From Chains to DAGs: Probing the Graph Structure of Reasoning in LLMs
This addresses the fundamental understanding of reasoning representations in LLMs, which is incremental as it builds on prior linear-chain assumptions.
The study tackled the problem of whether large language models internally represent multi-step reasoning as directed acyclic graphs rather than linear chains, finding that DAG structure is meaningfully encoded in hidden states with recoverability peaking in intermediate layers and varying by factors like node depth and model scale.
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 are 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 and where this structure emerges across layers. We associate each reasoning node with a textual realization and train lightweight probes to predict node depth, pairwise distance, and adjacency from hidden states. Using these probes, we analyze the emergence of DAG structure across layers, reconstruct approximate reasoning graphs, and evaluate controls that disrupt reasoning-relevant structure while preserving surface text. Across reasoning benchmarks, we find that DAG structure is meaningfully encoded in LLM representations, with recoverability peaking in intermediate layers, varying systematically by node depth, edge span, and model scale, and enabling nontrivial recovery of dependency graphs. These findings suggest that LLM reasoning is not purely sequential, but exhibits measurable internal graph structure.