从决策理论看测试时训练，解释如何稳定高效地调整模型。
A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt
- 将TTT视为核区的贝叶斯推断，用信号噪声比指导更新方向。
- 证明通过提示证据选择更新步数可获PAC-Bayes保证，防过拟合。
- 提出基于线性高斯模型的最优子空间选择规则，适合选注意力头。
测试时训练（TTT）通过参数更新将预训练模型适配到每个提示，提升在预训练与测试分布偏移下的准确率。然而其性能常受不稳定性及对超参数（如更新步数、子空间）敏感的影响。本文从决策理论视角出发，将TTT视为核区的隐式贝叶斯推断。在高斯过程基准下，我们发现当更新方向与提示的信噪比谱匹配且对齐查询相关特征方向时，可降低预测误差。由此得出三个结果：(1) 说明固定更新步数和子空间在分布偏移下失效，推动自适应策略；(2) 证明基于提示证据选择更新步数具有对抗过拟合的PAC-Bayes保证；(3) 在线性高斯修正模型下刻画贝叶斯最优更新子空间，提出用于选择Transformer块与注意力头的评分准则。该理论解释了TTT的实验不稳定性，迈向对何时、多远、向何方向调整的原理性指导。
原文摘要 · Abstract (English)
Test-time training (TTT) adapts a pretrained model to each prompt via parameter updates, improving accuracy under pretraining-to-test distribution shifts. Yet, its performance often suffers from instability and sensitivity to hyperparameters such as update steps and subspace. We explain this behavior through a decision-theoretic lens, treating TTT as implicit Bayesian inference in the kernel regime. Under a Gaussian process benchmark, we show that TTT reduces prediction error when updates are spectrally matched to the prompt's signal-to-noise ratio and aligned with query-relevant eigen-directions. This perspective underpins the following results: (1) we show when fixed update steps and subspaces fail under distribution shifts, motivating adaptive strategies; (2) we prove that selecting update steps via prompt evidence admits a PAC-Bayes guarantee against overfitting; and (3) we characterize the Bayes-optimal update subspace under a linear-Gaussian correction model, yielding a scoring rule for selecting Transformer blocks and heads. Our theory helps explain the empirical instability of TTT, taking a step toward principled guidance for when, how far, and which directions to adapt.
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