浅思深解：控制循环动态以实现可靠的测试时深度
Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth
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中文总结 AI 辅助
该研究针对循环深度推理器的测试时迭代问题，提出通过控制算子动态状态实现深度安全，提升了数独等任务的外推准确率，为循环模型的可靠深度推理提供了准则。
中文摘要 AI 辅助
循环深度推理器旨在通过在测试时进行更长时间的迭代更新来解决更难的问题，但额外的迭代可能会提升、保持或降低答案的质量。我们表明，训练后的算子的可测量属性——其有限时间动态状态（估计为收敛、边缘或漂移），可指示上述哪种情况发生。我们给出了深度安全的充分条件：一旦算子的每步位移相对于解码器裕度很小，进一步迭代下解码的答案不会改变。在算法任务上的实验表明，该任务针对每个难度层级使用800个未增强示例进行训练，收敛算子不会因增加深度而性能下降，且在某些任务上，增加深度可提升更难的未见实例（数独，在训练范围外从0.19提升至0.34）的准确率。单一终端不动点目标可使状态与深度行为同步：移除该目标会导致漂移并消除收益，将其添加到通用循环中可实现进位传播任务上的深度安全外推。我们给出了有用测试时深度的四个操作准则，并用其分类失败模式，作为一致性检查，对Huginn-3.5B应用相同测量，发现其属于非收敛类别。
英文摘要
Recurrent-depth reasoners aim to solve harder problems by iterating their update longer at test time, but additional iterations can improve, preserve, or degrade an answer. We show that a measurable property of the trained operator, its finite-time dynamical regime (estimated as settling, marginal, or drifting), indicates which of these occurs. We give a sufficient condition for depth-safety: once an operator's per-step displacement is small relative to the decoder margin, the decoded answer cannot change under further iterations. Empirically, on algorithmic tasks trained from $800$ unaugmented examples per difficulty tier, settling operators do not degrade with added depth, and on some tasks convert it into higher accuracy on harder unseen instances (Sudoku, $0.19$ to $0.34$ past the training horizon). A single terminal fixed-point objective moves the regime and the depth behavior together: removing it induces drift and removes the gains, and adding it to a generic recurrence yields depth-safe extrapolation on carry propagation. We give four operational criteria for useful test-time depth, use them to catalogue failure modes, and, as a consistency check, apply the same measurements to Huginn-3.5B, which falls in the non-settling family.
