Related papers: Lipschitz Certificates for Layered Network Structu…
In this work we propose lifted regression/reconstruction networks (LRRNs), which combine lifted neural networks with a guaranteed Lipschitz continuity property for the output layer. Lifted neural networks explicitly optimize an energy model…
Lipschitz constant is a fundamental property in certified robustness, as smaller values imply robustness to adversarial examples when a model is confident in its prediction. However, identifying the worst-case adversarial examples is known…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…
This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization,…
Deep neural networks have shown remarkable performance across a wide range of vision-based tasks, particularly due to the availability of large-scale datasets for training and better architectures. However, data seen in the real world are…
To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
Deep neural networks are notorious for being sensitive to small well-chosen perturbations, and estimating the regularity of such architectures is of utmost importance for safe and robust practical applications. In this paper, we investigate…
In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity properties of convolutional, pooling, and fully connected layers…
The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a…
Deep neural networks (DNNs) have emerged as a popular mathematical tool for function approximation due to their capability of modelling highly nonlinear functions. Their applications range from image classification and natural language…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
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…
In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar…
Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…
The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on…
The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining…
Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably,…
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…