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Training stability is of great importance to Transformers. In this work, we investigate the training dynamics of Transformers by examining the evolution of the attention layers. In particular, we track the attention entropy for each…

Despite scale driving substantial recent advancements in machine learning, reinforcement learning (RL) methods still primarily use small value functions. Naively scaling value functions -- including with a transformer architecture, which is…

Machine Learning · Computer Science 2026-02-03 Perry Dong , Kuo-Han Hung , Alexander Swerdlow , Dorsa Sadigh , Chelsea Finn

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

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

This work, based on Random Matrix Theory (RMT), introduces a novel early-stopping strategy for Transformer training dynamics. Utilizing the Power Law (PL) fit to tansformer attention matrices as a probe, we demarcate training into three…

Machine Learning · Computer Science 2025-12-30 Jing He , Hua Jiang , Cheng Li , Siqian Xin , Shuzhen Yang

It is common in deep learning to warm up the learning rate $\eta$, often by a linear schedule between $\eta_{\text{init}} = 0$ and a predetermined target $\eta_{\text{trgt}}$. In this paper, we show through systematic experiments using SGD…

Machine Learning · Computer Science 2024-11-05 Dayal Singh Kalra , Maissam Barkeshli

The Normalized Transformer, or nGPT (arXiv:2410.01131) achieves impressive training speedups and does not require weight decay or learning rate warmup. However, despite having hyperparameters that explicitly scale with model size, we…

Machine Learning · Computer Science 2026-05-04 Boris Shigida , Boris Hanin , Andrey Gromov

Transferring the optimal learning rate from small to large neural networks can enable efficient training at scales where hyperparameter tuning is otherwise prohibitively expensive. To this end, the Maximal Update Parameterization (muP)…

Machine Learning · Computer Science 2026-02-16 Atli Kosson , Jeremy Welborn , Yang Liu , Martin Jaggi , Xi Chen

Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…

Machine Learning · Computer Science 2024-12-02 Xueyan Niu , Bo Bai , Lei Deng , Wei Han

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

Machine Learning · Computer Science 2025-11-20 Jörg K. H. Franke , Urs Spiegelhalter , Marianna Nezhurina , Jenia Jitsev , Frank Hutter , Michael Hefenbrock

Though the transformer architectures have shown dominance in many natural language understanding tasks, there are still unsolved issues for the training of transformer models, especially the need for a principled way of warm-up which has…

Computation and Language · Computer Science 2021-06-01 Wei Zhu , Xiaoling Wang , Xipeng Qiu , Yuan Ni , Guotong Xie

In many real-world scenarios, data to train machine learning models becomes available over time. Unfortunately, these models struggle to continually learn new concepts without forgetting what has been learnt in the past. This phenomenon is…

Computation and Language · Computer Science 2023-01-16 Beyza Ermis , Giovanni Zappella , Martin Wistuba , Aditya Rawal , Cedric Archambeau

Scaling model sizes to scale performance has worked remarkably well for the current large language models paradigm. The research and empirical findings of various scaling studies led to novel scaling results and laws that guides subsequent…

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting,…

Computation and Language · Computer Science 2020-06-24 Zhuohan Li , Eric Wallace , Sheng Shen , Kevin Lin , Kurt Keutzer , Dan Klein , Joseph E. Gonzalez

We investigate the role of learning rate scheduling in the large-scale pre-training of large language models, focusing on its influence on downstream performance after supervised fine-tuning (SFT). Decay-based learning rate schedulers are…

Computation and Language · Computer Science 2026-03-18 Kazuki Yano , Shun Kiyono , Sosuke Kobayashi , Sho Takase , Jun Suzuki

Training deep learning models can be computationally expensive. Prior works have shown that increasing the batch size can potentially lead to better overall throughput. However, the batch size is frequently limited by the accelerator memory…

Machine Learning · Computer Science 2023-01-25 Muralidhar Andoorveedu , Zhanda Zhu , Bojian Zheng , Gennady Pekhimenko

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow…

Machine Learning · Computer Science 2020-06-30 Ruibin Xiong , Yunchang Yang , Di He , Kai Zheng , Shuxin Zheng , Chen Xing , Huishuai Zhang , Yanyan Lan , Liwei Wang , Tie-Yan Liu

Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data, especially in next-token prediction (NTP) tasks. However, the theoretical understanding of their…

Machine Learning · Computer Science 2024-10-01 Ruiquan Huang , Yingbin Liang , Jing Yang

Transformers have recently revolutionized many domains in modern machine learning and one salient discovery is their remarkable in-context learning capability, where models can solve an unseen task by utilizing task-specific prompts without…

Machine Learning · Computer Science 2023-10-10 Yu Huang , Yuan Cheng , Yingbin Liang

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern…

Machine Learning · Computer Science 2025-10-20 Zhiyuan Fan , Yifeng Liu , Qingyue Zhao , Angela Yuan , Quanquan Gu
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