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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

Deep neural networks can suffer from the exploding and vanishing activation problem, in which the networks fail to train properly because the neural signals either amplify or attenuate across the layers and become saturated. While other…

Machine Learning · Computer Science 2021-08-24 Hao-Yuan Chang , Kang L. Wang

Large language models (LLMs) have revolutionized natural language processing (NLP) tasks by achieving state-of-the-art performance across a range of benchmarks. Central to the success of these models is the integration of sophisticated…

Hardware Architecture · Computer Science 2025-02-18 Tianfan Peng , Jiajun Qin , Tianhua Xia , Sai Qian Zhang

Training state-of-the-art, deep neural networks is computationally expensive. One way to reduce the training time is to normalize the activities of the neurons. A recently introduced technique called batch normalization uses the…

Machine Learning · Statistics 2016-07-22 Jimmy Lei Ba , Jamie Ryan Kiros , Geoffrey E. Hinton

The success of neural networks such as convolutional neural networks (CNNs) has been largely attributed to their effective and widespread deployment on customised computing platforms, including field-programmable gate arrays (FPGAs) and…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-12 Zhuoheng Ran , Chong Wu , Renjie Xu , Maolin Che , Hong Yan

Normalization layers are essential in a Deep Convolutional Neural Network (DCNN). Various normalization methods have been proposed. The statistics used to normalize the feature maps can be computed at batch, channel, or instance level.…

Image and Video Processing · Electrical Eng. & Systems 2019-08-27 Xiao-Yun Zhou , Peichao Li , Zhao-Yang Wang , Guang-Zhong Yang

This study introduces a new normalization layer termed Batch Layer Normalization (BLN) to reduce the problem of internal covariate shift in deep neural network layers. As a combined version of batch and layer normalization, BLN adaptively…

Machine Learning · Computer Science 2023-01-16 Amir Ziaee , Erion Çano

Batch Normalization (BN) has become a core design block of modern Convolutional Neural Networks (CNNs). A typical modern CNN has a large number of BN layers in its lean and deep architecture. BN requires mean and variance calculations over…

Computer Vision and Pattern Recognition · Computer Science 2019-03-04 Wonkyung Jung , Daejin Jung , and Byeongho Kim , Sunjung Lee , Wonjong Rhee , Jung Ho Ahn

Batch normalization (BN) is a technique to normalize activations in intermediate layers of deep neural networks. Its tendency to improve accuracy and speed up training have established BN as a favorite technique in deep learning. Yet,…

Machine Learning · Computer Science 2018-12-03 Johan Bjorck , Carla Gomes , Bart Selman , Kilian Q. Weinberger

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

Vision Transformer (ViT) and its variants (e.g., Swin, PVT) have achieved great success in various computer vision tasks, owing to their capability to learn long-range contextual information. Layer Normalization (LN) is an essential…

Computer Vision and Pattern Recognition · Computer Science 2022-10-17 Wenqi Shao , Yixiao Ge , Zhaoyang Zhang , Xuyuan Xu , Xiaogang Wang , Ying Shan , Ping Luo

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

Batch normalization (BN) is a fundamental unit in modern deep networks, in which a linear transformation module was designed for improving BN's flexibility of fitting complex data distributions. In this paper, we demonstrate properly…

Computer Vision and Pattern Recognition · Computer Science 2020-12-01 Yuhui Xu , Lingxi Xie , Cihang Xie , Jieru Mei , Siyuan Qiao , Wei Shen , Hongkai Xiong , Alan Yuille

Network traffic classification (NTC) models often suffer severe performance degradation when deployed in real-world environments due to distribution shifts caused by changing network conditions. Existing robustness-enhancing approaches are…

Machine Learning · Computer Science 2026-05-19 Tongze Wang , Xiaohui Xie , Wenduo Wang , Chuyi Wang , Yong Cui

Convolutional Neural Networks (CNN) has become more popular choice for various tasks such as computer vision, speech recognition and natural language processing. Thanks to their large computational capability and throughput, GPUs ,which are…

Machine Learning · Computer Science 2018-11-28 Natan Liss , Chaim Baskin , Avi Mendelson , Alex M. Bronstein , Raja Giryes

Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and…

Computer Vision and Pattern Recognition · Computer Science 2026-05-15 Youssef Saied , François Fleuret

Self-supervised training methods for transformers have demonstrated remarkable performance across various domains. Previous transformer-based models, such as masked autoencoders (MAE), typically utilize a single normalization layer for both…

Computation and Language · Computer Science 2023-11-30 Xiaohui Chen , Yinkai Wang , Yuanqi Du , Soha Hassoun , Li-Ping Liu

Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight…

Machine Learning · Statistics 2018-10-25 Ira Shavitt , Eran Segal

The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for…

Machine Learning · Computer Science 2018-05-24 Hadi Ghauch , Hossein Shokri-Ghadikolaei , Carlo Fischione , Mikael Skoglund

Non-linear operations such as GELU, Layer normalization, and Softmax are essential yet costly building blocks of Transformer models. Several prior works simplified these operations with look-up tables or integer computations, but such…

Machine Learning · Computer Science 2021-12-07 Joonsang Yu , Junki Park , Seongmin Park , Minsoo Kim , Sihwa Lee , Dong Hyun Lee , Jungwook Choi