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We propose new methodologies for both unlearning random set of samples and class unlearning and show that they outperform existing methods. The main driver of our unlearning methods is the similarity of predictions to a retrained model on…

Machine Learning · Computer Science 2025-12-09 Ali Ebrahimpour-Boroojeny

Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that…

Machine Learning · Computer Science 2025-03-19 Dayal Singh Kalra , John Kirchenbauer , Maissam Barkeshli , Tom Goldstein

The Muon optimizer has recently attracted considerable attention for its strong empirical performance and use of orthogonalized updates on matrix-shaped parameters, yet its underlying mechanisms and relationship to adaptive optimizers such…

Machine Learning · Computer Science 2026-02-05 Xianbiao Qi , Marco Chen , Jiaquan Ye , Yelin He , Rong Xiao

Predicting user behavior is essential for intelligent assistant services, yet deep learning models often struggle to capture long-tailed behaviors. Large language models (LLMs), with their pretraining on vast corpora containing rich…

Computation and Language · Computer Science 2026-04-14 Fanjin Meng , Jingtao Ding , Jiahui Gong , Chen Yang , Hong Chen , Zuojian Wang , Haisheng Lu , Yong Li

The Muon optimizer has demonstrated remarkable empirical success in handling matrix-structured parameters for training neural networks. However, a significant gap remains between its practical performance and theoretical understanding.…

Machine Learning · Computer Science 2026-05-12 Da Chang , Yongxiang Liu , Ganzhao Yuan

Recently, Muon and related spectral optimizers have demonstrated strong empirical performance as scalable stochastic methods, often outperforming Adam. Yet their behaviour remains poorly understood. We analyze stochastic spectral…

Optimization and Control · Mathematics 2026-05-12 Elliot Paquette , Noah Marshall , Lucas Benigni , Guangyuan Wang , Atish Agarwala , Courtney Paquette

The pursuit of faster optimization algorithms remains an active and important research direction in deep learning. Recently, the Muon optimizer [JJB+24] has demonstrated promising empirical performance, but its theoretical foundation…

Machine Learning · Computer Science 2025-09-30 Lizhang Chen , Jonathan Li , Qiang Liu

The ever-growing scale of deep learning models and training data underscores the critical importance of efficient optimization methods. While preconditioned gradient methods such as Adam and AdamW are the de facto optimizers for training…

Optimization and Control · Mathematics 2026-02-06 Tim Tsz-Kit Lau , Qi Long , Weijie Su

The core bottleneck of Federated Learning (FL) lies in the communication rounds. That is, how to achieve more effective local updates is crucial for reducing communication rounds. Existing FL methods still primarily use element-wise local…

Machine Learning · Computer Science 2025-11-03 Junkang Liu , Fanhua Shang , Junchao Zhou , Hongying Liu , Yuanyuan Liu , Jin Liu

Multimodal learning, which integrates data from diverse sensory modes, plays a pivotal role in artificial intelligence. However, existing multimodal learning methods often struggle with challenges where some modalities appear more dominant…

Machine Learning · Computer Science 2024-04-02 Xiaohui Zhang , Jaehong Yoon , Mohit Bansal , Huaxiu Yao

Large Language Models (LLMs) have made significant strides in the field of artificial intelligence, showcasing their ability to interact with humans and influence human cognition through information dissemination. However, recent studies…

Computation and Language · Computer Science 2024-11-25 Qingquan Zhang , Qiqi Duan , Bo Yuan , Yuhui Shi , Jialin Liu

The impressive performance of large language models (LLMs) arises from their massive scale and heterogeneous module composition. However, this structural heterogeneity introduces additional optimization challenges. While adaptive optimizers…

Machine Learning · Computer Science 2026-05-08 Ziqing Wen , Zhouyang Liu , Jiahuan Wang , Ping Luo , Li Shen , Dongsheng Li , Tao Sun

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered…

Machine Learning · Computer Science 2025-09-08 Kaiyue Wen , David Hall , Tengyu Ma , Percy Liang

Deep learning typically requires training a very capable architecture using large datasets. However, many important learning problems demand an ability to draw valid inferences from small size datasets, and such problems pose a particular…

Machine Learning · Computer Science 2017-10-20 Dawit Mureja , Hyunsin Park , Chang D. Yoo

Traditional Reinforcement Learning (RL) algorithms assume the distribution of the data to be uniform or mostly uniform. However, this is not the case with most real-world applications like autonomous driving or in nature where animals roam.…

Machine Learning · Computer Science 2025-04-09 Dolton Fernandes , Pramod Kaushik , Harsh Shukla , Bapi Raju Surampudi

This paper investigates the impact of different optimizers on the grokking phenomenon, where models exhibit delayed generalization. We conducted experiments across seven numerical tasks (primarily modular arithmetic) using a modern…

Machine Learning · Computer Science 2025-04-23 Amund Tveit , Bjørn Remseth , Arve Skogvold

The emergence of Large Language Models (LLMs) with strong reasoning capabilities marks a significant milestone, unlocking new frontiers in complex problem-solving. However, training these reasoning models, typically using Reinforcement…

Machine Learning · Computer Science 2026-03-23 Qinghao Hu , Shang Yang , Junxian Guo , Xiaozhe Yao , Yujun Lin , Yuxian Gu , Han Cai , Chuang Gan , Ana Klimovic , Song Han

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce…

Optimization and Control · Mathematics 2026-04-03 Zhehang Du , Weijie Su

The memory challenges associated with training Large Language Models (LLMs) have become a critical concern, particularly when using the Adam optimizer. To address this issue, numerous memory-efficient techniques have been proposed, with…

Machine Learning · Computer Science 2025-02-12 Yiming Chen , Yuan Zhang , Yin Liu , Kun Yuan , Zaiwen Wen

Optimizers are crucial for the efficient training of Large Language Models (LLMs). While AdamW is the de facto standard, recent structure-aware optimizers like Muon have emerged, which regularize gradient updates by operating on entire…

Machine Learning · Computer Science 2025-10-07 Zehua Liu , Han Wu , Xiaojin Fu , Shuqi Liu , Xiongwei Han , Tao Zhong , Mingxuan Yuan