Related papers: Lipschitz Bound Analysis of Neural Networks

This note shows that, for a fixed Lipschitz constant $L > 0$, one layer neural networks that are $L$-Lipschitz are dense in the set of all $L$-Lipschitz functions with respect to the uniform norm on bounded sets.

The robustness of convolutional neural networks (CNNs) is vital to modern AI-driven systems. It can be quantified by formal verification by providing a certified lower bound, within which any perturbation does not alter the original input's…

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the…

In this work we show that adapting Deep Convolutional Neural Network training to the task of boundary detection can result in substantial improvements over the current state-of-the-art in boundary detection. Our contributions consist…

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs)…

In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

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…

It is well-known that standard neural networks, even with a high classification accuracy, are vulnerable to small $\ell_\infty$-norm bounded adversarial perturbations. Although many attempts have been made, most previous works either can…

We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…

Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer…

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…

Text classifiers suffer from small perturbations, that if chosen adversarially, can dramatically change the output of the model. Verification methods can provide robustness certificates against such adversarial perturbations, by computing a…

Shot boundary detection (SBD) is an important component of many video analysis tasks, such as action recognition, video indexing, summarization and editing. Previous work typically used a combination of low-level features like color…

For sensitive problems, such as medical imaging or fraud detection, Neural Network (NN) adoption has been slow due to concerns about their reliability, leading to a number of algorithms for explaining their decisions. NNs have also been…

Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…

In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks -- small modifications of the input that change the predictions. Besides rigorously studied $\ell_p$-bounded additive…

Convolutional Neural Networks (CNNs) dominate various computer vision tasks since Alex Krizhevsky showed that they can be trained effectively and reduced the top-5 error from 26.2 % to 15.3 % on the ImageNet large scale visual recognition…

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…

DNNs have been quickly and broadly exploited to improve the data analysis quality in many complex science and engineering applications. Today's DNNs are becoming deeper and wider because of increasing demand on the analysis quality and more…