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Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as…

Machine Learning · Computer Science 2025-02-11 Meyer Scetbon , Chao Ma , Wenbo Gong , Edward Meeds

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as…

Machine Learning · Computer Science 2026-05-22 Athanasios Glentis , Jiaxiang Li , Andi Han , Mingyi Hong

Adaptive optimizers such as Adam (Kingma & Ba, 2015) have been central to the success of large language models. However, they often require to maintain optimizer states throughout training, which can result in memory requirements several…

Machine Learning · Computer Science 2025-02-24 Chao Ma , Wenbo Gong , Meyer Scetbon , Edward Meeds

Software vulnerabilities are a primary threat to modern infrastructure. While static analysis and Graph Neural Networks have long served as the foundation for vulnerability detection, the emergence of Large Language Models (LLMs) has…

Cryptography and Security · Computer Science 2026-04-22 Zhengyang Shan , Xu Qian , Jiayun Xin , Minghui Xu , Yue Zhang , Zhen Yang , Hao Wu , Xiuzhen Cheng

Training large language models (LLMs) poses challenges due to their massive scale and heterogeneous architectures. While adaptive optimizers like AdamW help address gradient variations, they still struggle with efficient and effective…

Machine Learning · Computer Science 2025-06-03 Siyuan Li , Juanxi Tian , Zedong Wang , Xin Jin , Zicheng Liu , Wentao Zhang , Dan Xu

Reinforcement learning-based preference optimization is increasingly used to align list-wise generative recommenders with complex, multi-objective user feedback, yet existing optimizers such as Gradient-Bounded Policy Optimization (GBPO)…

Machine Learning · Computer Science 2026-02-16 Yu Xie , Xing Kai Ren , Ying Qi , Hu Yao

Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…

Machine Learning · Computer Science 2025-07-03 Di Zhang , Yihang Zhang

Large language models (LLMs) can generate syntactically valid optimization programs, yet often struggle to reliably choose an effective modeling strategy, leading to incorrect formulations and inefficient solver behavior. We propose SAGE, a…

Artificial Intelligence · Computer Science 2026-05-05 Ruiqing Zhao , Fengzhi Li , Yuan Zuo , Rui Liu , Yansong Liu , Yunfei Ma , Fanyu Meng , Junlan Feng

Adaptive gradient methods, such as Adam and LAMB, have demonstrated excellent performance in the training of large language models. Nevertheless, the need for adaptivity requires maintaining second-moment estimates of the per-parameter…

Computation and Language · Computer Science 2023-08-08 Yang Luo , Xiaozhe Ren , Zangwei Zheng , Zhuo Jiang , Xin Jiang , Yang You

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

As large language models (LLMs) achieve strong performance on traditional benchmarks, there is an urgent need for more challenging evaluation frameworks that probe deeper aspects of semantic understanding. We introduce SAGE (Semantic…

Artificial Intelligence · Computer Science 2025-09-26 Samarth Goel , Reagan J. Lee , Kannan Ramchandran

In this work, we question the necessity of adaptive gradient methods for training deep neural networks. SGD-SaI is a simple yet effective enhancement to stochastic gradient descent with momentum (SGDM). SGD-SaI performs learning rate…

Machine Learning · Computer Science 2024-12-18 Minghao Xu , Lichuan Xiang , Xu Cai , Hongkai Wen

Full fine-tuning of Large Language Models (LLMs) is notoriously memory-intensive, primarily because conventional optimizers such as SGD or Adam assume access to exact gradients derived from cached activations. Existing solutions either…

Machine Learning · Computer Science 2025-10-28 Jing Yang , Kaitong Cai , Yijia Fan , Yufeng Yang , Keze Wang

SGD and AdamW are the two most used optimizers for fine-tuning large neural networks in computer vision. When the two methods perform the same, SGD is preferable because it uses less memory (12 bytes/parameter with momentum and 8…

Computer Vision and Pattern Recognition · Computer Science 2023-10-11 Ananya Kumar , Ruoqi Shen , Sebastien Bubeck , Suriya Gunasekar

Despite the vast empirical evidence supporting the efficacy of adaptive optimization methods in deep learning, their theoretical understanding is far from complete. This work introduces novel SDEs for commonly used adaptive optimizers:…

Machine Learning · Computer Science 2025-03-12 Enea Monzio Compagnoni , Tianlin Liu , Rustem Islamov , Frank Norbert Proske , Antonio Orvieto , Aurelien Lucchi

Sharpness-Aware Minimization (SAM) optimizer enhances the generalization ability of the machine learning model by exploring the flat minima landscape through weight perturbations. Despite its empirical success, SAM introduces an additional…

Machine Learning · Computer Science 2025-06-02 Yifei Cheng , Li Shen , Hao Sun , Nan Yin , Xiaochun Cao , Enhong Chen

Adam has proven remarkable successful in training deep neural networks, but the mechanisms underlying its empirical successes and limitations remain underexplored. In this study, we demonstrate that the effectiveness of Adam stems largely…

Machine Learning · Computer Science 2025-07-10 Hanyang Peng , Shuang Qin , Yue Yu , Fangqing Jiang , Hui Wang , Wen Gao

The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it…

Machine Learning · Computer Science 2025-03-04 Bingrui Li , Wei Huang , Andi Han , Zhanpeng Zhou , Taiji Suzuki , Jun Zhu , Jianfei Chen

A new paradigm to estimate the gradient of a black-box scalar function is introduced, considering it as a member of a set of admissible gradients that are computed using existing function samples. Results on gradient estimate accuracy,…

Optimization and Control · Mathematics 2025-08-28 Lorenzo Sabug , Fredy Ruiz , Lorenzo Fagiano

Large language models are unable to continuously adapt and learn from new data during reasoning at inference time. To address this limitation, we propose that complex reasoning tasks be decomposed into atomic subtasks and introduce SAGE, a…

Computation and Language · Computer Science 2025-09-09 Jiacheng Wei , Faguo Wu , Xiao Zhang
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