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We advocate the replacement of standard alphas(mu)-based QCD perturbation theory, in which the coupling and truncated perturbative predictions are dependent on the chosen renormalisation scheme, by a Lambda-based approach in which QCD…

High Energy Physics - Phenomenology · Physics 2007-05-23 M. J. Dinsdale , C. J. Maxwell

Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

Machine Learning · Computer Science 2018-10-16 Yihan Gao , Chao Zhang , Jian Peng , Aditya Parameswaran

We study the effect of normalization schemes on token representations in deep transformers. Modeling their evolution as interacting particles on the sphere, we show that normalization acts as a form of speed regulation. This perspective…

Machine Learning · Computer Science 2025-11-12 Nikita Karagodin , Shu Ge , Yury Polyanskiy , Philippe Rigollet

As large language models (LLMs) grow in scale and specialization, routing--selecting the best model for a given input--has become essential for efficient and effective deployment. While recent methods rely on complex learned routing…

Machine Learning · Computer Science 2026-05-18 Yang Li

In recent years, a variety of normalization methods have been proposed to help train neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However,…

Machine Learning · Computer Science 2020-06-17 Jiacheng Sun , Xiangyong Cao , Hanwen Liang , Weiran Huang , Zewei Chen , Zhenguo Li

Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their…

Machine Learning · Computer Science 2025-02-05 Jiaqi Yang , Wei Xie , Xiaohua Xu

Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the…

Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after…

Machine Learning · Statistics 2017-06-02 Marine Le Morvan , Jean-Philippe Vert

Solid results from Transformers have made them prevailing architectures in various natural language and vision tasks. As a default component in Transformers, Layer Normalization (LN) normalizes activations within each token to boost the…

Computer Vision and Pattern Recognition · Computer Science 2022-08-03 Qiming Yang , Kai Zhang , Chaoxiang Lan , Zhi Yang , Zheyang Li , Wenming Tan , Jun Xiao , Shiliang Pu

We evaluate three simple, normalization-centric changes to improve Transformer training. First, we show that pre-norm residual connections (PreNorm) and smaller initializations enable warmup-free, validation-based training with large…

Computation and Language · Computer Science 2020-01-01 Toan Q. Nguyen , Julian Salazar

Machine Learning (ML) optimization frameworks have gained attention for their ability to accelerate the optimization of large-scale Quadratically Constrained Quadratic Programs (QCQPs) by learning shared problem structures. However,…

Optimization and Control · Mathematics 2024-10-08 Zhixiao Xiong , Fangyu Zong , Huigen Ye , Hua Xu

Normalization techniques are important in different advanced neural networks and different tasks. This work investigates a novel dynamic learning-to-normalize (L2N) problem by proposing Exemplar Normalization (EN), which is able to learn…

Computer Vision and Pattern Recognition · Computer Science 2020-03-23 Ruimao Zhang , Zhanglin Peng , Lingyun Wu , Zhen Li , Ping Luo

Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…

Machine Learning · Computer Science 2025-06-17 Chenglin Fan , Kijun Shin

Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight…

Machine Learning · Computer Science 2019-10-17 Biao Zhang , Rico Sennrich

Selecting a layer normalization (LN) strategy that stabilizes training and speeds convergence in Transformers remains difficult, even for today's large language models (LLM). We present a comprehensive analytical foundation for…

I propose a way to use non-Euclidean norms to formulate a QR-like factorization which can unlock interesting and potentially useful properties of non-Euclidean norms - for example the ability of $l^1$ norm to suppresss outliers or promote…

Numerical Analysis · Mathematics 2021-01-26 Reid Atcheson

The ability to generalize to unseen domains is crucial for machine learning systems deployed in the real world, especially when we only have data from limited training domains. In this paper, we propose a simple and effective regularization…

Machine Learning · Computer Science 2023-12-06 Zhenmei Shi , Yifei Ming , Ying Fan , Frederic Sala , Yingyu Liang

Transformers have emerged as the prevailing standard solution for various AI tasks, including computer vision and natural language processing. The widely adopted Query, Key, and Value formulation (QKV) has played a significant role in this.…

Computer Vision and Pattern Recognition · Computer Science 2023-05-31 Ali Borji

Layer normalization (LN) is a fundamental component in modern deep learning, but its per-sample centering and scaling introduce non-negligible inference overhead. RMSNorm improves efficiency by removing the centering operation, yet this may…

Machine Learning · Computer Science 2026-05-15 Yuxin Guo , Yihao Yue , Yunhao Ni , Yizhou Ruan , Jie Luo , Wenjun Wu , Lei Huang

We present fast and accurate ways to normalize two and three dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the…

Computational Geometry · Computer Science 2018-01-17 Walter F. Mascarenhas