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Related papers: Muon Optimizer Accelerates Grokking

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Grokking, the phenomenon of delayed generalization, is often attributed to the depth and compositional structure of deep neural networks. We study grokking in one of the simplest possible settings: the learning of a linear model with…

Machine Learning · Computer Science 2026-02-10 Nataraj Das , Atreya Vedantam , Chandrashekar Lakshminarayanan

Orthogonalized-update optimizers such as Muon improve training of matrix-valued parameters, but existing extensions typically either rescale updates after orthogonalization or use heavier whitening-based preconditioners before it. We…

Machine Learning · Computer Science 2026-05-12 Da Chang , Qiankun Shi , Lvgang Zhang , Yu Li , Ruijie Zhang , Yao Lu , Yongxiang Liu , Ganzhao Yuan

Adam with decoupled weight decay, also known as AdamW, is widely acclaimed for its superior performance in language modeling tasks, surpassing Adam with $\ell_2$ regularization in terms of generalization and optimization. However, this…

Machine Learning · Computer Science 2024-04-09 Shuo Xie , Zhiyuan Li

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing…

Machine Learning · Computer Science 2022-10-17 Ziming Liu , Ouail Kitouni , Niklas Nolte , Eric J. Michaud , Max Tegmark , Mike Williams

Atomistic foundation models constitute a paradigm shift in computational materials science by providing universal machine-learned interatomic potentials with broad transferability across chemical spaces. Although fine-tuning is essential…

Computational Physics · Physics 2025-12-08 Xiaoqing Liu , Yangshuai Wang , Teng Zhao

Equivariant neural networks encode geometric symmetries by construction, yet they are often difficult to optimize and can underperform less constrained architectures. A growing body of work addresses this through architectural modifications…

Machine Learning · Computer Science 2026-05-28 Teodor-Mihai Stupariu , Andrei Manolache

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

Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical…

Artificial Intelligence · Computer Science 2026-05-07 Yiheng Zhang , Kaiyan Zhao , Shaowu Wu , Yiming Wang , Jiajun Wu , Leong Hou U , Steve Drew , Xiaoguang Niu

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). Recent benchmark studies of…

Machine Learning · Computer Science 2026-02-02 Yifeng Liu , Angela Yuan , Quanquan Gu

Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization…

Machine Learning · Computer Science 2026-04-21 Joon Hyeok Kim , Yong-Hyun Park , Mattis Dalsætra Østby , Jiatao Gu

Neural network (NN) training is inherently a large-scale matrix optimization problem, yet the matrix structure of NN parameters has long been overlooked. Recently, the optimizer Muon \citep{jordanmuon}, which explicitly exploits this…

Machine Learning · Computer Science 2026-04-21 Chuan He , Zhanwang Deng , Zhaosong Lu

A range of recent optimizers have emerged that approximate the same "matrix-whitening" transformation in various ways. In this work, we systematically deconstruct such optimizers, aiming to disentangle the key components that explain…

Machine Learning · Computer Science 2025-10-30 Kevin Frans , Pieter Abbeel , Sergey Levine

Spectral bias, the tendency of neural networks to learn low frequencies first, can be both a blessing and a curse. While it enhances the generalization capabilities by suppressing high-frequency noise, it can be a limitation in scientific…

Machine Learning · Computer Science 2026-05-08 Shuai Jiang , Alexey Voronin , Eric Cyr , Ben Southworth

The paper presents the formulation, implementation, and evaluation of the ArcGD optimiser. The evaluation is conducted initially on a non-convex benchmark function and subsequently on a real-world ML dataset. The initial comparative study…

Machine Learning · Computer Science 2026-03-25 Nikhil Verma , Joonas Linnosmaa , Leonardo Espinosa-Leal , Napat Vajragupta

Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in…

Machine Learning · Computer Science 2026-05-20 Yury Demidovich , Abhishek Chakraborty , Grigory Malinovsky , Angelia Nedić , Peter Richtárik

Software configuration tuning is essential for optimizing a given performance objective (e.g., minimizing latency). Yet, due to the software's intrinsically complex configuration landscape and expensive measurement, there has been a rather…

Software Engineering · Computer Science 2024-03-18 Pengzhou Chen , Tao Chen , Miqing Li

AdamZ is an advanced variant of the Adam optimiser, developed to enhance convergence efficiency in neural network training. This optimiser dynamically adjusts the learning rate by incorporating mechanisms to address overshooting and…

Machine Learning · Computer Science 2024-11-26 Ilia Zaznov , Atta Badii , Alfonso Dufour , Julian Kunkel

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

Minimax optimization has served as the backbone of many machine learning (ML) problems. Although the convergence behavior of optimization algorithms has been extensively studied in the minimax settings, their generalization guarantees in…

Machine Learning · Statistics 2022-06-22 Asuman Ozdaglar , Sarath Pattathil , Jiawei Zhang , Kaiqing Zhang

Applying weight decay (WD) to matrix layers is standard practice in large-language-model pretraining. Prior work suggests that stochastic gradient noise induces a Brownian-like expansion of the weight matrices W, whose growth is…

Machine Learning · Computer Science 2026-01-09 Maksim Velikanov , Ilyas Chahed , Jingwei Zuo , Dhia Eddine Rhaiem , Younes Belkada , Hakim Hacid