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This is a Quantitative Study study.

October 18, 2025Open Access

Statistical Guarantees for High-Dimensional Stochastic Gradient Descent

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This paper demonstrates moment convergence for SGD and ASGD in high-dimensional settings, indicating key theoretical advancements.

High-dimensional stochastic gradient descent exhibits moment convergence in general norms, enhancing theoretical understanding.
The study establishes strong statistical guarantees for constant learning rates in SGD and ASGD algorithms.
Innovative coupling techniques from time series theory provide a fresh perspective on analyzing SGD's properties.
A probabilistic bound for ASGD is derived, closing gaps in existing theory while offering new analytical tools.

Li et al. (2025) studied this question.

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