Related papers: Lipschitz Properties for Deep Convolutional Networ…
Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the…
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,…
Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm.…
The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias…
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…
Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class…
While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this is the Lyapunov stability of the gradient descent…
Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…
Lipschitz constrained networks have gathered considerable attention in the deep learning community, with usages ranging from Wasserstein distance estimation to the training of certifiably robust classifiers. However they remain commonly…
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…
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…
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…
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…
This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go,…
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…