What Should Consistency Preserve? Readout-Geometric Information Transport for Semi-Supervised Regression

Consistency regularization is deceptively underspecified for scalar regression: matching two views does not determine which task information should remain invariant. We show that this missing choice separates useful unlabeled supervision from agreement that distorts the target coordinate or erases label-predictive geometry. We introduce Readout-Geometry Consistency, a unified framework that factorizes consistency into a readout-induced transport space and a source timescale. A task can therefore transport either its scalar coordinate or protected within-fiber geometry, using an online or temporally persistent source, through the same objective. We derive when coordinate transport reduces target risk, characterize the variance–lag trade-off of temporal sources, and establish first-order prediction invariance for protected tangent updates. Across image age estimation, text rating prediction, and speech quality assessment, RGC establishes new best reported means on two benchmarks and matches leading performance on the third, while controlled interventions confirm the predicted roles of view support, source timescale, and transport geometry.