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.
arXiv:2608. 12009v1 Announce Type: cross Abstract: Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness.
By Chenhan Jin, Shengze Xu, Binghui Xie, Kaiwen Zhou, Fan Jia, James Cheng, Tieyong Zeng
arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
By John Chiang
arXiv:2606. 01827v1 Announce Type: cross Abstract: Sharpness-Aware Minimization (SAM) has established itself as a powerful and widely adopted optimizer for training machine learning models.
By Dimitris Oikonomou, Nicolas Loizou
arXiv:2602. 03001v2 Announce Type: replace-cross Abstract: To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune.
By Hiroki Naganuma, Shagun Gupta, Youssef Briki, Ioannis Mitliagkas, Irina Rish, Parameswaran Raman, Hao-Jun Michael Shi
arXiv:2602. 05600v2 Announce Type: replace Abstract: Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima.
By Yikuan Zhang, Ning Yang, Yuhai Tu