Related papers: Lipschitz Bounded Equilibrium Networks
This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight…
Robustness with respect to weight perturbations underpins guarantees for generalization, pruning and quantization. Existing guarantees rely on Lipschitz bounds in parameter space, cover only plain feed-forward MLPs, and break under the…
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…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
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…
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…
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…
Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…
Overparameterized neural networks often show a benign overfitting property in the sense of achieving excellent generalization behavior despite the number of parameters exceeding the number of training examples. A promising direction to…
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…
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the…
This paper presents a study of robust policy networks in deep reinforcement learning. We investigate the benefits of policy parameterizations that naturally satisfy constraints on their Lipschitz bound, analyzing their empirical performance…
The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…
This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…
Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…
This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…
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…
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…