Researchers have identified a critical stabilization threshold for dynamic preconditioning in gradient descent methods. This threshold determines when the Polyak-Ruppert averaging technique, fundamental for online inference, maintains its asymptotic normality. The study proposes a preconditioner-isolating decomposition to analyze the error dynamics and establishes that the rate at which the preconditioning matrix stabilizes must exceed a specific threshold related to the step-size exponent. AI
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IMPACT Provides theoretical underpinnings for the stability of advanced optimization techniques used in training large-scale machine learning models.
RANK_REASON Academic paper published on arXiv detailing theoretical advancements in optimization algorithms.