מינימיזציה של סיכון אמפירי משוקלל ללמידת מכונה

תקציר מקורי באנגליתarXiv:2609.10767v1 Announce Type: cross Abstract: We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data. The training observations are generated from a fixed finite window of a stationary Gaussian sequence, and the sample weights are regularly varying. If the loss gradient at the population minimizer has Wiener-chaos rank $m$ and a nonzero low-frequency coefficient, then, in the long-memory interior regime, the finite-lag score reduces on the iterated-logarithm scale to a single weighted Hermite chaos. This yields an almost-sure Bahadur representation, an exact limsup law for the learned parameter, and, for $m\ge2$, the functional cluster set of the complete learning trajectory. Th