From Chains to DAGs: Probing the Graph Structure of Reasoning in LLMs

Abstract: Recent progress in LLMs has renewed interest in mechanistically characterizing how multi-step reasoning is represented and computed. While much prior work treats reasoning as a linear chain of steps, many reasoning problems are more naturally structured as directed acyclic graphs (DAGs), where intermediate conclusions may depend on multiple premises, branch into parallel sub-derivations, and later merge or be reused. Understanding whether such graph-structured reasoning is reflected in model internals remains an open question. In this work, we introduce Reasoning DAG Probing, a framework that directly asks whether LLM hidden states encode the geometry of a reasoning DAG in a linearly accessible form, and where this structure emerges across layers. Within this framework, we associate each reasoning node with a textual realization and train lightweight probes to predict two graph-theoretic properties from hidden states: node depth and pairwise node distance. We use these probes to analyze the layerwise emergence of DAG structure and evaluate controls that disrupt reasoning-relevant structure while preserving superficial textual properties. Our results provide evidence that reasoning DAG geometry is meaningfully encoded in intermediate layers, with recoverability varying systematically by node depth and model scale, suggesting that LLM reasoning is not only sequential but exhibits measurable internal graph structure.