AVERT: W1-Anchored Verification for Reliable Test-Time Adaptation in Regression

Test-time adaptation (TTA) for regression lacks the entropy-based confidence signal that classification TTA relies on, so naive adaptation can shift predictions in arbitrary directions. Analyzing four recent regression and time-series TTA methods, we identify four failure modes—negative transfer on low-shift data, unreliable low-order moment matching, over-adaptation, and label-shift confusion, where a near-perfect source model is corrected toward the source prediction distribution, moving predictions away from the target truth (on Concrete, SSA inflates MAE by $4.3\times$). We propose AVERT, a safe TTA framework built on three principles. (1) W1-anchoring: because target labels are standardized with source statistics, the 1-Wasserstein distance from a corrected prediction to the source label distribution is a label-free verification signal for regression TTA (correlation $+0.875$ with true MAE change), with a finite-sample concentration analysis. (2) Verification-gated adaptation: a non-parametric quantile-transport bridge (QTB) combined with a gated test-time self-supervised representation adaptation (TT-SRA), both verified and gated by the W1 anchor. (3) No-harm safeguards: a safe-return gate detects label-shift confusion and refuses adaptation. Across 15 regression benchmarks and three backbones, AVERT significantly outperforms Original ($p=1.8\times 10^{-2}$) and all six adaptation baselines (up to $p<10^{-18}$), achieves the lowest average MAE ($0.486$) with the best average rank on two of three backbones, is the only method that never catastrophically degrades on any of the 45 dataset–backbone combinations, and transfers to a fully external dataset with zero retuning.