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Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on…

Machine Learning · Computer Science 2019-08-27 Yang Liu , Jianpeng Zhang , Chao Gao , Jinghua Qu , Lixin Ji

This paper addresses the unconstrained minimization of smooth convex functions whose gradients are locally Holder continuous. Building on these results, we analyze the Scaled Gradient Algorithm (SGA) under local smoothness assumptions,…

Optimization and Control · Mathematics 2025-11-14 Susan Ghaderi , Morteza Rahimi , Yves Moreau , Masoud Ahookhosh

We consider approximation rates of sparsely connected deep rectified linear unit (ReLU) and rectified power unit (RePU) neural networks for functions in Besov spaces $B^\alpha_{q}(L^p)$ in arbitrary dimension $d$, on general domains. We…

Functional Analysis · Mathematics 2022-03-25 Mazen Ali , Anthony Nouy

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

We study the least-square regression problem with a two-layer fully-connected neural network, with ReLU activation function, trained by gradient flow. Our first result is a generalization result, that requires no assumptions on the…

Machine Learning · Computer Science 2024-10-10 Junhyung Park , Patrick Bloebaum , Shiva Prasad Kasiviswanathan

The classical line search for learning rate (LR) tuning in the stochastic gradient descent (SGD) algorithm can tame the convergence slowdown due to data-sampling noise. In a federated setting, wherein the client heterogeneity introduces a…

Machine Learning · Computer Science 2025-10-28 Geetika , Somya Tyagi , Bapi Chatterjee

Deep neural networks have achieved remarkable performance across various tasks when supplied with large-scale labeled data. However, the collection of labeled data can be time-consuming and labor-intensive. Semi-supervised learning (SSL),…

Machine Learning · Computer Science 2024-06-28 Chaoqi Liang , Guanglei Yang , Lifeng Qiao , Zitong Huang , Hongliang Yan , Yunchao Wei , Wangmeng Zuo

Federated learning (FL) is an emerging learning paradigm to tackle massively distributed data. In Federated Learning, a set of clients jointly perform a machine learning task under the coordination of a server. The FedAvg algorithm is one…

Machine Learning · Computer Science 2023-02-14 Junyi Li , Feihu Huang , Heng Huang

Deep neural networks have been shown to achieve state-of-the-art performance in several machine learning tasks. Stochastic Gradient Descent (SGD) is the preferred optimization algorithm for training these networks and asynchronous SGD…

Machine Learning · Computer Science 2016-04-06 Wei Zhang , Suyog Gupta , Xiangru Lian , Ji Liu

In this paper, we determine analytical bounds on the local Lipschitz constants of of affine functions composed with rectified linear units (ReLUs). Affine-ReLU functions represent a widely used layer in deep neural networks, due to the fact…

Machine Learning · Computer Science 2020-08-17 Trevor Avant , Kristi A. Morgansen

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…

Optimization and Control · Mathematics 2022-01-11 Xinlei Yi , Shengjun Zhang , Tao Yang , Tianyou Chai , Karl H. Johansson

The challenge of overfitting, in which the model memorizes the training data and fails to generalize to test data, has become increasingly significant in the training of large neural networks. To tackle this challenge, Sharpness-Aware…

Machine Learning · Computer Science 2023-10-12 Zixiang Chen , Junkai Zhang , Yiwen Kou , Xiangning Chen , Cho-Jui Hsieh , Quanquan Gu

Activation functions play a critical role in deep neural networks by shaping gradient flow, optimization stability, and generalization. While ReLU remains widely used due to its simplicity, it suffers from gradient sparsity and dead-neuron…

Machine Learning · Computer Science 2025-12-03 Ashkan Shakarami , Yousef Yeganeh , Azade Farshad , Lorenzo Nicolè , Stefano Ghidoni , Nassir Navab

In this paper, a novel neural network activation function, called Symmetrical Gaussian Error Linear Unit (SGELU), is proposed to obtain high performance. It is achieved by effectively integrating the property of the stochastic regularizer…

Machine Learning · Computer Science 2019-11-12 Chao Yu , Zhiguo Su

To reduce the long training time of large deep neural network (DNN) models, distributed synchronous stochastic gradient descent (S-SGD) is commonly used on a cluster of workers. However, the speedup brought by multiple workers is limited by…

Machine Learning · Computer Science 2020-03-03 Shaohuai Shi , Zhenheng Tang , Qiang Wang , Kaiyong Zhao , Xiaowen Chu

The un-rectifying technique expresses a non-linear point-wise activation function as a data-dependent variable, which means that the activation variable along with its input and output can all be employed in optimization. The ReLU network…

Machine Learning · Computer Science 2021-01-19 Wen-Liang Hwang , Shih-Shuo Tung

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective…

Optimization and Control · Mathematics 2018-06-04 Kevin Scaman , Francis Bach , Sébastien Bubeck , Yin Tat Lee , Laurent Massoulié

In this paper we focus on the problem of finding the optimal weights of the shallowest of neural networks consisting of a single Rectified Linear Unit (ReLU). These functions are of the form $\mathbf{x}\rightarrow…

Machine Learning · Computer Science 2019-04-02 Seyed Mohammadreza Mousavi Kalan , Mahdi Soltanolkotabi , A. Salman Avestimehr

We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…

Machine Learning · Computer Science 2017-11-22 Kenji Kawaguchi , Bo Xie , Vikas Verma , Le Song

The multiplicative structure of parameters and input data in the first layer of neural networks is explored to build connection between the landscape of the loss function with respect to parameters and the landscape of the model function…

Machine Learning · Computer Science 2021-11-30 Chao Ma , Lexing Ying