當更多採樣反而有害時：測試時縮放的模態天花板與相關性天花板

摘要

人們想太多；語言模型過度取樣，過多的努力反而可能讓兩者都給出更差的答案。推理系統透過多次取樣來回答難題（測試時擴展），取樣次數越多，正確答案就越常出現，因此覆蓋率——至少有一次正確嘗試的問題比例——會上升，看似有所進展。但部署的系統必須回傳一個答案，而在不知道哪次嘗試正確的情況下選擇答案，這個過程稱為選擇；選擇存在上限，一旦超過某個臨界點，額外的取樣只會讓模型更確信於一個錯誤的答案，同時每次取樣都在增加成本。覆蓋率持續攀升與選擇停滯之間的差距——即可識別性差距——正是模型能得出但無法選出的答案。因此真正的問題不在於是否取樣，而在於取樣到何種程度；答案是：不用太深。就選取答案而言，表決通常在幾十次取樣內便已收斂，達到眾數上限；就評估基準而言，收斂得更快，即相關性上限。超過這個範圍，額外的取樣只會消耗算力卻毫無貢獻，甚至可能使答案更糟。本文將這個截斷點轉化為單一數值——有效取樣數，而任何一次取樣過程都已揭示此數值。瓶頸在於辨識正確答案，而非產生答案。

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.