reconciles previously puzzling findings and implies that layer-wise function cannot be understood or effectively intervened upon in isolation, but only within the emergent global dynamical structure of the network.