Few-Query Quality Assessment for Unseen Machine Observers: Gauge-Invariant Decision Subspaces

Machine-oriented image quality is observer-dependent: visual models can prefer different processed versions of the same image. We study few-query calibration on a fixed content–candidate bank: source models provide complete responses, while a previously unseen observer reveals only a few candidate groups before its choices on other groups are predicted. A reconstruction-optimal low-rank basis can discard decisive candidate comparisons, and an empirical-Bayes posterior can depend on arbitrary factor coordinates unless its prior transforms with the basis. We introduce Gauge-Invariant Decision Subspaces (GIDS), which selects a decision-aligned subspace within a spectral dictionary and estimates its observer prior and residual noise in matching coordinates. Training simulates complete-group calibration; deployment uses a closed-form low-dimensional posterior. Theory establishes gauge-covariant prediction and a regret bound separating representation from posterior-identification error. Against a matched gauge-consistent SVD baseline, GIDS lowers observer-macro selection regret from 0.1282 to 0.1266 under CIFAR-10 architecture-family holdout, with mean improvements on prospectively frozen observers and a frozen CIFAR-100 domain. The results show the value of choosing a low-rank representation for decisions after calibration, rather than response reconstruction alone.