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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

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs…

Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets. To improve efficiency, recent work has explored model upscaling: initializing larger models from trained smaller…

Machine Learning · Computer Science 2026-02-12 Yuxin Ma , Nan Chen , Mateo Díaz , Soufiane Hayou , Dmitriy Kunisky , Soledad Villar

Hyperparameter tuning can dramatically impact training stability and final performance of large-scale models. Recent works on neural network parameterisations, such as $\mu$P, have enabled transfer of optimal global hyperparameters across…

Machine Learning · Computer Science 2025-12-30 Bruno Mlodozeniec , Pierre Ablin , Louis Béthune , Dan Busbridge , Michal Klein , Jason Ramapuram , Marco Cuturi

Hyperparameter transfer allows extrapolating optimal optimization hyperparameters from small to large scales, making it critical for training large language models (LLMs). This is done either by fitting a scaling law to the hyperparameters…

Machine Learning · Computer Science 2026-05-21 Dayal Singh Kalra , Maissam Barkeshli

The growing scale of deep learning models has rendered standard hyperparameter (HP) optimization prohibitively expensive. A promising solution is the use of scale-aware hyperparameters, which can enable direct transfer of optimal HPs from…

Machine Learning · Computer Science 2025-12-30 Nikhil Ghosh , Denny Wu , Alberto Bietti

We provide the first proof of learning rate transfer with width in a linear multi-layer perceptron (MLP) parametrized with $\mu$P, a neural network parameterization designed to ``maximize'' feature learning in the infinite-width limit. We…

Machine Learning · Statistics 2026-02-26 Soufiane Hayou

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

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…

Several variations of adaptive first-order and second-order optimization methods have been proposed to accelerate and scale the training of large language models. The performance of these optimization routines is highly sensitive to the…

Machine Learning · Computer Science 2026-02-25 Akshita Gupta , Marieme Ngom , Sam Foreman , Venkatram Vishwanath

Deeper modern architectures are costly to train, making hyperparameter transfer preferable to expensive repeated tuning. Maximal Update Parametrization ($\mu$P) helps explain why many hyperparameters transfer across width. Yet depth scaling…

Machine Learning · Computer Science 2026-02-10 Shenxi Wu , Haosong Zhang , Xingjian Ma , Shirui Bian , Yichi Zhang , Xi Chen , Wei Lin

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses $\mu$P parameterized networks, where the…

Machine Learning · Statistics 2023-12-11 Blake Bordelon , Lorenzo Noci , Mufan Bill Li , Boris Hanin , Cengiz Pehlevan

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal…

Artificial Intelligence · Computer Science 2026-01-09 Yunhua Zhou , Shuhao Xing , Junhao Huang , Xipeng Qiu , Qipeng Guo

The Maximal Update Parametrization ($\mu$P) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new…

Transfer learning is a useful technique for achieving improved performance and reducing training costs by leveraging the knowledge gained from source tasks and applying it to target tasks. Assessing the effectiveness of transfer learning…

Machine Learning · Computer Science 2023-06-12 Peizhong Ju , Sen Lin , Mark S. Squillante , Yingbin Liang , Ness B. Shroff

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new…

Theoretical studies on transfer learning or domain adaptation have so far focused on situations with a known hypothesis class or model; however in practice, some amount of model selection is usually involved, often appearing under the…

Machine Learning · Statistics 2023-10-13 Steve Hanneke , Samory Kpotufe , Yasaman Mahdaviyeh

Probabilistic Transformer (PT), a white-box probabilistic model for contextual word representation, has demonstrated substantial similarity to standard Transformers in both computational structure and downstream task performance on small…

Computation and Language · Computer Science 2026-04-29 Penghao Kuang , Haoyi Wu , Kewei Tu

Parameter transfer is a central paradigm in transfer learning, enabling knowledge reuse across tasks and domains by sharing model parameters between upstream and downstream models. However, when only a subset of parameters from the upstream…

Machine Learning · Computer Science 2026-01-08 Hua Yuan , Xuran Meng , Qiufeng Wang , Shiyu Xia , Ning Xu , Xu Yang , Jing Wang , Xin Geng , Yong Rui

Hyperparameter transfer has become an important component of modern large-scale training recipes. Existing methods, such as muP, primarily focus on transfer between model sizes, with transfer across batch sizes and training horizons often…

Machine Learning · Computer Science 2026-03-18 Egor Shulgin , Dimitri von Rütte , Tianyue H. Zhang , Niccolò Ajroldi , Bernhard Schölkopf , Antonio Orvieto
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