Curvature-Weighted Gradient Diversity: A Noise Measure for Geometry-Adaptive SGD Schedules

arXiv:2606.30455v1 Announce Type: new Abstract: The standard convergence analysis of mini-batch stochastic gradient descent (SGD) models gradient noise using a single variance term that treats all parameter directions equally, ignoring the fact that noise in high-curvature directions has less impact because learning rates are already constrained there. We introduce Curvature-Weighted Gradient Diversity (CWGD), a geometry-aware measure that weights per-sample gradient diversity by the inverse square root of the Hessian, providing a tighter proxy for the effective optimization noise. For strongl

Source: arXiv cs.LG — read the full report at the original publisher.

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