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Recent studies show that training deep neural networks (DNNs) with Lipschitz constraints are able to enhance adversarial robustness and other model properties such as stability. In this paper, we propose a layer-wise orthogonal training…

Machine Learning · Computer Science 2023-03-28 Xiaojun Xu , Linyi Li , Bo Li

Vision Transformers (ViTs) have emerged as popular models in computer vision, demonstrating state-of-the-art performance across various tasks. This success typically follows a two-stage strategy involving pre-training on large-scale…

Computer Vision and Pattern Recognition · Computer Science 2024-02-07 Zijun Long , Zaiqiao Meng , Gerardo Aragon Camarasa , Richard McCreadie

Image restoration, the recovery of clean images from degraded measurements, has applications in various domains like surveillance, defense, and medical imaging. Despite achieving state-of-the-art (SOTA) restoration performance, existing…

Computer Vision and Pattern Recognition · Computer Science 2026-03-30 Shubhi Shukla , Pravin Nair

Vision transformer has demonstrated promising performance on challenging computer vision tasks. However, directly training the vision transformers may yield unstable and sub-optimal results. Recent works propose to improve the performance…

Computer Vision and Pattern Recognition · Computer Science 2021-06-14 Chengyue Gong , Dilin Wang , Meng Li , Vikas Chandra , Qiang Liu

Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to…

Computer Vision and Pattern Recognition · Computer Science 2024-01-30 Shaeke Salman , Md Montasir Bin Shams , Xiuwen Liu

Self-attention and masked self-attention are at the heart of Transformers' outstanding success. Still, our mathematical understanding of attention, in particular of its Lipschitz properties - which are key when it comes to analyzing…

Machine Learning · Computer Science 2024-06-05 Valérie Castin , Pierre Ablin , Gabriel Peyré

Structured stochastic multi-armed bandits provide accelerated regret rates over the standard unstructured bandit problems. Most structured bandits, however, assume the knowledge of the structural parameter such as Lipschitz continuity,…

Machine Learning · Computer Science 2021-06-28 Hyejin Park , Seiyun Shin , Kwang-Sung Jun , Jungseul Ok

Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…

Machine Learning · Computer Science 2022-11-02 Leon Bungert , René Raab , Tim Roith , Leo Schwinn , Daniel Tenbrinck

Recent advances on Vision Transformer (ViT) and its improved variants have shown that self-attention-based networks surpass traditional Convolutional Neural Networks (CNNs) in most vision tasks. However, existing ViTs focus on the standard…

Computer Vision and Pattern Recognition · Computer Science 2022-05-24 Xiaofeng Mao , Gege Qi , Yuefeng Chen , Xiaodan Li , Ranjie Duan , Shaokai Ye , Yuan He , Hui Xue

Vision Transformers (ViTs) have achieved overwhelming success, yet they suffer from vulnerable resolution scalability, i.e., the performance drops drastically when presented with input resolutions that are unseen during training. We…

Computer Vision and Pattern Recognition · Computer Science 2023-04-04 Rui Tian , Zuxuan Wu , Qi Dai , Han Hu , Yu Qiao , Yu-Gang Jiang

Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving…

Optimization and Control · Mathematics 2020-06-23 Patrick L. Combettes , Jean-Christophe Pesquet

In this paper, we investigate the continual learning of Vision Transformers (ViT) for the challenging exemplar-free scenario, with special focus on how to efficiently distill the knowledge of its crucial self-attention mechanism (SAM). Our…

Computer Vision and Pattern Recognition · Computer Science 2022-05-06 Francesco Pelosin , Saurav Jha , Andrea Torsello , Bogdan Raducanu , Joost van de Weijer

We present a novel local Lipschitz bound for self-attention blocks of transformers. This bound is based on a refined closed-form expression for the spectral norm of the softmax function. The resulting bound is not only more accurate than in…

Machine Learning · Computer Science 2025-07-11 Nikolay Yudin , Alexander Gaponov , Sergei Kudriashov , Maxim Rakhuba

Lipschitz constants of neural networks have been explored in various contexts in deep learning, such as provable adversarial robustness, estimating Wasserstein distance, stabilising training of GANs, and formulating invertible neural…

Machine Learning · Statistics 2021-06-10 Hyunjik Kim , George Papamakarios , Andriy Mnih

This paper demonstrates the robustness of Lipschitz-regularized $\alpha$-divergences as objective functionals in generative modeling, showing they enable stable learning across a wide range of target distributions with minimal assumptions.…

Machine Learning · Statistics 2025-09-09 Ziyu Chen , Hyemin Gu , Markos A. Katsoulakis , Luc Rey-Bellet , Wei Zhu

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

Recent development in Large Language Models (LLMs) and Multi-modal Large Language Models (MLLMs) have leverage Attention-based Transformer architectures and achieved superior performance and generalization capabilities. They have since…

Computation and Language · Computer Science 2025-05-20 Yuze Zhao , Jintao Huang , Jinghan Hu , Xingjun Wang , Yunlin Mao , Daoze Zhang , Hong Zhang , Zeyinzi Jiang , Zhikai Wu , Baole Ai , Ang Wang , Wenmeng Zhou , Yingda Chen

This paper presents a study of robust policy networks in deep reinforcement learning. We investigate the benefits of policy parameterizations that naturally satisfy constraints on their Lipschitz bound, analyzing their empirical performance…

Machine Learning · Computer Science 2025-02-07 Nicholas H. Barbara , Ruigang Wang , Ian R. Manchester

Vision transformers (ViTs) have demonstrated remarkable performance in a variety of vision tasks. Despite their promising capabilities, training a ViT requires a large amount of diverse data. Several studies empirically found that using…

Computer Vision and Pattern Recognition · Computer Science 2024-05-24 Bum Jun Kim , Sang Woo Kim

Vision Transformer (ViT) architectures are becoming increasingly popular and widely employed to tackle computer vision applications. Their main feature is the capacity to extract global information through the self-attention mechanism,…

Computer Vision and Pattern Recognition · Computer Science 2024-05-06 Lorenzo Papa , Paolo Russo , Irene Amerini , Luping Zhou