Related papers: LipBaB: Computing exact Lipschitz constant of ReLU…

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…

This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…

The threat of adversarial examples has motivated work on training certifiably robust neural networks to facilitate efficient verification of local robustness at inference time. We formalize a notion of global robustness, which captures the…

Recent studies have highlighted the potential of Lipschitz-based methods for training certifiably robust neural networks against adversarial attacks. A key challenge, supported both theoretically and empirically, is that robustness demands…

Label noise remains a critical bottleneck for the generalization of supervised deep learning models, particularly when errors are structured rather than random. Standard robust training methods often fail in the presence of such…

Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the required network complexity to ensure closed-loop performance remains a fundamental…

This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for…

Sensitivity-based robustness certification has emerged as a practical approach for certifying neural network robustness, including in settings that require verifiable guarantees. A key advantage of these methods is that certification is…

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…

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…

We initiate the study of the inherent tradeoffs between the size of a neural network and its robustness, as measured by its Lipschitz constant. We make a precise conjecture that, for any Lipschitz activation function and for most datasets,…

While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for…

We provide a new local class-purity theorem for Lipschitz continuous DNN classifiers. In addition, we discuss how to achieve classification margin for training samples. Finally, we describe how to compute margin p-values for test samples.

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of…

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset…

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural…

We present knowledge continuity, a novel definition inspired by Lipschitz continuity which aims to certify the robustness of neural networks across input domains (such as continuous and discrete domains in vision and language,…

The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work…

This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th…

Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…