The paper introduces ZFO, a lightweight framework that separates direction selection from step-size determination in large‑scale neural network optimization. ZFO uses a trusted first‑order optimizer to pick a search direction and then performs only two additional objective evaluations to build a local curvature‑aware model, selecting an adaptive step within a bounded interval. The authors provide theoretical guarantees for reliable curvature estimation, near‑optimal step selection, and convergence to a stationary point, and demonstrate that ZFO improves optimization and final performance over fixed‑step first‑order baselines on language‑model fine‑tuning tasks.
By Cristian McGee, El Houcine Bergou, Aritra Dutta
arXiv:2606. 06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth.
By Leonardo Galli, Curtis Fox, Wiebke Bartolomaeus, Mark Schmidt, Holger Rauhut
The paper investigates the "edge of stability" phenomenon in deep learning, where Hessian eigenvalues remain stable above a classically predicted unstable threshold. It shows that many first‑order optimizers, including gradient descent, can violate this stability bound by up to a factor of 21.1, and that this deviation depends systematically on the optimizer used. The authors propose a new stability threshold based on the directional Hessian and gradient‑alignment score, which removes optimizer‑dependent offsets and offers consistent predictions while providing diagnostic tools to understand how optimizers balance temporal and spatial budgets.
By Jaerin Lee, Kyoung Mu Lee
arXiv:2601. 04710v2 Announce Type: replace-cross Abstract: Fine-tuning large language models (LLMs) achieves strong performance but is often limited by the memory overhead of backpropagation.
By Feihu Jin, Shipeng Cen, Ying Tan
arXiv:2609.08277v1 Announce Type: new
Abstract: We study zeroth-order optimization of non-convex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations...
By Alexander Ryabchenko, Jian Qian, Wenlong Mou
arXiv:2409. 03682v2 Announce Type: replace Abstract: Learning new tasks by leveraging prior experience is a fundamental trait of intelligent systems.
By El Mahdi Chayti, Martin Jaggi
arXiv:2606. 02857v1 Announce Type: cross Abstract: Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation.
By Liyan Tan, Yequan Zhao, Yifan Yang, Ruijie Zhang, Xinling Yu, Zheng Zhang
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:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
By Yushun Zhang
arXiv:2607. 21716v1 Announce Type: new Abstract: Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics.
By Alexandru Meterez, Pranav Ajit Nair, Depen Morwani, Cengiz Pehlevan, Sham Kakade, Alex Damian
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. 15665v1 Announce Type: new Abstract: Zeroth-order (ZO) optimization enables backpropagation-free fine-tuning of large language models, but existing ZO methods suffer from high-variance gradient estimators, making convergence unstable and highly sensitive to learning rates.
By Ziming Yu, Shuyao Xiao, Xingyu Zhao, Sike Wang, Pan Zhou, Peiyu Zang, Xiangda Yan, Yongjie Yang, Jia Li