Designing Preconditioners for SGD: Local Conditioning, Noise Floors, and Basin Stability

arXiv — cs.LGWednesday, November 26, 2025 at 5:00:00 AM
  • A recent study has introduced a novel approach to Stochastic Gradient Descent (SGD) by analyzing preconditioned SGD within the geometry defined by a symmetric positive definite matrix. This research identifies how both the convergence rate and stochastic noise floor are influenced by matrix-dependent factors, particularly in the context of nonconvex objectives, where a preconditioner-dependent basin stability guarantee is established.
  • This development is significant as it enhances the understanding of SGD's performance, particularly in Scientific Machine Learning (SciML), where managing training loss under stochastic updates is crucial. By providing explicit lower bounds for the probability of remaining in well-behaved local regions, this research could lead to more efficient training processes.
  • The findings resonate with ongoing discussions in the field regarding the challenges of SGD, especially its tendency to slow down during late training stages. Related studies have explored various optimization strategies and their effectiveness, highlighting the importance of addressing gradient noise and convergence issues, which are critical for improving training efficiency in deep learning applications.
— via World Pulse Now AI Editorial System

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