推理模型不只思考更久，它们的移动方式不同
Reasoning Models Don't Just Think Longer, They Move Differently
AI总结：
本文研究了推理训练模型在生成链式思维时的轨迹差异，发现通过长度校正后，不同领域中难度与轨迹几何的耦合关系存在显著差异，尤其是在代码领域中，推理训练模型表现出更直接的轨迹和更一致的局部曲率。
摘要：
经过训练的推理语言模型通常在更难的问题上消耗更多标记，但更长的思维链并不表明模型只是计算更多步骤或遵循不同的内部轨迹。我们通过在编程、数学和布尔可满足性问题中研究链式思维生成过程中的隐藏状态轨迹来区分这一区别。原始轨迹几何强烈受到生成长度的影响：更长的生成会机械地改变路径统计，因此在没有调整的情况下，基于难度的比较是误导的。在残差化轨迹统计后，难度在所有研究的领域中系统地与修正后的轨迹几何相关联。在代码领域中，最清晰的推理特定分离出现在更难的问题中，推理训练模型显示出更直接的修正轨迹和更一致的局部曲率，而与匹配的指令训练基线相比，这种差异更小。在数学和布尔可满足性问题中，修正后的难度-几何耦合较弱，但仍存在。提示阶段的线性探测不反映代码领域的分离，行为注释显示更强的修正耦合与策略转变和不确定性监控同时出现。这些发现确立了长度校正作为生成时间轨迹分析的先决条件，并表明推理训练可以与不同的修正轨迹几何相关联，这种效果的强度取决于领域。
英文摘要：
Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.
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。
