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Learning rate warm-up - increasing the learning rate at the beginning of training - has become a ubiquitous heuristic in modern deep learning, yet its theoretical foundations remain poorly understood. In this work, we provide a principled…

Machine Learning · Computer Science 2025-10-06 Foivos Alimisis , Rustem Islamov , Aurelien Lucchi

Learning rate warmup is a popular and practical technique in training large-scale deep neural networks. Despite the huge success in practice, the theoretical advantages of this strategy of gradually increasing the learning rate at the…

Machine Learning · Computer Science 2025-09-10 Yuxing Liu , Yuze Ge , Rui Pan , An Kang , Tong Zhang

Learning Rate Warmup is a popular heuristic for training neural networks, especially at larger batch sizes, despite limited understanding of its benefits. Warmup decreases the update size $\Delta \mathbf{w}_t = \eta_t \mathbf{u}_t$ early in…

Machine Learning · Computer Science 2024-11-01 Atli Kosson , Bettina Messmer , Martin Jaggi

The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its…

Machine Learning · Computer Science 2021-10-27 Liyuan Liu , Haoming Jiang , Pengcheng He , Weizhu Chen , Xiaodong Liu , Jianfeng Gao , Jiawei Han

Adaptive optimization algorithms such as Adam are widely used in deep learning. The stability of such algorithms is often improved with a warmup schedule for the learning rate. Motivated by the difficulty of choosing and tuning warmup…

Machine Learning · Computer Science 2021-03-23 Jerry Ma , Denis Yarats

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active,…

Machine Learning · Computer Science 2021-01-01 Jordan T. Ash , Ryan P. Adams

We study adaptive learning rate scheduling for norm-constrained optimizers (e.g., Muon and Lion). We introduce a generalized smoothness assumption under which local curvature decreases with the suboptimality gap and empirically verify that…

Machine Learning · Computer Science 2026-05-19 Artem Riabinin , Andrey Veprikov , Arman Bolatov , Martin Takáč , Aleksandr Beznosikov

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning…

The choice of initial learning rate can have a profound effect on the performance of deep networks. We present a class of neural networks with solvable training dynamics, and confirm their predictions empirically in practical deep learning…

Machine Learning · Statistics 2020-03-05 Aitor Lewkowycz , Yasaman Bahri , Ethan Dyer , Jascha Sohl-Dickstein , Guy Gur-Ari

Training large-scale models presents challenges not only in terms of resource requirements but also in terms of their convergence. For this reason, the learning rate (LR) is often decreased when the size of a model is increased. Such a…

Computation and Language · Computer Science 2025-05-30 Marco Gaido , Sara Papi , Luisa Bentivogli , Alessio Brutti , Mauro Cettolo , Roberto Gretter , Marco Matassoni , Mohamed Nabih , Matteo Negri

Training a neural network requires choosing a suitable learning rate, which involves a trade-off between speed and effectiveness of convergence. While there has been considerable theoretical and empirical analysis of how large the learning…

Machine Learning · Statistics 2023-05-29 Gaurav Iyer , Boris Hanin , David Rolnick

Deep learning models undergo a significant increase in the number of parameters they possess, leading to the execution of a larger number of operations during inference. This expansion significantly contributes to higher energy consumption…

Machine Learning · Computer Science 2023-07-04 Dario Lazzaro , Antonio Emanuele Cinà , Maura Pintor , Ambra Demontis , Battista Biggio , Fabio Roli , Marcello Pelillo

In this paper, we present SwiftLearn, a data-efficient approach to accelerate training of deep learning models using a subset of data samples selected during the warm-up stages of training. This subset is selected based on an importance…

This study delves into the plasticity of neural networks, offering empirical support for the notion that critical learning periods and warm-starting performance loss can be avoided through simple adjustments to learning hyperparameters. The…

Machine Learning · Computer Science 2025-10-14 Stanisław Pawlak

Data often arrives in sequence over time in real-world deep learning applications such as autonomous driving. When new training data is available, training the model from scratch undermines the benefit of leveraging the learned knowledge,…

Computer Vision and Pattern Recognition · Computer Science 2024-06-10 Maying Shen , Hongxu Yin , Pavlo Molchanov , Lei Mao , Jose M. Alvarez

Large-batch training has been essential in leveraging large-scale datasets and models in deep learning. While it is computationally beneficial to use large batch sizes, it often requires a specially designed learning rate (LR) schedule to…

Machine Learning · Computer Science 2021-07-14 Chiheon Kim , Saehoon Kim , Jongmin Kim , Donghoon Lee , Sungwoong Kim

Training deep neural networks using a large batch size has shown promising results and benefits many real-world applications. However, the optimizer converges slowly at early epochs and there is a gap between large-batch deep learning…

Machine Learning · Computer Science 2020-02-06 Zhouyuan Huo , Bin Gu , Heng Huang

Learning rate scheduling plays a critical role in the optimization of deep neural networks, directly influencing convergence speed, stability, and generalization. While existing schedulers such as cosine annealing, cyclical learning rates,…

Machine Learning · Computer Science 2026-03-05 Ayush K. Varshney , Šarūnas Girdzijauskas , Konstantinos Vandikas , Aneta Vulgarakis Feljan

Designing effective reasoning-capable LLMs typically requires training using Reinforcement Learning with Verifiable Rewards (RLVR) or distillation with carefully curated Long Chain of Thoughts (CoT), both of which depend heavily on…

Artificial Intelligence · Computer Science 2026-02-02 Safal Shrestha , Minwu Kim , Aadim Nepal , Anubhav Shrestha , Keith Ross

Large language models (LLMs) are routinely pre-trained on billions of tokens, only to restart the process over again once new data becomes available. A much cheaper and more efficient solution would be to enable the continual pre-training…

Computation and Language · Computer Science 2023-09-08 Kshitij Gupta , Benjamin Thérien , Adam Ibrahim , Mats L. Richter , Quentin Anthony , Eugene Belilovsky , Irina Rish , Timothée Lesort
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