FORTA: Feedback-Guided Predictive Distribution Repair under Heterogeneous Shift

Test-time adaptation is difficult because the appropriate correction can change as target conditions evolve. Methods built around a particular adaptation mechanism restrict how the predictive distribution can be corrected. This work studies test-time adaptation with sparse delayed feedback: predictions are made before labels are available, and only a small fraction of labels are released later. Adaptation is formulated as learning and allocating a time-varying set of predictive distribution corrections from a shared frozen representation. FORTA maintains complementary source-anchored corrections. Every supervised member continues learning from the same released feedback regardless of its current weight, while saved pre-feedback predictions determine future influence. This separates how the correction set evolves from which corrections shape the next prediction. The analysis characterizes an information boundary for label-free conditional adaptation and, in a source-anchored construction, establishes an allocation advantage over separately tuned anchors and fixed mixtures of optimized candidates. Across seven image and signal benchmarks, FORTA improves macro-F1 over the source predictor. We verify how feedback availability and regime duration affect adaptation, and when adaptive allocation improves predictive performance, through synthetic and matched-portfolio experiments.