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A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize…

Machine Learning · Statistics 2019-08-08 Judy Hoffman , Daniel A. Roberts , Sho Yaida

Robustness of deep learning models is a property that has recently gained increasing attention. We explore a notion of robustness for generative adversarial models that is pertinent to their internal interactive structure, and show that,…

Machine Learning · Computer Science 2019-10-11 Zhi Xu , Chengtao Li , Stefanie Jegelka

We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…

Systems and Control · Electrical Eng. & Systems 2021-10-27 Yassine Nemmour , Bernhard Schölkopf , Jia-Jie Zhu

Training foundation models on extensive datasets and then finetuning them on specific tasks has emerged as the mainstream approach in artificial intelligence. However, the model robustness, which is a critical aspect for safety, is often…

Computer Vision and Pattern Recognition · Computer Science 2023-12-15 Kai Qiu , Huishuai Zhang , Zhirong Wu , Stephen Lin

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…

Numerical Analysis · Mathematics 2023-01-04 David Lenz , Raine Yeh , Vijay Mahadevan , Iulian Grindeanu , Tom Peterka

Randomized smoothing is currently considered the state-of-the-art method to obtain certifiably robust classifiers. Despite its remarkable performance, the method is associated with various serious problems such as "certified accuracy…

Machine Learning · Computer Science 2024-03-11 Peter Súkeník , Aleksei Kuvshinov , Stephan Günnemann

Recent studies have shown that regularization techniques using soft labels, e.g., label smoothing, Mixup, and CutMix, not only enhance image classification accuracy but also mitigate miscalibration due to overconfident predictions, and…

Computer Vision and Pattern Recognition · Computer Science 2025-10-17 Jonghyun Park , Juyeop Kim , Jong-Seok Lee

Deep networks have achieved impressive results on a range of well-curated benchmark datasets. Surprisingly, their performance remains sensitive to perturbations that have little effect on human performance. In this work, we propose a novel…

Computer Vision and Pattern Recognition · Computer Science 2024-10-22 Jonas Ngnawe , Marianne Abemgnigni Njifon , Jonathan Heek , Yann Dauphin

Robust machine learning for regulatory genomics is studied under biologically and technically induced distribution shifts. Deep convolutional and attention based models achieve strong in distribution performance on DNA regulatory sequence…

Genomics · Quantitative Biology 2026-02-20 Yiyao Yang

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

Optimization and Control · Mathematics 2025-09-10 Jingfan Xia , Zhenwei Lin , Qi Deng

This work describes a Bayesian framework for reconstructing the boundaries that represent targeted features in an image, as well as the regularity (i.e., roughness vs. smoothness) of these boundaries.This regularity often carries crucial…

Numerical Analysis · Mathematics 2024-01-26 Babak Maboudi Afkham , Nicolai André Brogaard Riis , Yiqiu Dong , Per Christian Hansen

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…

Machine Learning · Statistics 2019-02-11 Krishna Pillutla , Vincent Roulet , Sham M. Kakade , Zaid Harchaoui

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

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However…

Machine Learning · Computer Science 2024-03-19 Blaise Delattre , Alexandre Araujo , Quentin Barthélemy , Alexandre Allauzen

We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by…

Machine Learning · Statistics 2021-12-02 Soon Hoe Lim , N. Benjamin Erichson , Liam Hodgkinson , Michael W. Mahoney

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Optimization and Control · Mathematics 2021-06-09 Mert Gürbüzbalaban , Andrzej Ruszczyński , Landi Zhu

Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…

Machine Learning · Statistics 2020-05-12 Saeed Saremi , Rupesh Srivastava

Randomized smoothing is a defensive technique to achieve enhanced robustness against adversarial examples which are small input perturbations that degrade the performance of neural network models. Conventional randomized smoothing adds…

Machine Learning · Computer Science 2024-07-17 Ryo Hase , Ye Wang , Toshiaki Koike-Akino , Jing Liu , Kieran Parsons

In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms…

Methodology · Statistics 2025-05-23 Michael Levine