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Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent…
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples. Thus, considerable effort has been invested into…
Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To…
Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on a wide range of tasks. However, recent studies have shown that DNNs are vulnerable to adversarial attacks, which have brought great concerns when…
We introduce a new framework for the exact point-wise $\ell_p$ robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation…
It is known that deep neural networks (DNNs) classify an input image by paying particular attention to certain specific pixels; a graphical representation of the magnitude of attention to each pixel is called a saliency-map. Saliency-maps…
In this paper we criticize the robustness measure traditionally employed to assess the performance of machine learning models deployed in adversarial settings. To mitigate the limitations of robustness, we introduce a new measure called…
In recent years numerous methods have been developed to formally verify the robustness of deep neural networks (DNNs). Though the proposed techniques are effective in providing mathematical guarantees about the DNNs behavior, it is not…
Deep neural networks are known to be overconfident when applied to out-of-distribution (OOD) inputs which clearly do not belong to any class. This is a problem in safety-critical applications since a reliable assessment of the uncertainty…
As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case…
With the rise of deep neural networks, the challenge of explaining the predictions of these networks has become increasingly recognized. While many methods for explaining the decisions of deep neural networks exist, there is currently no…
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts,…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…
Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing…
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths…
The study of proper rational mappings between balls in complex Euclidean spaces naturally leads to the relationship between the degree and imbedding dimension of such a mapping. The special case for monomial mappings is equivalent to the…
CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is an Extreme Value Theory (EVT) based robustness score for large-scale deep neural networks (DNNs). In this paper, we propose two extensions on this robustness score. First, we…
In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform…
We investigate the problems and challenges of evaluating the robustness of Differential Equation-based (DE) networks against synthetic distribution shifts. We propose a novel and simple accuracy metric which can be used to evaluate…
Deep neural networks (DNNs) are known to be vulnerable to adversarial geometric transformation. This paper aims to verify the robustness of large-scale DNNs against the combination of multiple geometric transformations with a provable…