Related papers: Adversarial flows: A gradient flow characterizatio…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
In recent years, deep neural networks demonstrated state-of-the-art performance in a large variety of tasks and therefore have been adopted in many applications. On the other hand, the latest studies revealed that neural networks are…
Adversarial examples are input examples that are specifically crafted to deceive machine learning classifiers. State-of-the-art adversarial example detection methods characterize an input example as adversarial either by quantifying the…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
The existence of adversarial examples underscores the importance of understanding the robustness of machine learning models. Bayesian neural networks (BNNs), due to their calibrated uncertainty, have been shown to posses favorable…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…
The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…
The notion of adversarial attacks on image classification models based on convolutional neural networks (CNN) is introduced in this work. To classify images, deep learning models called CNNs are frequently used. However, when the networks…
Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based…
We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy…
In recent years, the security of deep learning models achieves more and more attentions with the rapid development of neural networks, which are vulnerable to adversarial examples. Almost all existing gradient-based attack methods use the…
Deciding that two network flows are essentially the same is an important problem in intrusion detection and in tracing anonymous connections. A stepping stone or an anonymity network may try to prevent flow correlation by adding chaff…
The conventional understanding of adversarial training in generative adversarial networks (GANs) is that the discriminator is trained to estimate a divergence, and the generator learns to minimize this divergence. We argue that despite the…
Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…
Among generative neural models, flow matching techniques stand out for their simple applicability and good scaling properties. Here, velocity fields of curves connecting a simple latent and a target distribution are learned. Then the…
Despite remarkable achievements in deep learning across various domains, its inherent vulnerability to adversarial examples still remains a critical concern for practical deployment. Adversarial training has emerged as one of the most…
State-of-the-art adversarial attacks are aimed at neural network classifiers. By default, neural networks use gradient descent to minimize their loss function. The gradient of a classifier's loss function is used by gradient-based…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the problem to linear combinations of Dirac deltas and then perform…