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`Biologically inspired' activation functions, such as the logistic sigmoid, have been instrumental in the historical advancement of machine learning. However in the field of deep learning, they have been largely displaced by rectified…

Neural and Evolutionary Computing · Computer Science 2018-05-21 Gardave S Bhumbra

The choice of activation functions is crucial for modern deep neural networks. Popular hand-designed activation functions like Rectified Linear Unit(ReLU) and its variants show promising performance in various tasks and models. Swish, the…

Computer Vision and Pattern Recognition · Computer Science 2021-04-09 Yucong Zhou , Zezhou Zhu , Zhao Zhong

Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations…

Image and Video Processing · Electrical Eng. & Systems 2024-08-05 Joseph Shenouda , Yamin Zhou , Robert D. Nowak

Activation functions (AFs), which are pivotal to the success (or failure) of a neural network, have received increased attention in recent years, with researchers seeking to design novel AFs that improve some aspect of network performance.…

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

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

In this study, SoftReMish, a new activation function designed to improve the performance of convolutional neural networks (CNNs) in image classification tasks, is proposed. Using the MNIST dataset, a standard CNN architecture consisting of…

Computer Vision and Pattern Recognition · Computer Science 2025-07-09 Mustafa Bayram Gücen

Activation in deep neural networks is fundamental to achieving non-linear mappings. Traditional studies mainly focus on finding fixed activations for a particular set of learning tasks or model architectures. The research on flexible…

Neural and Evolutionary Computing · Computer Science 2020-08-20 Renlong Jie , Junbin Gao , Andrey Vasnev , Min-ngoc Tran

Large Language Models (LLMs) with billions of parameters have drastically transformed AI applications. However, their demanding computation during inference has raised significant challenges for deployment on resource-constrained devices.…

This paper proposes $\mathrm{dynActivation}$, a per-layer trainable activation defined as $f_i(x) = \mathrm{BaseAct}(x)(\alpha_i - \beta_i) + \beta_i x$, where $\alpha_i$ and $\beta_i$ are lightweight learned scalars that interpolate…

Machine Learning · Computer Science 2026-03-24 Alois Bachmann

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

We present a Statistical Mechanics (SM) model of deep neural networks, connecting the energy-based and the feed forward networks (FFN) approach. We infer that FFN can be understood as performing three basic steps: encoding, representation…

Machine Learning · Computer Science 2019-06-07 Mirco Milletarí , Thiparat Chotibut , Paolo E. Trevisanutto

A deep convolutional neural network (CNN) has been widely used in image classification and gives better classification accuracy than the other techniques. The softmax cross-entropy loss function is often used for classification tasks. There…

Computer Vision and Pattern Recognition · Computer Science 2020-04-20 Motoshi Abe , Junichi Miyao , Takio Kurita

The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network…

Machine Learning · Computer Science 2022-12-14 Shiyu Liu , Rohan Ghosh , Dylan Tan , Mehul Motani

Successive linear transforms followed by nonlinear "activation" functions can approximate nonlinear functions to arbitrary precision given sufficient layers. The number of necessary layers is dependent on, in part, by the nature of the…

Neural and Evolutionary Computing · Computer Science 2018-09-26 Andrei Nicolae

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

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

In recent years, deep neural networks (DNNs) achieved unprecedented performance in many low-level vision tasks. However, state-of-the-art results are typically achieved by very deep networks, which can reach tens of layers with tens of…

Computer Vision and Pattern Recognition · Computer Science 2018-03-28 Idan Kligvasser , Tamar Rott Shaham , Tomer Michaeli

Deep learning researchers have a keen interest in proposing two new novel activation functions which can boost network performance. A good choice of activation function can have significant consequences in improving network performance. A…

Machine Learning · Computer Science 2022-04-12 Koushik Biswas , Sandeep Kumar , Shilpak Banerjee , Ashish Kumar Pandey

We propose the Moderate Adaptive Linear Unit (MoLU), a novel activation function for deep neural networks, defined analytically as: f(x)=x \times (1+tanh(x))/2. MoLU combines mathematical elegance with empirical effectiveness, exhibiting…

Machine Learning · Computer Science 2025-07-16 Hankyul Koh , Joon-hyuk Ko , Wonho Jhe

In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In particular, it is a key contribution of this work to reveal that…

Numerical Analysis · Mathematics 2023-01-23 Lukas Gonon , Robin Graeber , Arnulf Jentzen