The paper investigates how momentum methods affect large‑batch training in a one‑pass setting using power‑law kernel regression. It derives critical learning rates for SGD, Polyak, and Nesterov, and shows how these rates depend on batch size, momentum, and model capacity. The authors provide scaling laws for risk dynamics, a three‑regime batch‑size phase diagram, and demonstrate that Polyak increases the critical batch size while Nesterov improves data efficiency in the large‑batch regime.
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.
By Depen Morwani, Alexandru Meterez, Pranav Nair, Sham Kakade
arXiv:2602.06797v3 Announce Type: replace-cross
Abstract: We study optimal learning rate (LR) schedules under the functional scaling law (FSL) framework (Li et al., 2025), which decomposes training d...
By Binghui Li, Zilin Wang, Fengling Chen, Shiyang Zhao, Ruiheng Zheng, Lei Wu
arXiv:2605. 24316v3 Announce Type: replace Abstract: Mini-batching is central to large-scale optimization, yet its role in statistical scaling laws remains limited.
By Ziyan Chen, Zhongzhu Zhou, Ding-Xuan Zhou
arXiv:2607. 12360v1 Announce Type: new Abstract: The cooldown phase of a warmup-stable-decay (WSD) learning-rate schedule, now a default in large-model pretraining, lowers the final training loss in some settings and does nothing in others.
By Subham Singh, Ashutosh Mishra, Subha Raut
arXiv:2605. 24316v2 Announce Type: replace Abstract: Scaling laws provide compact descriptions of how prediction error varies with compute, model size, and data, but existing theory mainly treats single-sample SGD or full data reuse, leaving the role of mini-batching unclear.
By Ziyan Chen, Zhongzhu Zhou, Ding-Xuan Zhou
arXiv:2609.07666v1 Announce Type: new
Abstract: Full-parameter fine-tuning of large language models has substantial memory costs because backpropagation stores activations and gradients. Zeroth-order...
By Yuyang Wang, Haoyu Yao, Pengcheng Xie
arXiv:2606. 04058v1 Announce Type: cross Abstract: Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon.
By Gagik Magakyan, Pablo Parrilo, Asuman Ozdaglar
The study investigates the delayed transition from memorization to generalization—known as grokking—in two‑hidden‑layer MLPs trained on modular arithmetic. By exploring 384 hyperparameter configurations, the authors derive a power‑law scaling relation for the onset time of generalization, showing that data complexity dominates over model capacity. A clear phase boundary at weight decay around 1.0 separates grokking from non‑grokking regimes, and weight norm trajectories indicate implicit regularization during the transition.
By Anish Kataria
arXiv:2608. 03197v1 Announce Type: new Abstract: Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear.
By Jiaxin Deng, Junbiao Pang
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
By Chiwun Yang
The paper derives an exact discrete‑time law that captures how learning‑rate schedules and weight decay interact in scale‑invariant neural networks, showing that a single scalar quantity governs the effective step size. It demonstrates that the balance point between contraction and expansion is intrinsically unstable, leading to recurrent dynamics when using constant learning rates with weight decay. The authors extend this analysis to various optimizers and datasets, confirming the law’s precision and showing that performance peaks sharply at the predicted boundary.
By Hasan Amin, Wei-Kai Chang, Rajiv Khanna