Testing for Stable Intervals in Non-Stationary Time Series

What the math gives to ML

The paper formalizes the existence of a useful stable period through an infimum over sliding-window suprema, rather than requiring stability over the full trajectory. Its transferable asset is a duration-aware stability functional combined with local smoothing and uncertainty calibration under dependent, non-stationary noise. In neural-network training, this can replace ad hoc patience rules with a statistically calibrated detector for plateaus in validation loss, gradient norms, or parameter drift. The most practical use is to trigger learning-rate decay or early stopping only when a sufficiently long stable interval is supported by the data.