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In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…

Machine Learning · Computer Science 2018-03-01 Raman Arora , Amitabh Basu , Poorya Mianjy , Anirbit Mukherjee

In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is…

Computer Vision and Pattern Recognition · Computer Science 2024-04-29 Yanbiao Ma , Licheng Jiao , Fang Liu , Lingling Li , Shuyuan Yang , Xu Liu

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

Activation functions have been shown to affect the performance of deep neural networks significantly. While the Rectified Linear Unit (ReLU) remains the dominant choice in practice, the optimal activation function for deep neural networks…

Machine Learning · Computer Science 2025-07-29 John Chidiac , Danielle Azar

This paper provides an analysis of state-of-the-art activation functions with respect to supervised classification of deep neural network. These activation functions comprise of Rectified Linear Units (ReLU), Exponential Linear Unit (ELU),…

Machine Learning · Computer Science 2021-04-07 Anh Nguyen , Khoa Pham , Dat Ngo , Thanh Ngo , Lam Pham

Formal certification of Neural Networks (NNs) is crucial for ensuring their safety, fairness, and robustness. Unfortunately, on the one hand, sound and complete certification algorithms of ReLU-based NNs do not scale to large-scale NNs. On…

Machine Learning · Computer Science 2023-05-24 Haitham Khedr , Yasser Shoukry

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…

Machine Learning · Statistics 2021-10-14 Nicola Picchiotti , Marco Gori

With the advancement of deep learning, reducing computational complexity and memory consumption has become a critical challenge, and ternary neural networks (NNs) that restrict parameters to $\{-1, 0, +1\}$ have attracted attention as a…

Machine Learning · Computer Science 2026-04-28 Yuta Nakahara , Manabu Kobayashi , Toshiyasu Matsushima

Activation function is crucial to the recent successes of deep neural networks. In this paper, we first propose a new activation function, Multiple Parametric Exponential Linear Units (MPELU), aiming to generalize and unify the rectified…

Computer Vision and Pattern Recognition · Computer Science 2017-01-18 Yang Li , Chunxiao Fan , Yong Li , Qiong Wu , Yue Ming

There has been growing interest in studying the complexity of Rectified Linear Unit (ReLU) based activation networks. Recent work investigates the evolution of the number of piecewise-linear partitions (linear regions) that are formed…

Machine Learning · Computer Science 2026-04-28 Mufhumudzi Muthivhi , Terence L. van Zyl

We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU,…

Machine Learning · Computer Science 2026-02-16 Maosen Tang , Alex Townsend

Although state-of-the-art Speech Foundational Models can produce high-quality text pseudo-labels, applying Semi-Supervised Learning (SSL) for in-the-wild real-world data remains challenging due to its richer and more complex acoustics…

Computation and Language · Computer Science 2026-03-16 Wen Ding , Fan Qian

Semi-supervised learning holds great promise for many real-world applications, due to its ability to leverage both unlabeled and expensive labeled data. However, most semi-supervised learning algorithms still heavily rely on the limited…

Machine Learning · Computer Science 2023-12-29 Huiling Qin , Xianyuan Zhan , Yuanxun Li , Yu Zheng

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

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.…

Training neural networks using limited annotations is an important problem in the medical domain. Deep Neural Networks (DNNs) typically require large, annotated datasets to achieve acceptable performance which, in the medical domain, are…

Computer Vision and Pattern Recognition · Computer Science 2024-10-28 Bethany H. Thompson , Gaetano Di Caterina , Jeremy P. Voisey

The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most…

Machine Learning · Computer Science 2020-04-14 Garrett Bingham , William Macke , Risto Miikkulainen

Deep neural networks have recently achieved state-of-the-art results in many machine learning problems, e.g., speech recognition or object recognition. Hitherto, work on rectified linear units (ReLU) provides empirical and theoretical…

Machine Learning · Computer Science 2015-05-12 Jakub Mikolaj Tomczak

Semi-supervised semantic segmentation aims to learn from a small amount of labeled data and plenty of unlabeled ones for the segmentation task. The most common approach is to generate pseudo-labels for unlabeled images to augment the…

Computer Vision and Pattern Recognition · Computer Science 2023-04-25 Rui Chen , Tao Chen , Qiong Wang , Yazhou Yao

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