Related papers: Training robust neural networks using Lipschitz bo…

Modern neural networks are expected to simultaneously satisfy a host of desirable properties: accurate fitting to training data, generalization to unseen inputs, parameter and computational efficiency, and robustness to adversarial…

Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees.…

Modern deep neural network (DNN) trainings utilize various training techniques, e.g., nonlinear activation functions, batch normalization, skip-connections, etc. Despite their effectiveness, it is still mysterious how they help accelerate…

The Jacobian matrix (or the gradient for single-output networks) is directly related to many important properties of neural networks, such as the function landscape, stationary points, (local) Lipschitz constants and robustness to…

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

Modern multimodal systems deployed in industrial and safety-critical environments must remain reliable under partial sensor failures, signal degradation, or cross-modal inconsistencies. This work introduces a mathematically grounded…

Adversarial training is widely used to improve the robustness of deep neural networks to adversarial attack. However, adversarial training is prone to overfitting, and the cause is far from clear. This work sheds light on the mechanisms…

A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed…

This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…

Regularizing the input gradient has shown to be effective in promoting the robustness of neural networks. The regularization of the input's Hessian is therefore a natural next step. A key challenge here is the computational complexity.…

Despite the high performance achieved by deep neural networks on various tasks, extensive studies have demonstrated that small tweaks in the input could fail the model predictions. This issue of deep neural networks has led to a number of…

A new approach for robust Hinfty filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of…

As NLP models achieved state-of-the-art performances over benchmarks and gained wide applications, it has been increasingly important to ensure the safe deployment of these models in the real world, e.g., making sure the models are robust…

The monotonic dependence of the outputs of a neural network on some of its inputs is a crucial inductive bias in many scenarios where domain knowledge dictates such behavior. This is especially important for interpretability and fairness…

Performance of trained neural network (NN) models, in terms of testing accuracy, has improved remarkably over the past several years, especially with the advent of deep learning. However, even the most accurate NNs can be biased toward a…

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we…

Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…

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…

Motivated by the fragility of neural network (NN) controllers in safety-critical applications, we present a data-driven framework for verifying the risk of stochastic dynamical systems with NN controllers. Given a stochastic control system,…

Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have…