Related papers: A Geometric Framework for Adversarial Vulnerabilit…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

Driven by massive amounts of data and important advances in computational resources, new deep learning systems have achieved outstanding results in a large spectrum of applications. Nevertheless, our current theoretical understanding on the…

Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework,…

Artificial neural networks can achieve impressive performances, and even outperform humans in some specific tasks. Nevertheless, unlike biological brains, the artificial neural networks suffer from tiny perturbations in sensory input, under…

Deep learning models are known to be vulnerable to adversarial attacks. Adversarial learning is therefore becoming a crucial task. We propose a new vision on neural network robustness using Riemannian geometry and foliation theory. The idea…

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…

Recent work has demonstrated that deep neural networks are vulnerable to adversarial examples---inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings…

Biological neural networks have evolved to maintain performance despite significant circuit damage. To survive damage, biological network architectures have both intrinsic resilience to component loss and also activate recovery programs…

This tutorial aims to introduce the fundamentals of adversarial robustness of deep learning, presenting a well-structured review of up-to-date techniques to assess the vulnerability of various types of deep learning models to adversarial…

Recently, adversarial deception becomes one of the most considerable threats to deep neural networks. However, compared to extensive research in new designs of various adversarial attacks and defenses, the neural networks' intrinsic…

Neural networks are prone to misclassify slightly modified input images. Recently, many defences have been proposed, but none have improved the robustness of neural networks consistently. Here, we propose to use adversarial attacks as a…

This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…

Adversarial attacks against computer vision systems have emerged as a critical research area that challenges the fundamental assumptions about neural network robustness and security. This comprehensive survey examines the evolving landscape…

Adversarial examples reveal critical vulnerabilities in deep neural networks by exploiting their sensitivity to imperceptible input perturbations. While adversarial training remains the predominant defense strategy, it often incurs…

As neural networks become the tool of choice to solve an increasing variety of problems in our society, adversarial attacks become critical. The possibility of generating data instances deliberately designed to fool a network's analysis can…

The reliability of a learning model is key to the successful deployment of machine learning in various industries. Creating a robust model, particularly one unaffected by adversarial attacks, requires a comprehensive understanding of the…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…

This work provides a computable, direct, and mathematically rigorous approximation to the differential geometry of class manifolds for high-dimensional data, along with nonlinear projections from input space onto these class manifolds. The…