面包还是法棍？一项关于任务拓扑、长度泛化和推理轨迹益处的研究
Boule or Baguette? A Study on Task Topology, Length Generalization, and the Benefit of Reasoning Traces
AI总结：
本研究通过PITA数据集探讨推理轨迹在不同任务拓扑和长度泛化中的表现，揭示了RT模型在广度任务中的优势及深度任务的局限性。
摘要：
近年来，推理模型取得了显著进步：神经网络在生成最终输出前会生成中间推理轨迹（RTs）。尽管进展迅速，我们对推理轨迹如何支持推理以及这一范式的局限性仍不完整。为了促进更清晰的理解，我们引入了PITA：一个包含超过2300万条命题逻辑语句及其相应证明的大型数据集。作为稳健推理的基准，我们专注于长度泛化：如果模型被训练以确定具有固定长度证明的语句的真值或假值，它在需要更长证明的语句上能有多好？我们提出了（1）任务深度和（2）任务广度的概念，分别衡量（1）解决一个任务中的示例所需的步骤数和（2）一个任务中不同示例的数量。我们通过PITA的不同子集变化这些量，发现RT模型在广度和浅度的子集上泛化良好，而在狭窄和深度的子集上相对于非RT基线模型表现较差。为了确定我们的结果是否专属于PITA还是普遍现象，我们将其与基于三段论的简单合成任务进行了比较。我们得出的理论表明了限制RT模型在深度任务上表现的 fundamental scalings，并突显了其在广度任务上的泛化优势。我们的发现总体上识别了使用推理轨迹的固有优势和局限性。
英文摘要：
Recent years have witnessed meteoric progress in reasoning models: neural networks that generate intermediate reasoning traces (RTs) before producing a final output. Despite the rapid advancement, our understanding of how RTs support reasoning, and where this paradigm fails, remain incomplete. To promote greater clarity, we introduce PITA: a novel large-scale dataset of over 23 million statements in propositional logic and their corresponding proofs. As a benchmark for robust reasoning, we focus on length generalization: if a model is trained to determine truth or falsity on statements with proofs up to fixed length, how well does it generalize to statements requiring longer proofs? We propose notions of (1) task depth and (2) task breadth, which measure respectively (1) the number of proof steps required to solve a proposition and (2) the number of unique propositions within a task family. We vary these quantities across subsets of PITA, and find that RT models generalize well on relatively broad and shallow subsets, while deteriorating on relatively narrow and deep subsets compared to non-RT baselines. As a controlled point of comparison, we study a separate, tractable transitive inference task that exhibits qualitatively similar behavior. Our accompanying theory explains the scalings observed in this simpler setting, suggesting one mechanism by which breadth can favor RT models while depth can expose long-context weaknesses. Our findings suggest salient benefits and limitations of proof-like reasoning traces in controlled length-generalization settings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
