arXiv:2605.05592cs.LGcs.IT2026-05被引 1

投票提升模型性能的机制远比想象复杂,可能非单调甚至多次反转。

When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation

  • 基于交换性假设,揭示投票效果由潜在正确率分布决定
  • 发现投票曲线可出现无限次趋势变化,且形状不唯一对应分布
  • 提出签名函数新视角,区分不同信息获取方式的估计能力

多数投票是少数可改善固定随机预测器的黑箱干预手段:重复调用成本低于修改高能力模型。经典固定能力理论认为投票行为单调——超过多数阈值则增益,低于则受损。我们证明该图景根本不完备。在德·芬内蒂对可交换重复准确性的表示下,投票受每例正确概率的潜在分布支配。即使简单混合分布也能生成显著不同的投票曲线,包括非单调行为,甚至在显式构造中出现无穷多趋势转变。完整潜在律决定曲线,但曲线无法还原律。投票实际恢复的是带符号的投票签名:在每个二项方差尺度上,记录超过而非低于多数阈值的潜在质量。主定理证明完整奇预算曲线与该签名等价:曲线增量为带符号的豪斯多夫矩,且全曲线可唯一还原签名。此视角解释形状现象、分支对称不可识别性、可实现性、变异性和端点速率。同时区分估计范式:直接获取每例成功概率信息可目标全签名,而固定深度分组标签仅揭示有限前缀。

原文摘要 · Abstract (English)

Majority voting is one of the few black-box interventions that can improve a fixed stochastic predictor: repeated access can be cheaper than changing a high-capability model. Classical fixed-competence theory makes this intervention look monotone -- more votes help above the majority threshold and hurt below it. We show that this picture is fundamentally incomplete. Under the de Finetti representation for exchangeable repeated correctness, voting is governed by a latent distribution of per-example correctness probabilities. Even simple latent mixtures can generate sharply different voting curves, including nonmonotone behavior and, in an explicit construction, infinitely many trend changes. The full latent law determines the curve, but the curve does not determine the law. The exact object recovered by voting is a signed voting signature: at each binomial variance scale, it records excess latent mass above rather than below the majority threshold. Our main theorem proves that the complete odd-budget curve and this signature are equivalent: the curve increments are signed Hausdorff moments, and the full curve recovers the signature uniquely. This viewpoint explains shape phenomena, branch-symmetric nonidentifiability, realizability, variation, and endpoint rates. It also separates estimation regimes: direct per-example success-probability information targets the full signature, whereas fixed-depth grouped labels reveal only a finite prefix.

集成学习投票机制概率建模统计推断

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