English
Related papers

Related papers: Sophia: A Scalable Stochastic Second-order Optimiz…

200 papers

Fine-tuning large language models (LLMs) with classic first-order optimizers entails prohibitive GPU memory due to the backpropagation process. Recent works have turned to zeroth-order optimizers for fine-tuning, which save substantial…

Machine Learning · Computer Science 2025-02-19 Yanjun Zhao , Sizhe Dang , Haishan Ye , Guang Dai , Yi Qian , Ivor W. Tsang

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…

Optimization and Control · Mathematics 2022-02-01 Dinesh Singh , Hardik Tankaria , Makoto Yamada

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…

Machine Learning · Computer Science 2025-02-12 Son Nguyen , Bo Liu , Lizhang Chen , Qiang Liu

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…

Optimization and Control · Mathematics 2017-11-02 Mingrui Liu , Tianbao Yang

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

Numerical Analysis · Mathematics 2020-09-15 Stefania Bellavia , Gianmarco Gurioli

Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with…

Image and Video Processing · Electrical Eng. & Systems 2026-01-30 Yichi Zhang , Fengqing Zhu

Second-order optimization uses curvature information about the objective function, which can help in faster convergence. However, such methods typically require expensive computation of the Hessian matrix, preventing their usage in a…

Machine Learning · Computer Science 2022-11-03 Mohamed Elsayed , A. Rupam Mahmood

We develop Policy Gradient with Second-Order Momentum (PG-SOM), a lightweight second-order optimisation scheme for reinforcement-learning policies. PG-SOM augments the classical REINFORCE update with two exponentially weighted statistics: a…

Machine Learning · Computer Science 2025-05-20 Tianyu Sun

Pruning neural networks reduces inference time and memory costs. On standard hardware, these benefits will be especially prominent if coarse-grained structures, like feature maps, are pruned. We devise two novel saliency-based methods for…

Machine Learning · Computer Science 2023-09-26 Manuel Nonnenmacher , Thomas Pfeil , Ingo Steinwart , David Reeb

Pruning remains an effective strategy for reducing both the costs and environmental impact associated with deploying large neural networks (NNs) while maintaining performance. Classical methods, such as OBD (LeCun et al., 1989) and OBS…

Machine Learning · Computer Science 2026-01-21 Ivo Gollini Navarrete , Nicolás Mauricio Cuadrado Ávila , Martin Takáč , Samuel Horváth

As large language models (LLMs) continue to scale, deployment is increasingly bottlenecked by the memory wall, motivating a shift toward extremely low-bit quantization. However, most quantization-aware training (QAT) methods apply hard…

Machine Learning · Computer Science 2026-01-29 Guoan Wang , Feiyu Wang , Zongwei Lv , Yikun Zong , Tong Yang

Second-order methods offer an attractive path toward more sample-efficient LLM training, but their practical use is often blocked by the systems cost of maintaining and updating large matrix-based optimizer states. We introduce…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-18 Yishun Lu , Junhao Zhang , Zeyu Yang , Wes Armour

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…

Optimization and Control · Mathematics 2023-01-27 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Optimization and Control · Mathematics 2016-02-29 Farbod Roosta-Khorasani , Michael W. Mahoney

Standard first-order stochastic optimization algorithms base their updates solely on the average mini-batch gradient, and it has been shown that tracking additional quantities such as the curvature can help de-sensitize common…

Machine Learning · Computer Science 2020-11-11 Ricky T. Q. Chen , Dami Choi , Lukas Balles , David Duvenaud , Philipp Hennig

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size.…

Machine Learning · Computer Science 2021-09-14 Majid Jahani , Sergey Rusakov , Zheng Shi , Peter Richtárik , Michael W. Mahoney , Martin Takáč

This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…

Optimization and Control · Mathematics 2026-03-10 Lesi Chen , Junru Li , El Mahdi Chayti , Jingzhao Zhang

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…

Machine Learning · Computer Science 2017-01-31 Diederik P. Kingma , Jimmy Ba

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…

Machine Learning · Computer Science 2019-12-04 Michael R. Zhang , James Lucas , Geoffrey Hinton , Jimmy Ba

There is growing evidence of the effectiveness of Shampoo, a higher-order preconditioning method, over Adam in deep learning optimization tasks. However, Shampoo's drawbacks include additional hyperparameters and computational overhead when…

Machine Learning · Computer Science 2025-02-03 Nikhil Vyas , Depen Morwani , Rosie Zhao , Mujin Kwun , Itai Shapira , David Brandfonbrener , Lucas Janson , Sham Kakade