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Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a…

We introduce the "exponential linear unit" (ELU) which speeds up learning in deep neural networks and leads to higher classification accuracies. Like rectified linear units (ReLUs), leaky ReLUs (LReLUs) and parametrized ReLUs (PReLUs), ELUs…

Machine Learning · Computer Science 2016-02-23 Djork-Arné Clevert , Thomas Unterthiner , Sepp Hochreiter

Network embedding represents network nodes by a low-dimensional informative vector. While it is generally effective for various downstream tasks, it may leak some private information of networks, such as hidden private links. In this work,…

Machine Learning · Computer Science 2022-05-31 Xiao Han , Leye Wang , Junjie Wu , Yuncong Yang

While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are…

Machine Learning · Computer Science 2019-02-07 Sahil Singla , Soheil Feizi

Traditional approaches to differential privacy assume a fixed privacy requirement $\epsilon$ for a computation, and attempt to maximize the accuracy of the computation subject to the privacy constraint. As differential privacy is…

Machine Learning · Computer Science 2017-06-01 Katrina Ligett , Seth Neel , Aaron Roth , Bo Waggoner , Z. Steven Wu

For most state-of-the-art architectures, Rectified Linear Unit (ReLU) becomes a standard component accompanied with each layer. Although ReLU can ease the network training to an extent, the character of blocking negative values may suppress…

Computer Vision and Pattern Recognition · Computer Science 2017-11-20 Xuanyi Dong , Guoliang Kang , Kun Zhan , Yi Yang

Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the required network complexity to ensure closed-loop performance remains a fundamental…

Systems and Control · Electrical Eng. & Systems 2026-01-26 Xingchen Li , Keyou You

Billions of text analysis requests containing private emails, personal text messages, and sensitive online reviews, are processed by recurrent neural networks (RNNs) deployed on public clouds every day. Although prior secure networks…

Cryptography and Security · Computer Science 2021-09-13 Bo Feng , Qian Lou , Lei Jiang , Geoffrey C. Fox

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

The privacy of data is a major challenge in machine learning as a trained model may expose sensitive information of the enclosed dataset. Besides, the limited computation capability and capacity of edge devices have made cloud-hosted…

Machine Learning · Computer Science 2020-05-15 Behnam Khaleghi , Mohsen Imani , Tajana Rosing

We introduce CryptGPU, a system for privacy-preserving machine learning that implements all operations on the GPU (graphics processing unit). Just as GPUs played a pivotal role in the success of modern deep learning, they are also essential…

Cryptography and Security · Computer Science 2021-04-23 Sijun Tan , Brian Knott , Yuan Tian , David J. Wu

Neural networks have demonstrated a wide range of successes, but their ``black box" nature raises concerns about transparency and reliability. Previous research on ReLU networks has sought to unwrap these networks into linear models based…

Machine Learning · Computer Science 2025-06-24 Seongwoo Lim , Won Jo , Joohyung Lee , Jaesik Choi

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a…

Machine Learning · Statistics 2020-07-20 Agustinus Kristiadi , Matthias Hein , Philipp Hennig

A wide variety of deep neural applications increasingly rely on the cloud to perform their compute-heavy inference. This common practice requires sending private and privileged data over the network to remote servers, exposing it to the…

Cryptography and Security · Computer Science 2020-10-29 Fatemehsadat Mireshghallah , Mohammadkazem Taram , Prakash Ramrakhyani , Dean Tullsen , Hadi Esmaeilzadeh

We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…

Optimization and Control · Mathematics 2019-05-30 Chulhee Yun , Suvrit Sra , Ali Jadbabaie

Deep Learning plays a significant role in assisting humans in many aspects of their lives. As these networks tend to get deeper over time, they extract more features to increase accuracy at the cost of additional inference latency. This…

Machine Learning · Computer Science 2021-08-12 Mehrshad Zandigohar , Deniz Erdogmus , Gunar Schirner

Each year, deep learning demonstrates new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to…

Machine Learning · Computer Science 2023-03-28 Hong Jun Jeon , Yifan Zhu , Benjamin Van Roy

Rectifier neuron units (ReLUs) have been widely used in deep convolutional networks. An ReLU converts negative values to zeros, and does not change positive values, which leads to a high sparsity of neurons. In this work, we first examine…

Computer Vision and Pattern Recognition · Computer Science 2017-05-16 Shaohuai Shi , Xiaowen Chu

We study the approximation of the median of $d$ inputs using ReLU neural networks. We present depth-width tradeoffs under several settings, culminating in a constant-depth, linear-width construction that achieves exponentially small…

Machine Learning · Computer Science 2026-02-10 Abhigyan Dutta , Itay Safran , Paul Valiant

We introduce S++, a simple, robust, and deployable framework for training a neural network (NN) using private data from multiple sources, using secret-shared secure function evaluation. In short, consider a virtual third party to whom every…

Cryptography and Security · Computer Science 2021-01-29 Prashanthi Ramachandran , Shivam Agarwal , Arup Mondal , Aastha Shah , Debayan Gupta