אופטימיזציה סטוכסטית תחת ספקטרום פאולר: גבולות צמודים וניתוח שפל

תקציר מקורי באנגליתarXiv:2609.36271v1 Announce Type: new Abstract: Recent work has established that power-law spectral conditions on data enable tight convergence bounds for deterministic gradient descent, resolving the conflict between classical exponential bounds and observed power-law learning curves. In this work, we extend this result to the stochastic regime of high-dimensional machine learning. We provide two main contributions: (1) We generalize the power-law spectral theory to Stochastic Gradient Descent (SGD), showing that the same spectral exponents govern stochastic dynamics; (2) For the fundamental case of isotropic Gaussian data, we provide a precise analysis of data shuffling, deriving exact constants that prove Single Shuffle is strictly superior to Flip-Flop and IID sampling. Our results bri