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Nonlinear activation functions are widely recognized for enhancing the expressivity of neural networks, which is the primary reason for their widespread implementation. In this work, we focus on ReLU activation and reveal a novel and…

Machine Learning · Computer Science 2025-10-22 Chaoyue Liu , Han Bi , Like Hui , Xiao Liu

Non-linear activation functions are crucial in Convolutional Neural Networks. However, until now they have not been well described in the frequency domain. In this work, we study the spectral behavior of ReLU, a popular activation function.…

Machine Learning · Computer Science 2025-05-13 Christodoulos Kechris , Jonathan Dan , Jose Miranda , David Atienza

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

Methodology · Statistics 2023-11-01 Juntong Chen

Activation functions (AFs) play a pivotal role in the performance of neural networks. The Rectified Linear Unit (ReLU) is currently the most commonly used AF. Several replacements to ReLU have been suggested but improvements have proven…

Neural and Evolutionary Computing · Computer Science 2022-06-27 Raz Lapid , Moshe Sipper

Active learning methods aim to improve sample complexity in machine learning. In this work, we investigate an active learning scheme via a novel gradient-free cutting-plane training method for ReLU networks of arbitrary depth and develop a…

Machine Learning · Computer Science 2025-06-26 Erica Zhang , Fangzhao Zhang , Mert Pilanci

Classifiers that are linear in their parameters, and trained by optimizing a convex loss function, have predictable behavior with respect to changes in the training data, initial conditions, and optimization. Such desirable properties are…

Machine Learning · Computer Science 2020-12-22 Alessandro Achille , Aditya Golatkar , Avinash Ravichandran , Marzia Polito , Stefano Soatto

The application of the deep learning model in classification plays an important role in the accurate detection of the target objects. However, the accuracy is affected by the activation function in the hidden and output layer. In this…

Computer Vision and Pattern Recognition · Computer Science 2023-05-22 Md. Mehedi Hasan , Md. Ali Hossain , Azmain Yakin Srizon , Abu Sayeed

We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as TeLU(x)=xtanh(exp(x)). TeLU's design is grounded in the core principles of key activation functions, achieving strong…

Machine Learning · Computer Science 2025-01-03 Alfredo Fernandez , Ankur Mali

Deep neural networks paved the way for significant improvements in image visual categorization during the last years. However, even though the tasks are highly varying, differing in complexity and difficulty, existing solutions mostly build…

Machine Learning · Computer Science 2019-10-29 Mina Basirat , Peter M. Roth

We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU,…

Machine Learning · Computer Science 2026-02-16 Maosen Tang , Alex Townsend

We propose the Gaussian Error Linear Unit (GELU), a high-performing neural network activation function. The GELU activation function is $x\Phi(x)$, where $\Phi(x)$ the standard Gaussian cumulative distribution function. The GELU…

Machine Learning · Computer Science 2023-06-07 Dan Hendrycks , Kevin Gimpel

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the…

Machine Learning · Computer Science 2025-08-12 Jeremy Diamzon , Daniele Venturi

Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent.…

Neural and Evolutionary Computing · Computer Science 2015-04-22 Forest Agostinelli , Matthew Hoffman , Peter Sadowski , Pierre Baldi

We theoretically discuss why deep neural networks (DNNs) performs better than other models in some cases by investigating statistical properties of DNNs for non-smooth functions. While DNNs have empirically shown higher performance than…

Machine Learning · Statistics 2018-07-10 Masaaki Imaizumi , Kenji Fukumizu

For most state-of-the-art architectures, Rectified Linear Unit (ReLU) becomes a standard component accompanied with each layer. Although ReLU can ease the network training to an extent, the character of blocking negative values may suppress…

Computer Vision and Pattern Recognition · Computer Science 2017-11-20 Xuanyi Dong , Guoliang Kang , Kun Zhan , Yi Yang

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…

Machine Learning · Computer Science 2026-03-26 Emi Zeger , Mert Pilanci

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…

Machine Learning · Computer Science 2023-11-08 Xuan Qi , Yi Wei

Deep learning is currently extensively employed across a range of research domains. The continuous advancements in deep learning techniques contribute to solving intricate challenges. Activation functions (AF) are fundamental components…

Machine Learning · Computer Science 2024-06-03 Asmaa Benchama , Khalid Zebbara

Many industrial and real life problems exhibit highly nonlinear periodic behaviors and the conventional methods may fall short of finding their analytical or closed form solutions. Such problems demand some cutting edge computational tools…

Machine Learning · Computer Science 2023-04-20 Jamshaid Ul Rahman , Faiza Makhdoom , Dianchen Lu

Element-wise activation functions play a critical role in deep neural networks via affecting the expressivity power and the learning dynamics. Learning-based activation functions have recently gained increasing attention and success. We…

Machine Learning · Computer Science 2020-10-05 Dengsheng Chen , Jun Li , Kai Xu