Subspace-Coded Parallel Exploration for Forward-Only Test-Time Adaptation

Zeroth-order (ZO) optimization enables forward-only test-time adaptation (TTA), avoiding the computation and memory overhead of backpropagation. However, existing direction-centric approaches face an exploration–exploitation dilemma in capturing gradient energy: exploiting promising directions may overlook complementary gradient components, whereas broader exploration typically requires additional forward evaluations. To address this limitation, we propose **S**ubspace-**C**oded **O**ptimization via **P**arallel **E**xploration (**SCOPE**), a novel TTA framework that shifts from individual direction selection to higher-dimensional subspace exploration. Specifically, we introduce a perturbation encoding scheme that assigns different samples within a batch complementary combinations of shared basis directions, rather than applying the same perturbation to all samples. A lightweight least-squares estimator jointly decodes their loss differences to estimate batch-average directional responses for a shared prompt update. To support batch-coupled objectives such as feature-statistic alignment, we further decompose their batch-level loss differences into exact sample-wise contributions, preserving the original adaptation objective while making its feedback compatible with the perturbation codes. Together, these designs embed multi-directional measurements into existing batch computation, broadening gradient-energy coverage with only two forward passes. Extensive experiments across mild, continual, and wild TTA settings, together with natural-shift and quantized models, demonstrate the effectiveness and efficiency of SCOPE. Code will be publicly available.