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Deep feedforward neural networks with piecewise linear activations are currently producing the state-of-the-art results in several public datasets. The combination of deep learning models and piecewise linear activation functions allows for…

Computer Vision and Pattern Recognition · Computer Science 2015-11-03 Zhibin Liao , Gustavo Carneiro

Activation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community.…

Machine Learning · Computer Science 2022-03-01 Hock Hung Chieng , Noorhaniza Wahid , Pauline Ong

The activation function deployed in a deep neural network has great influence on the performance of the network at initialisation, which in turn has implications for training. In this paper we study how to avoid two problems at…

Machine Learning · Computer Science 2021-05-18 Michael Murray , Vinayak Abrol , Jared Tanner

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

ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of…

Machine Learning · Computer Science 2019-06-13 Jonathan Fiat , Eran Malach , Shai Shalev-Shwartz

In many information processing systems, it may be desirable to ensure that any change of the input, whether by shifting or scaling, results in a corresponding change in the system response. While deep neural networks are gradually replacing…

Computer Vision and Pattern Recognition · Computer Science 2024-02-22 Sébastien Herbreteau , Emmanuel Moebel , Charles Kervrann

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

We consider functions from the real numbers to the real numbers, output by a neural network with 1 hidden activation layer, arbitrary width, and ReLU activation function. We assume that the parameters of the neural network are chosen…

Machine Learning · Computer Science 2023-04-20 David Holmes

This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural…

Machine Learning · Computer Science 2019-05-08 I. Daubechies , R. DeVore , S. Foucart , B. Hanin , G. Petrova

Dynamic adaptation in single-neuron response plays a fundamental role in neural coding in biological neural networks. Yet, most neural activation functions used in artificial networks are fixed and mostly considered as an inconsequential…

Machine Learning · Computer Science 2020-06-23 Victor Geadah , Giancarlo Kerg , Stefan Horoi , Guy Wolf , Guillaume Lajoie

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

Machine Learning · Statistics 2021-11-03 Lu Lu , Yanhui Su , George Em Karniadakis

Fourier Analysis Network (FAN) was recently proposed as a simple way to improve neural network performance by replacing part of Rectified Linear Unit (ReLU) activations with sine and cosine functions. Although several studies have reported…

Machine Learning · Computer Science 2026-03-16 Sam Jeong , Hae Yong Kim

The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep…

Machine Learning · Computer Science 2020-12-10 Mohit Goyal , Rajan Goyal , Brejesh Lall

In this paper, we propose novel quaternion activation functions where we modify either the quaternion magnitude or the phase, as an alternative to the commonly used split activation functions. We define criteria that are relevant for…

Machine Learning · Computer Science 2024-06-25 Johannes Pöppelbaum , Andreas Schwung

When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local…

Optimization and Control · Mathematics 2026-03-19 Jiatai Tong , Yilin Zhu , Thiago Serra , Samuel Burer

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output…

Machine Learning · Computer Science 2023-07-19 Shayan Aziznejad , Harshit Gupta , Joaquim Campos , Michael Unser

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

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

Numerical Analysis · Mathematics 2021-01-01 Ronald DeVore , Boris Hanin , Guergana Petrova

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…

Machine Learning · Statistics 2015-10-13 Chen-Yu Lee , Patrick W. Gallagher , Zhuowen Tu

Inducing and leveraging sparse activations during training and inference is a promising avenue for improving the computational efficiency of deep networks, which is increasingly important as network sizes continue to grow and their…

Machine Learning · Computer Science 2024-02-27 Ilan Price , Nicholas Daultry Ball , Samuel C. H. Lam , Adam C. Jones , Jared Tanner