arXiv:2602. 11557v2 Announce Type: replace Abstract: A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries.
arXiv:2402.11215v4 Announce Type: replace Abstract: The choice of batch size in minibatch stochastic gradient optimization is critical for both optimization and generalization performance in large-sc...
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.
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.
arXiv:2609.06064v1 Announce Type: cross Abstract: Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical stu...
arXiv:2607. 16261v1 Announce Type: cross Abstract: Modern optimizers combine gradients from the current mini-batch with historical optimization state, such as momentum or adaptive moments.
arXiv:2610.00446v1 Announce Type: cross Abstract: As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its v...
arXiv:2607. 01474v1 Announce Type: new Abstract: Class imbalance poses a critical challenge in federated learning (FL), where underrepresented classes suffer from poor predictive performance yet cannot be addressed by standard centralized techniques due to privacy and heterogeneity constraints.
arXiv:2607. 08104v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is a cornerstone of modern optimization.
arXiv:2602. 02431v2 Announce Type: replace-cross Abstract: It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning.
arXiv:2606. 19179v1 Announce Type: cross Abstract: Stochastic momentum methods such as heavy ball (HB), Nesterov momentum, and variants of Accelerated SGD (ASGD) [Kidambi et al.
arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.
arXiv:2602. 10204v2 Announce Type: replace Abstract: We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.