相关论文: Approximating Lipschitz continuous functions with …

Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz…

Lipschitz-constrained neural networks have many applications in machine learning. Since designing and training expressive Lipschitz-constrained networks is very challenging, there is a need for improved methods and a better theoretical…

Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize…

Adversarial attacks against machine learning models are a rather hefty obstacle to our increasing reliance on these models. Due to this, provably robust (certified) machine learning models are a major topic of interest. Lipschitz continuous…

Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…

A Random Vector Functional Link (RVFL) network is a depth-2 neural network with random inner weights and biases. Only the outer weights of such an architecture are to be learned, so the learning process boils down to a linear optimization…

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both…

We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…

1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and…

The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of nonsmooth vector-valued…

This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite…

It has been shown that a neural network's Lipschitz constant can be leveraged to derive robustness guarantees, to improve generalizability via regularization or even to construct invertible networks. Therefore, a number of methods varying…

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…

Generative adversarial networks (GANs) are so complex that the existing learning theories do not provide a satisfactory explanation for why GANs have great success in practice. The same situation also remains largely open for deep neural…

We present a new neural network to approximate convex functions. This network has the particularity to approximate the function with cuts and can be easily adapted to partial convexity. We give an universal approximation theorem in the full…

We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…

Graph neural networks (GNNs) have recently been demonstrated to perform well on a variety of network-based tasks such as decentralized control and resource allocation, and provide computationally efficient methods for these tasks which have…

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…

Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…