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First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these…

Machine Learning · Computer Science 2025-07-29 Yue Hu , Zanxia Cao , Yingchao Liu

Differentiable architecture search (DARTS) has been a popular one-shot paradigm for NAS due to its high efficiency. It introduces trainable architecture parameters to represent the importance of candidate operations and proposes…

Computer Vision and Pattern Recognition · Computer Science 2022-02-01 Xiaoxing Wang , Wenxuan Guo , Junchi Yan , Jianlin Su , Xiaokang Yang

Bilevel optimization problems consist of minimizing a value function whose evaluation depends on the solution of an inner optimization problem. These problems are typically tackled using first-order methods that require computing the…

Optimization and Control · Mathematics 2026-01-30 Marco Rando , Samuel Vaiter

The hybrid-high order (HHO) scheme has many successful applications including linear elasticity as the first step towards computational solid mechanics. The striking advantage is the simplicity among other higher-order nonconforming schemes…

Numerical Analysis · Mathematics 2026-04-10 Carsten Carstensen , Ngoc Tien Tran

We propose an efficient layer-specific optimization (ELO) method designed to enhance continual pretraining (CP) for specific languages in multilingual large language models (MLLMs). This approach addresses the common challenges of high…

Computation and Language · Computer Science 2026-01-21 HanGyeol Yoo , ChangSu Choi , Minjun Kim , Seohyun Song , SeungWoo Song , Inho Won , Jongyoul Park , Cheoneum Park , KyungTae Lim

We propose a framework for online meta-optimization of parameters that govern optimization, called Amortized Proximal Optimization (APO). We first interpret various existing neural network optimizers as approximate stochastic proximal point…

Machine Learning · Computer Science 2022-03-02 Juhan Bae , Paul Vicol , Jeff Z. HaoChen , Roger Grosse

Large language models (LLMs) are notoriously memory-intensive during training, particularly with the popular AdamW optimizer. This memory burden necessitates using more or higher-end GPUs or reducing batch sizes, limiting training…

Machine Learning · Computer Science 2025-02-18 Hanqing Zhu , Zhenyu Zhang , Wenyan Cong , Xi Liu , Sem Park , Vikas Chandra , Bo Long , David Z. Pan , Zhangyang Wang , Jinwon Lee

Neural network training requires a large amount of computation and thus GPUs are often used for the acceleration. While they improve the performance, GPUs are underutilized during the training.This paper proposes out-of-order (ooo)…

Machine Learning · Computer Science 2021-10-05 Hyungjun Oh , Hyungjun Oh , HyeongJu Kim , Jiwon Seo

Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some…

Machine Learning · Computer Science 2025-11-03 Matin Ansaripour , Shayan Talaei , Giorgi Nadiradze , Dan Alistarh

Differentially private zeroth-order optimization methods have recently gained popularity in private fine tuning of machine learning models due to their reduced memory requirements. Current approaches for privatizing zeroth-order methods…

Optimization and Control · Mathematics 2025-07-10 Devansh Gupta , Meisam Razaviyayn , Vatsal Sharan

In this paper, we introduce Dynamic Layer Operations (DLO), a novel approach for vertically scaling transformer-based Large Language Models (LLMs) by dynamically expanding, activating, or skipping layers using a sophisticated routing policy…

Machine Learning · Computer Science 2024-07-17 Zhen Tan , Daize Dong , Xinyu Zhao , Jie Peng , Yu Cheng , Tianlong Chen

Despite the great achievements of the modern deep neural networks (DNNs), the vulnerability/robustness of state-of-the-art DNNs raises security concerns in many application domains requiring high reliability. Various adversarial attacks are…

Machine Learning · Computer Science 2020-02-20 Pu Zhao , Pin-Yu Chen , Siyue Wang , Xue Lin

DPO (Direct Preference Optimization) has become a widely used offline preference optimization algorithm due to its simplicity and training stability. However, DPO is prone to overfitting and collapse. To address these challenges, we propose…

Machine Learning · Computer Science 2025-08-26 Rui Wang , Qianguo Sun , Chao Song , Junlong Wu , Tianrong Chen , Zhiyun Zeng , Yu Li

Zeroth-order optimization is an important research topic in machine learning. In recent years, it has become a key tool in black-box adversarial attack to neural network based image classifiers. However, existing zeroth-order optimization…

Machine Learning · Computer Science 2019-03-21 Haishan Ye , Zhichao Huang , Cong Fang , Chris Junchi Li , Tong Zhang

Differentiable Neural Architecture Search (NAS) provides a promising avenue for automating the complex design of deep learning (DL) models. However, current differentiable NAS methods often face constraints in efficiency, operation…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Lunchen Xie , Eugenio Lomurno , Matteo Gambella , Danilo Ardagna , Manual Roveri , Matteo Matteucci , Qingjiang Shi

We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the…

Machine Learning · Computer Science 2018-11-06 Jia Li , Cong Fang , Zhouchen Lin

Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can…

Machine Learning · Computer Science 2026-05-28 Qiyuan Chen , Xian Wu , Yi Wang , Xianhao Chen

Recent optimizers such as Lion and Muon have demonstrated strong empirical performance by normalizing gradient momentum via linear minimization oracles (LMOs). While variance reduction has been explored to accelerate LMO-based methods, it…

Machine Learning · Computer Science 2026-05-08 Won-Jun Jang , Si-Hyeon Lee

Training LLMs relies on distributed implementations using multiple GPUs to compute gradients in parallel with sharded optimizers. However, synchronizing gradients in data parallel setups introduces communication overhead that grows with the…

Machine Learning · Computer Science 2025-10-15 Adel Nabli , Louis Fournier , Pierre Erbacher , Louis Serrano , Eugene Belilovsky , Edouard Oyallon

Classic zeroth-order optimization approaches typically optimize for a smoothed version of the original function, i.e., the expected objective under randomly perturbed model parameters. This can be interpreted as encouraging the loss values…

Machine Learning · Computer Science 2025-10-21 Xuchen Gong , Tian Li
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