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Weight decay is a broadly used technique for training state-of-the-art deep networks from image classification to large language models. Despite its widespread usage and being extensively studied in the classical literature, its role…

Machine Learning · Computer Science 2024-11-06 Francesco D'Angelo , Maksym Andriushchenko , Aditya Varre , Nicolas Flammarion

Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose L-2 penalty on the…

Machine Learning · Computer Science 2019-08-09 Kensuke Nakamura , Byung-Woo Hong

Learning rate configuration is a fundamental aspect of modern deep learning. The prevailing practice of applying a uniform learning rate across all layers overlooks the structural heterogeneity of Transformers, potentially limiting their…

Machine Learning · Computer Science 2026-05-28 Di He , Songjun Tu , Keyu Wang , Lu Yin , Shiwei Liu

The prevailing paradigm in large language model (LLM) development is to pretrain a base model, then perform further training to improve performance and model behavior. However, hyperparameter optimization and scaling laws have been studied…

Machine Learning · Computer Science 2026-02-12 Tessa Han , Sebastian Bordt , Hanlin Zhang , Sham Kakade

Recent work on pruning large language models (LLMs) has shown that one can eliminate a large number of parameters without compromising performance, making pruning a promising strategy to reduce LLM model size. Existing LLM pruning…

Machine Learning · Computer Science 2024-10-16 Haiquan Lu , Yefan Zhou , Shiwei Liu , Zhangyang Wang , Michael W. Mahoney , Yaoqing Yang

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which…

Computation and Language · Computer Science 2024-10-17 Andrea Pinto , Tomer Galanti , Randall Balestriero

In the real open world, data tends to follow long-tailed class distributions, motivating the well-studied long-tailed recognition (LTR) problem. Naive training produces models that are biased toward common classes in terms of higher…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 Shaden Alshammari , Yu-Xiong Wang , Deva Ramanan , Shu Kong

Weight decay is a simple yet powerful regularization technique that has been very widely used in training of deep neural networks (DNNs). While weight decay has attracted much attention, previous studies fail to discover some overlooked…

Machine Learning · Computer Science 2024-08-19 Zeke Xie , Zhiqiang Xu , Jingzhao Zhang , Issei Sato , Masashi Sugiyama

Weight decay is a standard technique to improve generalization performance in modern deep neural network optimization, and is also widely adopted in federated learning (FL) to prevent overfitting in local clients. In this paper, we first…

Machine Learning · Computer Science 2024-02-19 Junbo Li , Ang Li , Chong Tian , Qirong Ho , Eric P. Xing , Hongyi Wang

Unraveling the reasons behind the remarkable success and exceptional generalization capabilities of deep neural networks presents a formidable challenge. Recent insights from random matrix theory, specifically those concerning the spectral…

Machine Learning · Statistics 2023-04-10 Xuanzhe Xiao , Zeng Li , Chuanlong Xie , Fengwei Zhou

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting…

Machine Learning · Computer Science 2018-04-25 Leslie N. Smith

We propose adaptive weight decay, which automatically tunes the hyper-parameter for weight decay during each training iteration. For classification problems, we propose changing the value of the weight decay hyper-parameter on the fly based…

Machine Learning · Computer Science 2023-12-05 Amin Ghiasi , Ali Shafahi , Reza Ardekani

This study investigates how weight decay affects the update behavior of individual neurons in deep neural networks through a combination of applied analysis and experimentation. Weight decay can cause the expected magnitude and angular…

Machine Learning · Computer Science 2024-06-04 Atli Kosson , Bettina Messmer , Martin Jaggi

Recognition problems in long-tailed data, in which the sample size per class is heavily skewed, have gained importance because the distribution of the sample size per class in a dataset is generally exponential unless the sample size is…

Machine Learning · Computer Science 2024-04-30 Naoya Hasegawa , Issei Sato

Learning rate decay (lrDecay) is a \emph{de facto} technique for training modern neural networks. It starts with a large learning rate and then decays it multiple times. It is empirically observed to help both optimization and…

Machine Learning · Computer Science 2019-09-27 Kaichao You , Mingsheng Long , Jianmin Wang , Michael I. Jordan

Current transformer language models are trained with uniform computational budgets across all layers, implicitly assuming layer homogeneity. We challenge this assumption through empirical analysis of SmolLM2-135M, a 30-layer, 135M-parameter…

Machine Learning · Computer Science 2026-03-23 Tomasz Wietrzykowski

Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of $L_2$…

Machine Learning · Computer Science 2018-10-30 Guodong Zhang , Chaoqi Wang , Bowen Xu , Roger Grosse

Weight decay is a widely used technique for training Deep Neural Networks(DNN). It greatly affects generalization performance but the underlying mechanisms are not fully understood. Recent works show that for layers followed by…

Machine Learning · Computer Science 2021-03-30 Yucong Zhou , Yunxiao Sun , Zhao Zhong

Weight decay is widely used as a regularizer in large language models, yet its precise role in shaping Transformer loss landscapes remains theoretically underexplored. This paper provides the first rigorous functional-analytic…

Machine Learning · Computer Science 2026-05-08 Abhijit Das , Sayantan Dutta

Weight decay is one of the most widely used forms of regularization in deep learning, and has been shown to improve generalization and robustness. The optimization objective driving weight decay is a sum of losses plus a term proportional…

Machine Learning · Computer Science 2023-07-07 Liu Yang , Jifan Zhang , Joseph Shenouda , Dimitris Papailiopoulos , Kangwook Lee , Robert D. Nowak
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