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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

In this paper, we study the trainability of rectified linear unit (ReLU) networks. A ReLU neuron is said to be dead if it only outputs a constant for any input. Two death states of neurons are introduced; tentative and permanent death. A…

Machine Learning · Computer Science 2020-10-23 Yeonjong Shin , George Em Karniadakis

This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…

Optimization and Control · Mathematics 2022-06-07 Georgia Perakis , Asterios Tsiourvas

Recent seminal work at the intersection of deep neural networks practice and random matrix theory has linked the convergence speed and robustness of these networks with the combination of random weight initialization and nonlinear…

Machine Learning · Computer Science 2019-05-07 Pierre H. Richemond , Yike Guo

Activation functions shape the outputs of artificial neurons and, therefore, are integral parts of neural networks in general and deep learning in particular. Some activation functions, such as logistic and relu, have been used for many…

Machine Learning · Computer Science 2021-01-26 Johannes Lederer

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for…

Machine Learning · Computer Science 2018-12-31 Difan Zou , Yuan Cao , Dongruo Zhou , Quanquan Gu

Activation functions are essential to introduce nonlinearity into neural networks, with the Rectified Linear Unit (ReLU) often favored for its simplicity and effectiveness. Motivated by the structural similarity between a shallow…

Machine Learning · Computer Science 2024-01-30 Jiayun Li , Yuxiao Cheng , Yiwen Lu , Zhuofan Xia , Yilin Mo , Gao Huang

Rectified linear activation units are important components for state-of-the-art deep convolutional networks. In this paper, we propose a novel S-shaped rectified linear activation unit (SReLU) to learn both convex and non-convex functions,…

Computer Vision and Pattern Recognition · Computer Science 2015-12-23 Xiaojie Jin , Chunyan Xu , Jiashi Feng , Yunchao Wei , Junjun Xiong , Shuicheng Yan

The ongoing decarbonisation of power systems is driving an increasing reliance on distributed energy resources, which introduces complex and nonlinear interactions that are difficult to capture in conventional optimisation models. As a…

Systems and Control · Electrical Eng. & Systems 2026-01-22 Yogesh Pipada Sunil Kumar , S. Ali Pourmousavi , Jon A. R. Liisberg , Julian Lesmos-Vinasco

Rectified linear units, or ReLUs, have become the preferred activation function for artificial neural networks. In this paper we consider two basic learning problems assuming that the underlying data follow a generative model based on a…

Machine Learning · Statistics 2018-03-13 Arya Mazumdar , Ankit Singh Rawat

In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear…

Machine Learning · Computer Science 2015-11-30 Bing Xu , Naiyan Wang , Tianqi Chen , Mu Li

The efficacy of deep learning models has been called into question by the presence of adversarial examples. Addressing the vulnerability of deep learning models to adversarial examples is crucial for ensuring their continued development and…

Machine Learning · Computer Science 2024-05-08 Korn Sooksatra , Greg Hamerly , Pablo Rivas

The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix…

Machine Learning · Computer Science 2018-05-29 Kai Zhong , Zhao Song , Prateek Jain , Inderjit S. Dhillon

In this work, we propose to train a deep neural network by distributed optimization over a graph. Two nonlinear functions are considered: the rectified linear unit (ReLU) and a linear unit with both lower and upper cutoffs (DCutLU). The…

Machine Learning · Computer Science 2017-06-20 Guoqiang Zhang , W. Bastiaan Kleijn

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

Machine Learning · Computer Science 2025-11-11 Longqing Ye

Adversarial training is an effective method to improve the machine learning (ML) model robustness. Most existing studies typically consider the Rectified linear unit (ReLU) activation function and centralized training environments. In this…

Machine Learning · Computer Science 2025-12-05 Long Dang , Thushari Hapuarachchi , Kaiqi Xiong , Jing Lin

We are interested in assessing the use of neural networks as surrogate models to approximate and minimize objective functions in optimization problems. While neural networks are widely used for machine learning tasks such as classification…

Machine Learning · Computer Science 2023-11-22 Tommaso Giovannelli , Oumaima Sohab , Luis Nunes Vicente

The number of linear regions is one of the distinct properties of the neural networks using piecewise linear activation functions such as ReLU, comparing with those conventional ones using other activation functions. Previous studies showed…

Machine Learning · Computer Science 2020-07-15 Rui Zhu , Bo Lin , Haixu Tang

Neural networks are increasingly used as surrogates in optimization problems to replace computationally expensive models. However, embedding ReLU neural networks in mathematical programs introduces significant computational challenges,…

Optimization and Control · Mathematics 2026-04-03 Giacomo Lastrucci , Tanuj Karia , Victor Schulte , Dominik Bongartz , Artur M. Schweidtmann

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear…

Machine Learning · Computer Science 2023-08-02 Minhyeok Lee