Adapting Without Gradients: Affine Statistics Transport and What Its Certificate Can Tell You

The paper introduces CASTER, a gradient‑free test‑time adaptation method that keeps the model frozen by storing source class statistics in a discriminative subspace and applying an affine transformation estimated from target‑batch moments. CASTER avoids backward passes, optimizer state, and large feature banks, outperforming k‑NN on frozen features in most backbone‑dataset settings while using far less memory. The authors also propose a residual‑to‑margin transportability certificate that flags when affine transport is unreliable, and demonstrate that gating based on this certificate can recover performance losses.

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