AI模型越准，越难验证其可靠性，这是根本限制。
The Verification Tax: Fundamental Limits of AI Auditing in the Rare-Error Regime
- 证明校准误差估计存在理论极限，无法突破
- 模型越精确，验证难度指数级上升，23%对比无法区分
- 自评估无效，需主动查询才能可靠检测偏差
深度学习中最受引用的校准结果——在CIFAR-100上温度后调整的ECE为0.012（Guo等，2017）——低于统计噪声下限。我们证明这并非实验缺陷，而是一种规律：以模型错误率ε为条件，校准误差估计的极小极大率为Θ((Lε/m)^{1/3})，任何估计器都无法超越此界。这一“验证税”表明，随着模型性能提升，验证其校准性变得愈发根本困难——计算方向相反却指数级加剧。我们建立四项颠覆常规评估实践的结果：(1) 无标签自评估对校准毫无信息量，上限恒定且与算力无关；(2) 在mε≈1处出现尖锐相变，低于该值时偏差不可检测；(3) 主动查询可消除利普希茨常数，使估计退化为检测；(4) 验证成本随流水线深度以速率L^K指数增长。我们在五个基准（MMLU、TruthfulQA、ARC-Challenge、HellaSwag、WinoGrande；约27,000项）上验证，涵盖6个大语言模型（5个系列，参数规模8B–405B），共27个模型-基准组合，使用基于logprob的置信度，95%自助置信区间与置换检验。自评估不显著在80%组合中成立。在前沿模型中，23%的成对比较无法区别于噪声，意味着可信的校准声明必须报告验证下限，并在性能接近基准分辨能力时优先采用主动查询。
原文摘要 · Abstract (English)
The most cited calibration result in deep learning -- post-temperature-scaling ECE of 0.012 on CIFAR-100 (Guo et al., 2017) -- is below the statistical noise floor. We prove this is not a failure of the experiment but a law: the minimax rate for estimating calibration error with model error rate epsilon is Theta((Lepsilon/m)^{1/3}), and no estimator can beat it. This "verification tax" implies that as AI models improve, verifying their calibration becomes fundamentally harder -- with the same exponent in opposite directions. We establish four results that contradict standard evaluation practice: (1) self-evaluation without labels provides exactly zero information about calibration, bounded by a constant independent of compute; (2) a sharp phase transition at mepsilon approx 1 below which miscalibration is undetectable; (3) active querying eliminates the Lipschitz constant, collapsing estimation to detection; (4) verification cost grows exponentially with pipeline depth at rate L^K. We validate across five benchmarks (MMLU, TruthfulQA, ARC-Challenge, HellaSwag, WinoGrande; ~27,000 items) with 6 LLMs from 5 families (8B-405B parameters, 27 benchmark-model pairs with logprob-based confidence), 95% bootstrap CIs, and permutation tests. Self-evaluation non-significance holds in 80% of pairs. Across frontier models, 23% of pairwise comparisons are indistinguishable from noise, implying that credible calibration claims must report verification floors and prioritize active querying once gains approach benchmark resolution.
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