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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

In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the…

Quantum Physics · Physics 2024-04-10 Wei Zi , Siyi Wang , Hyunji Kim , Xiaoming Sun , Anupam Chattopadhyay , Patrick Rebentrost

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

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

Neural networks in general, from MLPs and CNNs to attention-based Transformers, are constructed from layers of linear combinations followed by nonlinear operations such as ReLU, Sigmoid, or Softmax. Despite their strength, these…

Machine Learning · Computer Science 2025-10-09 Weiguo Lu , Gangnan Yuan , Hong-kun Zhang , Shangyang Li

Artificial Neural Networks (ANN) have been employed for a range of modelling and prediction tasks using financial data. However, evidence on their predictive performance, especially for time-series data, has been mixed. Whereas some…

Risk Management · Quantitative Finance 2022-05-17 Philipp Ratz

We propose a novel CNN architecture called ACTNET for robust instance image retrieval from large-scale datasets. Our key innovation is a learnable activation layer designed to improve the signal-to-noise ratio (SNR) of deep convolutional…

Computer Vision and Pattern Recognition · Computer Science 2020-10-26 Syed Sameed Husain , Eng-Jon Ong , Miroslaw Bober

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…

Optimization and Control · Mathematics 2025-02-06 Christoph Plate , Mirko Hahn , Alexander Klimek , Caroline Ganzer , Kai Sundmacher , Sebastian Sager

In this paper, we introduce a novel type of Rectified Linear Unit (ReLU), called a Dual Rectified Linear Unit (DReLU). A DReLU, which comes with an unbounded positive and negative image, can be used as a drop-in replacement for a tanh…

Computation and Language · Computer Science 2019-03-01 Fréderic Godin , Jonas Degrave , Joni Dambre , Wesley De Neve

In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…

Machine Learning · Computer Science 2023-10-20 Sammy Khalife , Hongyu Cheng , Amitabh Basu

Convolution Neural Networks (CNN) have been extremely successful in solving intensive computer vision tasks. The convolutional filters used in CNNs have played a major role in this success, by extracting useful features from the inputs.…

Computer Vision and Pattern Recognition · Computer Science 2020-01-08 Pravendra Singh , Pratik Mazumder , Vinay P. Namboodiri

This paper proposes a learnable nonlinear activation mechanism specifically for convolutional neural network (CNN) termed as LENI, which learns to enhance the negative information in CNNs. In sharp contrast to ReLU which cuts off the…

Computer Vision and Pattern Recognition · Computer Science 2023-06-21 Zhicheng Cai , Chenglei Peng , Qiu Shen

ReLU (rectified linear units) neural network has received significant attention since its emergence. In this paper, a univariate ReLU (UReLU) neural network is proposed to both modelling the nonlinear dynamic system and revealing insights…

Systems and Control · Electrical Eng. & Systems 2020-03-06 Xinglong Liang , Jun Xu

Micro expression recognition (MER)is a very challenging task as the expression lives very short in nature and demands feature modeling with the involvement of both spatial and temporal dynamics. Existing MER systems exploit CNN networks to…

Computer Vision and Pattern Recognition · Computer Science 2020-05-19 Monu Verma , Santosh Kumar Vipparthi , Girdhari Singh

For about 10 years, detecting the presence of a secret message hidden in an image was performed with an Ensemble Classifier trained with Rich features. In recent years, studies such as Xu et al. have indicated that well-designed…

Computer Vision and Pattern Recognition · Computer Science 2018-03-02 Mehdi Yedroudj , Frederic Comby , Marc Chaumont

An activation function has crucial role in a deep neural network. A simple rectified linear unit (ReLU) are widely used for the activation function. In this paper, a weighted sigmoid gate unit (WiG) is proposed as the activation function.…

Computer Vision and Pattern Recognition · Computer Science 2018-10-04 Masayuki Tanaka

Convolutional Neural Networks (CNNs) have been successfully applied to many computer vision tasks, such as image classification. By performing linear combinations and element-wise nonlinear operations, these networks can be thought of as…

Computer Vision and Pattern Recognition · Computer Science 2017-03-21 Kaicheng Yu , Mathieu Salzmann

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

Activation functions are fundamental to deep neural networks, governing gradient flow, optimization stability, and representational capacity. Within historic deep architectures, while ReLU has been the dominant choice for the activation…

Machine Learning · Computer Science 2026-03-10 Mingi Kang , Zai Yang , Jeova Farias Sales Rocha Neto

In this paper, we present a novel and general network structure towards accelerating the inference process of convolutional neural networks, which is more complicated in network structure yet with less inference complexity. The core idea is…

Computer Vision and Pattern Recognition · Computer Science 2017-05-16 Xuanyi Dong , Junshi Huang , Yi Yang , Shuicheng Yan