Recent progress in large language models 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.

翻译：大型语言模型的最新进展重新激发了人们对多步推理如何被表示和计算的机制性研究的兴趣。尽管许多先前工作将推理视为一个线性步骤链，但许多推理问题更自然地结构化为有向无环图（DAGs），其中中间结论可能依赖于多个前提，分支为并行子推导，并在后续合并或被重用。理解这种图结构推理是否反映在模型内部仍然是一个悬而未决的问题。在本工作中，我们引入了“推理有向无环图探测”框架，该框架直接探究大语言模型的隐藏状态是否以线性可访问的形式编码了推理有向无环图的几何结构，以及这种结构在哪些层中出现。在此框架内，我们将每个推理节点与一个文本实现相关联，并训练轻量级探测器从隐藏状态预测两个图论属性：节点深度和节点对距离。我们使用这些探测器分析有向无环图结构的逐层涌现，并评估那些破坏推理相关结构同时保留表面文本属性的对照实验。我们的结果提供了证据，表明推理有向无环图的几何结构在中间层中被有意义地编码，其可恢复性随节点深度和模型规模系统性地变化，这表明大语言模型的推理不仅是顺序的，而且展现出可测量的内部图结构。