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The training of artificial neural networks (ANNs) with rectified linear unit (ReLU) activation via gradient descent (GD) type optimization schemes is nowadays a common industrially relevant procedure. Till this day in the scientific…

机器学习 · 计算机科学 2023-04-13 Simon Eberle , Arnulf Jentzen , Adrian Riekert , Georg S. Weiss

We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks. First, we emphatically show that it is unsurprising…

数值分析 · 数学 2020-11-02 Austin R. Benson , Anil Damle , Alex Townsend

Understanding to what extent neural networks memorize training data is an intriguing question with practical and theoretical implications. In this paper we show that in some cases a significant fraction of the training data can in fact be…

机器学习 · 计算机科学 2022-12-06 Niv Haim , Gal Vardi , Gilad Yehudai , Ohad Shamir , Michal Irani

We study the training of deep neural networks by gradient descent where floating-point arithmetic is used to compute the gradients. In this framework and under realistic assumptions, we demonstrate that it is highly unlikely to find ReLU…

机器学习 · 计算机科学 2023-11-16 Clemens Karner , Vladimir Kazeev , Philipp Christian Petersen

Differential privacy (DP) is by far the most widely accepted framework for mitigating privacy risks in machine learning. However, exactly how small the privacy parameter $\epsilon$ needs to be to protect against certain privacy risks in…

机器学习 · 计算机科学 2023-08-11 Chuan Guo , Alexandre Sablayrolles , Maziar Sanjabi

Machine unlearning enables the removal of specific data from ML models to uphold the right to be forgotten. While approximate unlearning algorithms offer efficient alternatives to full retraining, this work reveals that they fail to…

机器学习 · 计算机科学 2025-07-29 Yaxin Xiao , Qingqing Ye , Li Hu , Huadi Zheng , Haibo Hu , Zi Liang , Haoyang Li , Yijie Jiao

The growing complexity of Deep Neural Networks (DNNs) has led to the adoption of Split Inference (SI), a collaborative paradigm that partitions computation between edge devices and the cloud to reduce latency and protect user privacy.…

计算机视觉与模式识别 · 计算机科学 2025-08-29 Yixiang Qiu , Yanhan Liu , Hongyao Yu , Hao Fang , Bin Chen , Shu-Tao Xia , Ke Xu

In this paper, we investigate one of the most fundamental nonconvex learning problems, ReLU regression, in the Differential Privacy (DP) model. Previous studies on private ReLU regression heavily rely on stringent assumptions, such as…

机器学习 · 计算机科学 2025-06-11 Meng Ding , Mingxi Lei , Shaowei Wang , Tianhang Zheng , Di Wang , Jinhui Xu

Federated Learning (FL) is designed to prevent data leakage through collaborative model training without centralized data storage. However, it remains vulnerable to gradient reconstruction attacks that recover original training data from…

机器学习 · 计算机科学 2024-11-07 Yuxiao Chen , Gamze Gürsoy , Qi Lei

Federated Learning (FL) trains a black-box and high-dimensional model among different clients by exchanging parameters instead of direct data sharing, which mitigates the privacy leak incurred by machine learning. However, FL still suffers…

机器学习 · 计算机科学 2024-03-05 Qi Tan , Qi Li , Yi Zhao , Zhuotao Liu , Xiaobing Guo , Ke Xu

Ensuring privacy-preserving inference on cryptographically secure data is a well-known computational challenge. To alleviate the bottleneck of costly cryptographic computations in non-linear activations, recent methods have suggested…

机器学习 · 计算机科学 2024-08-21 Saswat Das , Marco Romanelli , Ferdinando Fioretto

In this article we investigate blow up phenomena for gradient descent optimization methods in the training of artificial neural networks (ANNs). Our theoretical analysis is focused on shallow ANNs with one neuron on the input layer, one…

最优化与控制 · 数学 2022-11-29 Davide Gallon , Arnulf Jentzen , Felix Lindner

Gradient leakage has been identified as a potential source of privacy breaches in modern image processing systems, where the adversary can completely reconstruct the training images from leaked gradients. However, existing methods are…

计算机视觉与模式识别 · 计算机科学 2024-06-17 Jiayang Meng , Tao Huang , Hong Chen , Cuiping Li

Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut…

无序系统与神经网络 · 物理学 2024-05-06 Carlo Baldassi , Enrico M. Malatesta , Riccardo Zecchina

Modern deep learning requires large volumes of data, which could contain sensitive or private information that cannot be leaked. Recent work has shown for homogeneous neural networks a large portion of this training data could be…

机器学习 · 计算机科学 2023-11-13 Noel Loo , Ramin Hasani , Mathias Lechner , Alexander Amini , Daniela Rus

Discriminatively trained, deterministic neural networks are the de facto choice for classification problems. However, even though they achieve state-of-the-art results on in-domain test sets, they tend to be overconfident on…

机器学习 · 计算机科学 2024-03-28 Ahmad Rashid , Serena Hacker , Guojun Zhang , Agustinus Kristiadi , Pascal Poupart

Data privacy has become an increasingly important issue in Machine Learning (ML), where many approaches have been developed to tackle this challenge, e.g. cryptography (Homomorphic Encryption (HE), Differential Privacy (DP), etc.) and…

机器学习 · 计算机科学 2022-09-13 Hanchi Ren , Jingjing Deng , Xianghua Xie

Neural networks with REctified Linear Unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the…

机器学习 · 统计学 2019-05-01 Gang Wang , Georgios B. Giannakis , Jie Chen

In this work, we consider the approximation of a large class of bounded functions, with minimal regularity assumptions, by ReLU neural networks. We show that the approximation error can be bounded from above by a quantity proportional to…

机器学习 · 统计学 2026-02-27 Owen Davis , Gianluca Geraci , Mohammad Motamed

Within the machine learning community, reconstruction attacks are a principal attack of concern and have been identified even in federated learning, which was designed with privacy preservation in mind. In federated learning, it has been…