Variance-Guided Time-Series Correction

Post-hoc correction offers a lightweight paradigm to mitigate residual errors in frozen models. The central challenge is deciding which relationships finite calibration data can support, as similar residual energies often correspond to fundamentally different corrective values. Through multi-seed spectral diagnostics, we reveal that residual errors conflate persistent compensable patterns with stochastic training-run variations, motivating a correction rule that dynamically adapts its dependency structure. To resolve this, we formulate this choice as covariance-resolution selection, ranging from coordinate-wise scaling to channel, phase, and neighboring-mode interactions. Theoretically, our analysis characterizes linearly recoverable error, decomposes the benefit of expanding structure into additional recoverable signal and fitted-operator excess, and bounds corrective-gain estimation error uniformly over norm-bounded classes. The resulting framework fits closed-form candidates and selects their resolution, ridge multiplier, and fitting source using cross-fitted validation. Across an extensive 320-case evaluation matrix, our method improves $279/320$ settings with an average relative MSE reduction of $6.34\%$, compared with $3.72\%$ for the best fixed resolution. It also improves outputs already enhanced by post-hoc adapters or training losses. These results establish structural resolution as an effective decision variable, showing that adapting complexity to calibration support enables reliable correction from a single frozen checkpoint.