Related papers: Demystifying Lipschitz verification: positive matr…

The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on…

Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…

The success of deep learning relies on the availability of large-scale annotated data sets, the acquisition of which can be costly, requiring expert domain knowledge. Semi-supervised learning (SSL) mitigates this challenge by exploiting the…

The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network. We introduce a semidefinite programming hierarchy to…

Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…

To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving…

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…

Neural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods…

This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…

Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…

Semidefinite programming (SDP) relaxation has emerged as a promising approach for neural network verification, offering tighter bounds than other convex relaxation methods for deep neural networks (DNNs) with ReLU activations. However, we…

The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum…

Recent research has revealed that high compression of Deep Neural Networks (DNNs), e.g., massive pruning of the weight matrix of a DNN, leads to a severe drop in accuracy and susceptibility to adversarial attacks. Integration of network…

Feature attributions are a popular tool for explaining the behavior of Deep Neural Networks (DNNs), but have recently been shown to be vulnerable to attacks that produce divergent explanations for nearby inputs. This lack of robustness is…

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…

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…

Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising…