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We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

Machine Learning · Computer Science 2025-11-14 Eliot Beyler , Francis Bach

Deep neural network classifiers suffer from adversarial vulnerability: well-crafted, unnoticeable changes to the input data can affect the classifier decision. In this regard, the study of powerful adversarial attacks can help shed light on…

Machine Learning · Computer Science 2020-07-07 Hadi M. Dolatabadi , Sarah Erfani , Christopher Leckie

The reliance on deep learning algorithms has grown significantly in recent years. Yet, these models are highly vulnerable to adversarial attacks, which introduce visually imperceptible perturbations into testing data to induce…

Machine Learning · Computer Science 2019-06-14 Rajeev Sahay , Rehana Mahfuz , Aly El Gamal

This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…

Machine Learning · Computer Science 2024-02-02 Kaiwen Hou

We study the convergence of gradient flows related to learning deep linear neural networks (where the activation function is the identity map) from data. In this case, the composition of the network layers amounts to simply multiplying the…

Optimization and Control · Mathematics 2020-10-16 Bubacarr Bah , Holger Rauhut , Ulrich Terstiege , Michael Westdickenberg

This paper investigates a family of methods for defending against adversarial attacks that owe part of their success to creating a noisy, discontinuous, or otherwise rugged loss landscape that adversaries find difficult to navigate. A…

Machine Learning · Computer Science 2022-08-08 Panagiotis Eustratiadis , Henry Gouk , Da Li , Timothy Hospedales

In recent years, deep learning has shown itself to be an incredibly valuable tool in cybersecurity as it helps network intrusion detection systems to classify attacks and detect new ones. Adversarial learning is the process of utilizing…

Cryptography and Security · Computer Science 2022-06-30 Jared Mathews , Prosenjit Chatterjee , Shankar Banik , Cory Nance

Graph neural networks (GNNs) which apply the deep neural networks to graph data have achieved significant performance for the task of semi-supervised node classification. However, only few work has addressed the adversarial robustness of…

Machine Learning · Computer Science 2019-10-16 Kaidi Xu , Hongge Chen , Sijia Liu , Pin-Yu Chen , Tsui-Wei Weng , Mingyi Hong , Xue Lin

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density $\pi$ given only its score $\nabla \log \pi$. Our method approximates the Wasserstein gradient flow on…

Machine Learning · Computer Science 2025-10-21 Vasily Ilin , Peter Sushko , Jingwei Hu

We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification,…

Machine Learning · Computer Science 2021-11-05 Nam Ho-Nguyen , Stephen J. Wright

Deep neural networks are vulnerable to adversarial examples, i.e., carefully-perturbed inputs aimed to mislead classification. This work proposes a detection method based on combining non-linear dimensionality reduction and density…

Machine Learning · Computer Science 2019-05-02 Francesco Crecchi , Davide Bacciu , Battista Biggio

Deep Convolution Neural Networks (CNNs) can easily be fooled by subtle, imperceptible changes to the input images. To address this vulnerability, adversarial training creates perturbation patterns and includes them in the training set to…

Computer Vision and Pattern Recognition · Computer Science 2022-09-19 Muzammal Naseer , Salman Khan , Munawar Hayat , Fahad Shahbaz Khan , Fatih Porikli

This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows…

Numerical Analysis · Mathematics 2015-12-08 Guillaume Charpiat , Giacomo Nardi , Gabriel Peyré , François-Xavier Vialard

We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate these neurons with the distribution of adversarial attacks…

Machine Learning · Computer Science 2022-02-01 Chandresh Pravin , Ivan Martino , Giuseppe Nicosia , Varun Ojha

Despite being effective in many application areas, Deep Neural Networks (DNNs) are vulnerable to being attacked. In object recognition, the attack takes the form of a small perturbation added to an image, that causes the DNN to misclassify,…

Machine Learning · Computer Science 2025-01-14 T. Windeatt

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

Machine Learning · Statistics 2024-09-12 Yifan Chen , Daniel Zhengyu Huang , Jiaoyang Huang , Sebastian Reich , Andrew M. Stuart

Deep neural networks have been proved that they are vulnerable to adversarial examples, which are generated by adding human-imperceptible perturbations to images. To defend these adversarial examples, various detection based methods have…

Computer Vision and Pattern Recognition · Computer Science 2021-02-24 Kejiang Chen , Yuefeng Chen , Hang Zhou , Chuan Qin , Xiaofeng Mao , Weiming Zhang , Nenghai Yu

We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by…

Machine Learning · Computer Science 2025-12-29 Zhao Ding , Chenguang Duan , Yuling Jiao , Ruoxuan Li , Jerry Zhijian Yang , Pingwen Zhang

This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the…

Optimization and Control · Mathematics 2023-12-08 Mitsuru Toyoda , Akatsuki Nishioka , Mirai Tanaka

Recent work has developed methods for learning deep network classifiers that are provably robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this…

Machine Learning · Computer Science 2018-11-26 Eric Wong , Frank R. Schmidt , Jan Hendrik Metzen , J. Zico Kolter