arXiv Machine Learning By Mitchell Scott, Tianshi Xu, Ziyuan Tang, Alexandra Pichette-Emmons, Qiang Ye, Yousef Saad, Yuanzhe Xi

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

Read the original on arXiv Machine Learning →

arXiv:2511. 19716v3 Announce Type: replace-cross Abstract: Stochastic Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

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On the Condition Number Upper Bound of the L-BFGS Inverse Hessian Approximation Matrix with a Two-Sided Geometric Envelope Safeguarding Mechanism

The limited-memory BFGS (L-BFGS) algorithm is a cornerstone of large-scale optimization due to its linear memory and computational costs. However, in ill-conditioned or non-convex landscapes, the implicit inverse Hessian approximation can suffer from an exploding condition number, leading to numerical instability and degraded convergence.