AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-20
A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt
Test-time training (TTT) adapts a pretrained model to each prompt through parameter updates and improves accuracy under distribution shifts, but its performance is often unstable and sensitive to hyperparameters such as update steps and subspace. Treating TTT as implicit Bayesian inference in the kernel regime, the authors show on a Gaussian process benchmark 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. From this perspective they characterize when fixed update steps and subspaces fail, prove a PAC-Bayes guarantee for selecting update steps via prompt evidence, and derive a scoring rule for choosing Transformer blocks and heads.