A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt

Abstract: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.

Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)

arXiv:2606.15569 [cs.LG]

(or arXiv:2606.15569v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.15569 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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