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

• URL: http://arxiv.org/abs/2606.15569v1
• Date: Sun, 14 Jun 2026 03:16:40 GMT
• Title: A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt
• Abstract summary: Test-time training adapts a pretrained model to each prompt via parameter updates.<n>We treat TTT as implicit Bayesian inference in the kernel regime.<n>We show that TTT reduces prediction error when updates are spectrally matched to the prompt's signal-to-noise ratio.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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