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Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…

Numerical Analysis · Mathematics 2025-09-23 Daniel Obmann , Gyeongha Hwang , Markus Haltmeier

With the widespread use of machine learning, concerns over its security and reliability have become prevalent. As such, many have developed defenses to harden neural networks against adversarial examples, imperceptibly perturbed inputs that…

Machine Learning · Computer Science 2022-05-09 Pratik Vaishnavi , Kevin Eykholt , Amir Rahmati

Two main challenges in Reinforcement Learning (RL) are designing appropriate reward functions and ensuring the safety of the learned policy. To address these challenges, we present a theoretical framework for Inverse Reinforcement Learning…

Machine Learning · Computer Science 2023-06-02 Andreas Schlaginhaufen , Maryam Kamgarpour

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Machine Learning · Computer Science 2022-11-03 Kosio Beshkov , Jonas Verhellen , Mikkel Elle Lepperød

Adversarial robustness studies the worst-case performance of a machine learning model to ensure safety and reliability. With the proliferation of deep-learning-based technology, the potential risks associated with model development and…

Machine Learning · Computer Science 2023-01-06 Pin-Yu Chen , Sijia Liu

We study the robustness of machine learning approaches to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial…

Disordered Systems and Neural Networks · Physics 2024-01-26 Si Jiang , Sirui Lu , Dong-Ling Deng

We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…

Machine Learning · Statistics 2026-03-19 Max Schölpple , Liu Fanghui , Ingo Steinwart

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…

Machine Learning · Statistics 2020-10-30 Cesare Molinari , Mathurin Massias , Lorenzo Rosasco , Silvia Villa

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

Numerical Analysis · Mathematics 2026-05-26 Sandra R. Babyale , Jodi Mead

Regularized learning is a fundamental technique in online optimization, machine learning and many other fields of computer science. A natural question that arises in these settings is how regularized learning algorithms behave when faced…

Computer Science and Game Theory · Computer Science 2017-09-11 Panayotis Mertikopoulos , Christos Papadimitriou , Georgios Piliouras

Despite unconditional feature inversion being the foundation of many image synthesis applications, training an inverter demands a high computational budget, large decoding capacity and imposing conditions such as autoregressive priors. To…

Computer Vision and Pattern Recognition · Computer Science 2022-10-24 Renan A. Rojas-Gomez , Raymond A. Yeh , Minh N. Do , Anh Nguyen

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…

Machine Learning · Computer Science 2025-11-04 Longwei Wang , Ifrat Ikhtear Uddin , KC Santosh , Chaowei Zhang , Xiao Qin , Yang Zhou

Artificial intelligence, particularly through recent advancements in deep learning, has achieved exceptional performances in many tasks in fields such as natural language processing and computer vision. In addition to desirable evaluation…

Machine Learning · Computer Science 2024-03-04 Sean Xie , Soroush Vosoughi , Saeed Hassanpour

Convolution Neural Networks, known as ConvNets exceptionally perform well in many complex machine learning tasks. The architecture of ConvNets demands the huge and rich amount of data and involves with a vast number of parameters that leads…

Computer Vision and Pattern Recognition · Computer Science 2017-12-14 Pushparaja Murugan , Shanmugasundaram Durairaj

Despite apparent human-level performances of deep neural networks (DNN), they behave fundamentally differently from humans. They easily change predictions when small corruptions such as blur and noise are applied on the input (lack of…

Computer Vision and Pattern Recognition · Computer Science 2020-03-10 Sanghyuk Chun , Seong Joon Oh , Sangdoo Yun , Dongyoon Han , Junsuk Choe , Youngjoon Yoo

Adversarial training often suffers from a robustness-accuracy trade-off, where achieving high robustness comes at the cost of accuracy. One approach to mitigate this trade-off is leveraging invariance regularization, which encourages model…

Machine Learning · Computer Science 2025-08-29 Futa Waseda , Ching-Chun Chang , Isao Echizen

Robustness is widely regarded as a fundamental problem in the analysis of machine learning (ML) models. Most often robustness equates with deciding the non-existence of adversarial examples, where adversarial examples denote situations…

Machine Learning · Computer Science 2023-12-19 Yacine Izza , Joao Marques-Silva

Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…

Machine Learning · Statistics 2025-03-20 Antônio H. RIbeiro , Thomas B. Schön , Dave Zahariah , Francis Bach

A crucial aspect in reliable machine learning is to design a deployable system in generalizing new related but unobserved environments. Domain generalization aims to alleviate such a prediction gap between the observed and unseen…

Machine Learning · Computer Science 2021-06-01 Changjian Shui , Boyu Wang , Christian Gagné

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…

Optimization and Control · Mathematics 2022-04-22 Cristian Vega , Cesare Molinari , Lorenzo Rosasco , Silvia Villa