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. In particular, the perturbation radius $ρ$ is typically treated as an isolated tuning parameter, despite defining the neighborhood in which SAM measures sharpness.
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:2604. 14669v2 Announce Type: replace Abstract: Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored.
By Minhak Song, Liang Zhang, Bingcong Li, Niao He, Michael Muehlebach, Sewoong Oh
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
By Hoki Kim, Jinseong Park, Yujin Choi, Jaewook Lee
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv:2607. 13631v1 Announce Type: new Abstract: The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc.
By Jasraj Singh, Enea Monzio Compagnoni, Antonio Orvieto
arXiv:2506. 21833v2 Announce Type: replace Abstract: Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization are increasingly proposed as memory-efficient, backpropagation-free alternatives for large language model (LLM) fine-tuning, yet their benefits are typically evaluated only against standard backpropagation (BP), omitting memory-efficient variants such as activation checkpointing.
By Kunjal Panchal, Sunav Choudhary, Yuriy Brun, Hui Guan
arXiv:2606. 18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate.
By Pierre Marion
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.
By Naoki Sato, Hiroki Naganuma, Hideaki Iiduka
arXiv:2602. 14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms.
By Rotem Mulayoff, Sebastian U. Stich
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:2606. 25086v1 Announce Type: new Abstract: Many modern Language Model (LM) pipelines return an averaged model, such as an exponential moving average of the training iterates, rather than the final iterate itself.
By Kwok Chun Au, Adam Block