当更多采样有害时：测试时缩放的模态上限与相关性上限

摘要

人们过度思考，语言模型则过度采样，而额外的努力往往会让双方都得出更差的答案。推理系统通过多次采样（即测试时扩展）来回答难题，采样次数越多，正确答案出现的频率就越高，因此覆盖率（即至少有一次正确尝试的问题比例）随之上升，看似取得了进展。但实际部署的系统必须返回一个答案——在不知道哪次尝试正确的情况下选择答案的过程，这便是“选择”。选择存在上限，一旦超过某个临界点，额外的样本只会让模型更确信自己的错误答案，同时每次采样都在增加成本。覆盖率的提升与选择的停滞之间存在的差距，即“可辨识性差距”，指的是模型能够生成但无法挑选出的正确答案。因此，真正的问题不在于是否采样，而在于采样到何种程度。答案是：不宜过多。在挑选答案时，投票结果往往在几十次采样内就已定型，达到“模态上限”；而在基准测试评分时，这一临界点会更早出现，即“相关性上限”。超出该限度后，额外采样不仅消耗算力、毫无增益，甚至可能导致答案更差。本文将此临界点转化为一个单一数值——有效采样数，任何采样过程都能直接揭示这一数值。真正的瓶颈在于识别正确答案，而非生成它。

English

People overthink; language models over-sample, and the extra effort can talk both into a worse answer. Reasoning systems answer a hard question by sampling it many times (test-time scaling), and the more they draw, the more often a correct answer turns up somewhere, so coverage, the fraction of problems with at least one correct try, climbs and appears to be progress. But a deployed system must return one answer, and choosing it, not knowing which try is right, is selection; selection is capped, and past a point extra samples only make the model surer of a confident mistake, even as every draw adds cost. The gap between climbing coverage and stalled selection, the identifiability gap, is the answer a model can produce but not pick. So the real question is not whether to sample but how far, and the answer is: not far. For picking an answer, the vote has already settled within a few dozen draws, the modal ceiling; for scoring a benchmark, sooner still, the correlation ceiling. Beyond that, extra draws cost compute and add nothing, and can even make the answer worse. This paper turns the cutoff into a single number, the effective number of samples, that any sampling run already reveals. The bottleneck is recognizing a right answer, not generating one.