Related papers: Hierarchical Verification for Adversarial Robustne…

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

A neural network consisting of piecewise affine building blocks, such as fully-connected layers and ReLU activations, is itself a piecewise affine function supported on a polyhedral complex. This complex has been previously studied to…

Formal verification of neural networks is critical for their safe adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and…

This work starts with the intention of using mathematics to understand the intriguing vulnerability observed by ~\citet{szegedy2013} within artificial neural networks. Along the way, we will develop some novel tools with applications far…

Convex relaxations have emerged as a promising approach for verifying desirable properties of neural networks like robustness to adversarial perturbations. Widely used Linear Programming (LP) relaxations only work well when networks are…

Recently, deep learning approaches have been extensively investigated to reconstruct images from accelerated magnetic resonance image (MRI) acquisition. Although these approaches provide significant performance gain compared to compressed…

The vulnerability to adversarial attacks has been a critical issue for deep neural networks. Addressing this issue requires a reliable way to evaluate the robustness of a network. Recently, several methods have been developed to compute…

The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing…

Proving local robustness is crucial to increase the reliability of neural networks. While many verifiers prove robustness in $L_\infty$ $\epsilon$-balls, very little work deals with robustness verification in $L_0$ $\epsilon$-balls,…

We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…

Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as…

Vision Transformers are being increasingly deployed in safety-critical applications that demand high reliability. It is crucial to ensure the correctness of their execution in spite of potential errors such as transient hardware errors. We…

Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper…

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification…

Recent approaches in the theoretical analysis of model-based deep learning architectures have studied the convergence of gradient descent in shallow ReLU networks that arise from generative models whose hidden layers are sparse. Motivated…

Patch robustness certification is an emerging kind of provable defense technique against adversarial patch attacks for deep learning systems. Certified detection ensures the detection of all patched harmful versions of certified samples,…

We introduce the concept of provably robust adversarial examples for deep neural networks - connected input regions constructed from standard adversarial examples which are guaranteed to be robust to a set of real-world perturbations (such…

Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…

Deep Neural Network-based systems are now the state-of-the-art in many robotics tasks, but their application in safety-critical domains remains dangerous without formal guarantees on network robustness. Small perturbations to sensor inputs…

This work introduces HyParLyVe (Hyperplane Partitioned Lyapunov Verifier), a novel algorithm for sound and complete verification of neural Lyapunov candidates by interpreting shallow ReLU networks as hyperplane arrangements. This…