跳转至

冲突监督改变的是承诺而非能力：在惯例无关评分下归零的12.29个标准差数据排布效应

Conflicting Supervision Moves Commitment, Not Capability: A \(12.29\sigma\) Arrangement Effect That Is Exactly Zero Under a Convention-Agnostic Score

作者 (Authors) ： Wenhui Chen
提交时间 (Submitted) ： 2026 年 9 月 23 日 (23 September 2026)
主要学科 (Primary Subject) ： 人工智能 (Artificial Intelligence, cs.AI)
arXiv 标识符 (arXiv ID) ： arXiv:2610.00234 [cs.AI]

文章背景与核心概要

在大语言模型 (Large Language Model, LLM) 的监督微调 (Supervised Fine-Tuning, SFT) 与训练中，当训练数据包含两种互不兼容但各自正确的表达惯例时，数据的输入顺序往往会对最终评测产生显著干扰，常被认为深刻影响了模型能力。本文通过严格控制训练预算与数据集，深入剖析了学习率调度器与数据排布之间的相互作用机制，证明数据排序所引发的剧烈波动并未真正改变模型的底层“能力”，而仅仅是决定了模型在没有明确指令时优先“承诺”遵循哪一种特定惯例。令人惊叹的是，当引入“惯例无关”的评估准则 (只要模型在任一合规惯例下求解正确即可) 时，此前高达 \(12.29\sigma\) 的巨大排布偏差直接归零，模型综合准确率在各种数据排布下保持高度守恒。进一步实验发现，只需在提示词 (Prompt) 中显式注明当前生效的惯例，即可轻松化解数据顺序带来的偏好锁定，并释放出高达 87.5% 的能力上限，为大模型数据工程与公平评测提供了极具穿透力的新视角。

📌 核心要点

📌 Summary

面对同一批问题，如果采用两种互不相容却各自正确的表达规范对机器学习模型展开训练，模型究竟会学到什么？作者在严格控制训练算力预算、训练数据集以及优化路径的前提下，深入探究了数据的先后排列顺序与学习率调度策略如何联手塑造模型的最终表现。

This paper investigates what happens when a machine learning model is trained on identical problems written under two incompatible yet equally correct conventions. By keeping the training budget, dataset, and path strictly controlled, the author examines how the arrangement of data and the learning rate schedule influence model outcomes.

该项研究的核心结论包括：

Key takeaways from the research include:

  • 学习率调度器充当加权平均算子 (The Learning Rate Schedule as an Averaging Operator) ： 在优化算法中，数据排布效应与学习率调度是以互相独立的乘法因子形式发挥作用的。学习率衰减策略能够避免大步长与未收缩的余项在最终一步发生剧烈碰撞，从而有效平抑了数据顺序带来的影响；而恒定学习率策略则不具备这种平抑机制。
  • 惯例承诺与底层能力的辨析 (Commitment vs. Capability) ： 研究证明，“顺序至关重要”与“顺序无关紧要”实际上只是同一控制旋钮的两端。训练数据的排布顺序只是促使模型在无约束时“承诺”遵循某一种具体惯例，而并未真正改变其解决问题的底层“能力”。
  • 惯例无关下的能力守恒 (Convention-Agnostic Conservation) ： 在引入不区分惯例的综合评估指标后，原本测得的 \(12.29\sigma\) 剧烈排布跳变效应直接归零 (在十二个测试组中，\(\text{acc}_A + \text{acc}_B\) 的总和波动始终保持在 9.7% 的极小范围内) 。
  • 提示词干预消除偏差 (Prompt Intervention) ： 只要在提示词中显式标注当前生效的规范惯例，即可绕过数据顺序带来的排布锁定，并成功恢复高达 87.5% 的联合能力上限。
  • The Learning Rate Schedule as an Averaging Operator: The arrangement effect and schedule enter the optimization as separate, multiplied factors. While decaying schedules prevent large step sizes and uncontracted remainders from colliding at the final step, constant schedules do not, which moderates ordering effects.
  • Commitment vs. Capability: "Order matters" and "order does not matter" are demonstrated to be two ends of a single knob. Training order forces a model to commit to a specific convention rather than altering its underlying capability.
  • Convention-Agnostic Conservation: The measured \(12.29\sigma\) arrangement switch drops to exactly zero under a convention-agnostic metric (\(\text{acc}_A + \text{acc}_B\) remains constant within 9.7% across twelve arms).
  • Prompt Intervention: Marking the active convention explicitly in the prompt bypasses the ordering switch and recovers 87.5% of the union ceiling.

📄 论文摘要

📄 Abstract

如果用两种互不兼容、但各自完全正确的表达惯例来书写同一批问题，并以此训练模型，那么这些数据的输入先后顺序究竟会在模型参数中留下怎样的印记？学习率调度策略绝非这一问题的旁观背景，它本质上是一个加权平均算子，正是它决定了最终的答案。我们从理论上证明了一个上界：在该上界中，数据排布和学习率调度以完全解耦的乘法因子形式作用于数据排序效应——排布方式仅体现为分块周期 (Block Period) ，而调度策略则仅决定了最终模型状态能对训练历程中的某一个特定时刻施加多大的权重。衰减型学习率调度器无法在同一个时刻同时出现大步长与未收缩的余项；相反，恒定学习率调度器在训练的最后一步恰恰会遭遇这种冲突。尽管在预训练阶段已有研究指出衰减调度能够平抑排序效应，但揭示其内在机理、实现两者因素的数学分离，以及对这两部分进行严格受控的定量测量，则是本文的核心原创贡献。我们在同一语料库、相同算力预算下设计了十种数据排序，除优化路径外完全保持一致，并在仅有 lr_scheduler_type 不同的两类调度策略下各运行了一次：在恒定学习率下，中间分布在分配份额上跨越了 0.2221，对比底限达到 11.63，且随着排布分块程度的加深呈现单调变化。而在所有已发表实验所普遍采用的单次余弦 (Cosine) 衰减调度下，原本自身分辨率足以分辨出约十种状态的十个实验组，最终仅坍缩为两种可区分的状态。“顺序重要”与“顺序无关”，本质上不过是同一个旋钮的两端。优化路径真正在参数中刻下的，仅仅是模型到底承诺遵循哪一种惯例，而传统的精确匹配 (Exact-Match) 基准测试根本无法洞察这一真相。在全部十二个实验分支中，尽管惯例分配份额在 0.04 到 0.87 之间大幅波动，但两者的准确率之和 \(\text{acc}_A + \text{acc}_B\) 的变动幅度始终保持在 9.7% 以内；因此，本文所测量到的高达 \(12.29\sigma\) 的排布跳变效应，在不区分具体惯例的评估指标下其实恰好归零。该守恒定律在采用衰减调度的模型组中表现得尤为纯粹，而恒定学习率组因包含更多噪声而不易直接观测。只要在提示词中明确标注当前生效的惯例，这种由数据排序引起的跳变就会彻底瓦解，并能达到联合能力上限的 87.5%。

💬 [原文引用 / Original Quote]: "Train a model on the same problems written under two incompatible conventions, both correct, and ask what the ordering of that data writes into the parameters. The learning-rate schedule is not a background condition for that question. It is the averaging operator, and it decides the answer. We prove a bound in which the arrangement and the schedule enter the ordering effect as separate multiplied factors: the arrangement only as a block period, the schedule only as how much weight the endpoint can place on any one moment of the run. A decaying schedule cannot put a large step size and an uncontracted remainder at the same moment; a constant one does exactly that at the last step. That decay moderates ordering effects has been reported in pretraining; the mechanism, the separation, and a controlled measurement of both halves are ours. Ten orderings of one corpus, one budget, everything but the path held fixed, run twice under families differing in lr_scheduler_type and nothing else: at a constant rate the interior spans 0.2221 in allocation, 11.63 contrast floors, monotone in how blocked the arrangement is. Under the single cosine every published arm uses, the same ten arms occupy two distinguishable states where their own resolution would allow about ten. 'Order matters' and 'order does not matter' are the two ends of one knob. What the path writes is which convention the model commits to, and no exact-match benchmark can see it. Across twelve arms acc_A+acc_B is constant to within 9.7% while the allocation share runs 0.04 to 0.87, so the 12.29-sigma arrangement switch this paper measures is exactly zero under a convention-agnostic metric. That conservation is quoted from the decayed family throughout, the constant-rate one being a noisier place to read it. Marking the convention in the prompt collapses the switch and reaches 87.5% of the union ceiling."

🛠️ 论文元数据与全文链接