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Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…

Machine Learning · Statistics 2026-05-28 Jürgen Dölz , Michael Multerer , Michele Palma

The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…

Machine Learning · Computer Science 2023-08-22 Ouail Kitouni , Niklas Nolte , Mike Williams

There has long been plenty of theoretical and empirical evidence supporting the success of ensemble learning. Deep ensembles in particular take advantage of training randomness and expressivity of individual neural networks to gain…

Machine Learning · Computer Science 2024-03-21 Anh Bui , Vy Vo , Tung Pham , Dinh Phung , Trung Le

Ensemble learning is a process by which multiple base learners are strategically generated and combined into one composite learner. There are two features that are essential to an ensemble's performance, the individual accuracies of the…

Machine Learning · Computer Science 2021-09-30 Wenjing Li , Randy C. Paffenroth , David Berthiaume

The ensemble of deep neural networks has been shown, both theoretically and empirically, to improve generalization accuracy on the unseen test set. However, the high training cost hinders its efficiency since we need a sufficient number of…

Machine Learning · Computer Science 2021-12-28 Wentao Zhang , Jiawei Jiang , Yingxia Shao , Bin Cui

Text generation models are notoriously vulnerable to errors in the training data. With the wide-spread availability of massive amounts of web-crawled data becoming more commonplace, how can we enhance the robustness of models trained on a…

Computation and Language · Computer Science 2024-03-20 Tianjian Li , Haoran Xu , Philipp Koehn , Daniel Khashabi , Kenton Murray

High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior…

Computer Vision and Pattern Recognition · Computer Science 2018-11-02 Yusuke Tsuzuku , Issei Sato , Masashi Sugiyama

Due to the inherent imbalance in real-world datasets, na\"ive Empirical Risk Minimization (ERM) tends to bias the learning process towards the majority classes, hindering generalization to minority classes. To rebalance the learning…

Machine Learning · Computer Science 2025-12-09 Zitai Wang , Qianqian Xu , Zhiyong Yang , Zhikang Xu , Linchao Zhang , Xiaochun Cao , Qingming Huang

Ensemble-based adversarial training is a principled approach to achieve robustness against adversarial attacks. An important technique of this approach is to control the transferability of adversarial examples among ensemble members. We…

Computer Vision and Pattern Recognition · Computer Science 2022-02-08 Anh Bui , Trung Le , He Zhao , Paul Montague , Olivier deVel , Tamas Abraham , Dinh Phung

In the context of adversarial robustness, a single model does not usually have enough power to defend against all possible adversarial attacks, and as a result, has sub-optimal robustness. Consequently, an emerging line of work has focused…

Machine Learning · Computer Science 2022-06-08 Dinghuai Zhang , Hongyang Zhang , Aaron Courville , Yoshua Bengio , Pradeep Ravikumar , Arun Sai Suggala

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

Machine Learning · Computer Science 2022-01-27 Saber Jafarpour , Alexander Davydov , Anton V. Proskurnikov , Francesco Bullo

Numerous real-world decisions rely on machine learning algorithms and require calibrated uncertainty estimates. However, modern methods often yield overconfident, uncalibrated predictions. The dominant approach to quantifying the…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

Machine Learning · Computer Science 2021-12-13 Saber Jafarpour , Matthew Abate , Alexander Davydov , Francesco Bullo , Samuel Coogan

It has been recognized that the diversity of base learners is of utmost importance to a good ensemble. This paper defines a novel measurement of diversity, termed as exclusivity. With the designed exclusivity, we further propose an ensemble…

Machine Learning · Computer Science 2016-05-17 Xiaojie Guo

Adversarial attacks have rendered high security risks on modern deep learning systems. Adversarial training can significantly enhance the robustness of neural network models by suppressing the non-robust features. However, the models often…

Machine Learning · Computer Science 2021-03-30 Yi Cai , Xuefei Ning , Huazhong Yang , Yu Wang

Ensembles of neural networks achieve superior performance compared to stand-alone networks in terms of accuracy, uncertainty calibration and robustness to dataset shift. \emph{Deep ensembles}, a state-of-the-art method for uncertainty…

Machine Learning · Computer Science 2022-02-23 Sheheryar Zaidi , Arber Zela , Thomas Elsken , Chris Holmes , Frank Hutter , Yee Whye Teh

Randomized smoothing is the state-of-the-art approach to construct image classifiers that are provably robust against additive adversarial perturbations of bounded magnitude. However, it is more complicated to construct reasonable…

Computer Vision and Pattern Recognition · Computer Science 2024-08-12 Dmitrii Korzh , Mikhail Pautov , Olga Tsymboi , Ivan Oseledets

Deep learning approaches such as convolutional neural nets have consistently outperformed previous methods on challenging tasks such as dense, semantic segmentation. However, the various proposed networks perform differently, with behaviour…

Computer Vision and Pattern Recognition · Computer Science 2017-11-07 Konstantinos Kamnitsas , Wenjia Bai , Enzo Ferrante , Steven McDonagh , Matthew Sinclair , Nick Pawlowski , Martin Rajchl , Matthew Lee , Bernhard Kainz , Daniel Rueckert , Ben Glocker

Ensemble learning has achieved remarkable success in machine learning, but its reliance on numerous base learners limits its application in resource-constrained environments. This paper introduces an innovative "Margin-Maximizing…

Machine Learning · Computer Science 2024-09-20 Jinghui Yuan , Hao Chen , Renwei Luo , Feiping Nie

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead…

Machine Learning · Computer Science 2025-11-27 Erh-Chung Chen , Pin-Yu Chen , I-Hsin Chung , Che-Rung Lee