English
Related papers

Related papers: Can convolutional ResNets approximately preserve i…

200 papers

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Optimization and Control · Mathematics 2014-12-09 Samuel Vaiter , Gabriel Peyré , Jalal M. Fadili

Convex $\ell_1$ regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can…

Optimization and Control · Mathematics 2022-06-01 Konstantin Pieper , Armenak Petrosyan

Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…

Machine Learning · Computer Science 2017-11-10 Hyeonwoo Noh , Tackgeun You , Jonghwan Mun , Bohyung Han

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

Numerous recent works utilize bi-Lipschitz regularization of neural network layers to preserve relative distances between data instances in the feature spaces of each layer. This distance sensitivity with respect to the data aids in tasks…

Machine Learning · Statistics 2022-03-17 Jeffrey Willette , Hae Beom Lee , Juho Lee , Sung Ju Hwang

The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual…

Machine Learning · Computer Science 2022-02-02 Laurent Meunier , Blaise Delattre , Alexandre Araujo , Alexandre Allauzen

The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…

High Energy Physics - Phenomenology · Physics 2024-08-02 Tomona Kinugawa , Tetsuo Hyodo

Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…

Machine Learning · Computer Science 2025-11-11 Shay Moran , Elizaveta Nesterova

Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…

Machine Learning · Computer Science 2026-02-02 Christiaan P. Opperman , Anna S. Bosman , Katherine M. Malan

Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…

Machine Learning · Computer Science 2024-03-11 Lachlan Simpson , Kyle Millar , Adriel Cheng , Cheng-Chew Lim , Hong Gunn Chew

Robustness with respect to weight perturbations underpins guarantees for generalization, pruning and quantization. Existing guarantees rely on Lipschitz bounds in parameter space, cover only plain feed-forward MLPs, and break under the…

Machine Learning · Computer Science 2025-06-16 Antoine Gonon , Nicolas Brisebarre , Elisa Riccietti , Rémi Gribonval

Regularization, whether explicit in terms of a penalty in the loss or implicit in the choice of algorithm, is a cornerstone of modern machine learning. Indeed, controlling the complexity of the model class is particularly important when…

Machine Learning · Statistics 2024-10-22 Matteo Vilucchio , Nikolaos Tsilivis , Bruno Loureiro , Julia Kempe

Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Paul Hamelbeck , Johannes Schiffer

Several image processing tasks, such as image classification and object detection, have been significantly improved using Convolutional Neural Networks (CNN). Like ResNet and EfficientNet, many architectures have achieved outstanding…

Computer Vision and Pattern Recognition · Computer Science 2022-01-11 Claudio Filipi Gonçalves dos Santos , João Paulo Papa

The analysis of neural network training beyond their linearization regime remains an outstanding open question, even in the simplest setup of a single hidden-layer. The limit of infinitely wide networks provides an appealing route forward…

Machine Learning · Computer Science 2020-06-19 Jaume de Dios , Joan Bruna

Propagation-based X-ray phase contrast enables nanoscale imaging of biological tissue by probing not only the attenuation, but also the real part of the refractive index of the sample. Since only intensities of diffracted waves can be…

Numerical Analysis · Mathematics 2017-09-11 Simon Maretzke , Thorsten Hohage

Research in computational deep learning has directed considerable efforts towards hardware-oriented optimisations for deep neural networks, via the simplification of the activation functions, or the quantization of both activations and…

Machine Learning · Computer Science 2020-11-04 Gian Paolo Leonardi , Matteo Spallanzani

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…

Computation · Statistics 2019-12-23 Xun Shen , Jiancang Zhuang , Xingguo Zhang

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…

Machine Learning · Computer Science 2023-01-18 Mahyar Fazlyab , Alexander Robey , Hamed Hassani , Manfred Morari , George J. Pappas

Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for…

Machine Learning · Computer Science 2026-02-18 Takashi Furuya , Davide Murari , Carola-Bibiane Schönlieb