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

Abstract

Recent progress in large language models has renewed interest in how multi-step reasoning is represented internally. While prior work often treats reasoning as a linear chain, many reasoning problems can be more naturally modeled as directed acyclic graphs (DAGs), where intermediate conclusions branch, merge, and are reused. Whether such graph structure is reflected in model internals remains unclear. We introduce Reasoning DAG Probing, a framework for testing whether LLM hidden states linearly encode properties of an underlying reasoning DAG. We formalize each premise, intermediate conclusion, and final answer as a DAG node, and train lightweight probes to predict node depth, pairwise distance, and adjacency from hidden states. Using these probes, we analyze the layerwise emergence of DAG structure, reconstruct approximate reasoning graphs, and evaluate controls that disrupt reasoning-relevant structure. Across logical, mathematical, and code reasoning benchmarks, we find that DAG structure is meaningfully encoded in LLM representations: recoverability peaks in intermediate layers; later layers preferentially recover deeper nodes and longer-range dependencies; larger models exhibit stronger DAG recoverability. During autoregressive generation, post-trained models exhibit clearer, progressively strengthening DAG structure, which broadly anticipates answer correctness trends. These findings suggest that LLM reasoning is not purely sequential, but exhibits measurable internal graph structure.