Related papers: Reachability Analysis of Deep Neural Networks with…
Output reachability and adversarial robustness are among the most relevant safety properties of neural networks. We show that in the context of Message Passing Neural Networks (MPNN), a common Graph Neural Network (GNN) model, formal…
Model attribution is a critical component of deep neural networks (DNNs) for its interpretability to complex models. Recent studies bring up attention to the security of attribution methods as they are vulnerable to attribution attacks that…
In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral…
We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output…
This paper proposes a sensitivity analysis framework based on set valued mapping for deep neural networks (DNN) to understand and compute how the solutions (model weights) of DNN respond to perturbations in the training data. As a DNN may…
In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies…
We propose rigorous lower and upper error bounds for neural network (NN) approximations to PDEs by efficiently computing the Riesz representations of suitable extension and restrictions of the NN residual towards geometrically simpler…
This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN for a target input is…
When autonomous vehicles encounter untrained scenarios, ensuring safety hinges on effective safety verification to prevent accidents stemming from unexpected model decisions. Reachability analysis, a method of safety verification, offers…
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…
Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are…
Neural networks have recently become popular for a wide variety of uses, but have seen limited application in safety-critical domains such as robotics near and around humans. This is because it remains an open challenge to train a neural…
Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…
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…
This paper studies the approximation capacity of neural networks with an arbitrary activation function and with norm constraint on the weights. Upper and lower bounds on the approximation error of these networks are computed for smooth…
Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…
We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
This paper analyzes regularization terms proposed recently for improving the adversarial robustness of deep neural networks (DNNs), from a theoretical point of view. Specifically, we study possible connections between several effective…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…