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As hyperbolic deep learning grows in popularity, so does the need for adversarial robustness in the context of such a non-Euclidean geometry. To this end, this paper proposes hyperbolic alternatives to the commonly used FGM and PGD…

Machine Learning · Computer Science 2024-12-03 Max van Spengler , Jan Zahálka , Pascal Mettes

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

Machine Learning · Computer Science 2025-08-26 Menglin Yang , Min Zhou , Tong Zhang , Jiahong Liu , Zhihao Li , Lujia Pan , Hui Xiong , Irwin King

Recent breakthroughs in defenses against adversarial examples, like adversarial training, make the neural networks robust against various classes of attackers (e.g., first-order gradient-based attacks). However, it is an open question…

Machine Learning · Computer Science 2019-06-07 Shiqi Wang , Yizheng Chen , Ahmed Abdou , Suman Jana

Adversarial attacks, particularly the Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD) pose significant threats to the robustness of deep learning models in image classification. This paper explores and refines defense…

Cryptography and Security · Computer Science 2025-05-15 Hetvi Waghela , Jaydip Sen , Sneha Rakshit

The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in safety-critical applications. Most existing methods either…

Machine Learning · Computer Science 2021-02-25 Leo Schwinn , An Nguyen , René Raab , Leon Bungert , Daniel Tenbrinck , Dario Zanca , Martin Burger , Bjoern Eskofier

Adversarial attacks on deep neural network models have seen rapid development and are extensively used to study the stability of these networks. Among various adversarial strategies, Projected Gradient Descent (PGD) is a widely adopted…

Machine Learning · Computer Science 2024-10-17 Dayana Savostianova , Emanuele Zangrando , Francesco Tudisco

Non-Euclidean foundation models increasingly place representations in curved spaces such as hyperbolic geometry. We show that this geometry creates a boundary-driven asymmetry that backdoor triggers can exploit. Near the boundary, small…

Machine Learning · Computer Science 2025-10-09 Ali Baheri

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

Machine Learning · Computer Science 2026-05-15 Dionisia Naddeo , Jonas Linkerhägner , Nicola Toschi , Geri Skenderi , Veronica Lachi

The nature of deep neural networks has given rise to a variety of attacks, but little work has been done to address the effect of adversarial attacks on segmentation models trained on MRI datasets. In light of the grave consequences that…

Image and Video Processing · Electrical Eng. & Systems 2024-01-23 Zhongxuan Wang , Leo Xu

Despite their remarkable performance, deep neural networks exhibit a critical vulnerability: small, often imperceptible, adversarial perturbations can lead to drastically altered model predictions. Given the stringent reliability demands of…

Machine Learning · Computer Science 2025-12-16 Mohammad Mahdi Razmjoo , Mohammad Mahdi Sharifian , Saeed Bagheri Shouraki

Segmentation is considered to be a very crucial task in medical image analysis. This task has been easier since deep learning models have taken over with its high performing behavior. However, deep learning models dependency on large data…

Image and Video Processing · Electrical Eng. & Systems 2021-05-26 Mst. Tasnim Pervin , Linmi Tao , Aminul Huq , Zuoxiang He , Li Huo

Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic…

Machine Learning · Computer Science 2021-02-11 Diego Lazcano , Nicolás Fredes , Werner Creixell

Adversarial attacks on Graph Neural Networks aim to perturb the performance of the learner by carefully modifying the graph topology and node attributes. Existing methods achieve attack stealthiness by constraining the modification budget…

Machine Learning · Computer Science 2025-06-10 Kai Yuan , Jiahao Zhang , Yidi Wang , Xiaobing Pei

With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of…

Machine Learning · Computer Science 2023-01-24 Eric Qu , Dongmian Zou

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

Machine Learning · Statistics 2020-05-29 Gian Maria Marconi , Lorenzo Rosasco , Carlo Ciliberto

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

Machine Learning · Computer Science 2019-10-30 Qi Liu , Maximilian Nickel , Douwe Kiela

Adversarial training, especially projected gradient descent (PGD), has proven to be a successful approach for improving robustness against adversarial attacks. After adversarial training, gradients of models with respect to their inputs…

Machine Learning · Statistics 2023-04-21 Ricardo Bigolin Lanfredi , Joyce D. Schroeder , Tolga Tasdizen

The reliance on deep learning algorithms has grown significantly in recent years. Yet, these models are highly vulnerable to adversarial attacks, which introduce visually imperceptible perturbations into testing data to induce…

Machine Learning · Computer Science 2019-06-14 Rajeev Sahay , Rehana Mahfuz , Aly El Gamal

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

Machine Learning · Computer Science 2018-06-29 Octavian-Eugen Ganea , Gary Bécigneul , Thomas Hofmann

Deep networks are well-known to be fragile to adversarial attacks. We conduct an empirical analysis of deep representations under the state-of-the-art attack method called PGD, and find that the attack causes the internal representation to…

Machine Learning · Computer Science 2019-10-29 Chengzhi Mao , Ziyuan Zhong , Junfeng Yang , Carl Vondrick , Baishakhi Ray
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