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Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the…
Ideally, what confuses neural network should be confusing to humans. However, recent experiments have shown that small, imperceptible perturbations can change the network prediction. To address this gap in perception, we propose a novel…
Deep neural networks have achieved remarkable performance in various applications but are extremely vulnerable to adversarial perturbation. The most representative and promising methods that can enhance model robustness, such as adversarial…
This paper studies how encouraging semantically-aligned features during deep neural network training can increase network robustness. Recent works observed that Adversarial Training leads to robust models, whose learnt features appear to…
Effective regularisation of neural networks is essential to combat overfitting due to the large number of parameters involved. We present an empirical analogue to the Lipschitz constant of a feed-forward neural network, which we refer to as…
Adversarial training has been shown as an effective approach to improve the robustness of image classifiers against white-box attacks. However, its effectiveness against black-box attacks is more nuanced. In this work, we demonstrate that…
Convolutional neural networks (CNNs) are vulnerable to adversarial examples, and studies show that increasing the model capacity of an architecture topology (e.g., width expansion) can bring consistent robustness improvements. This reveals…
Deep neural networks (DNNs) are known to be vulnerable to adversarial attacks. A range of defense methods have been proposed to train adversarially robust DNNs, among which adversarial training has demonstrated promising results. However,…
There exists a vast number of adversarial attacks and defences for machine learning algorithms of various types which makes assessing the robustness of algorithms a daunting task. To make matters worse, there is an intrinsic bias in these…
For sensitive problems, such as medical imaging or fraud detection, Neural Network (NN) adoption has been slow due to concerns about their reliability, leading to a number of algorithms for explaining their decisions. NNs have also been…
Despite the tremendous success of deep neural networks across various tasks, their vulnerability to imperceptible adversarial perturbations has hindered their deployment in the real world. Recently, works on randomized ensembles have…
Improving adversarial robustness of neural networks remains a major challenge. Fundamentally, training a neural network via gradient descent is a parameter estimation problem. In adaptive control, maintaining persistency of excitation (PoE)…
Robustness to adversarial attacks was shown to require a larger model capacity, and thus a larger memory footprint. In this paper, we introduce an approach to obtain robust yet compact models by pruning randomly-initialized binary networks.…
In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of…
While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for…
Adversarial training is a powerful type of defense against adversarial examples. Previous empirical results suggest that adversarial training requires wider networks for better performances. However, it remains elusive how neural network…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
To evaluate the robustness of non-classifier models, we propose probabilistic local equivalence, based on the notion of randomized smoothing, as a way to quantitatively evaluate the robustness of an arbitrary function. In addition, to…
It has been widely recognized that adversarial examples can be easily crafted to fool deep networks, which mainly root from the locally non-linear behavior nearby input examples. Applying mixup in training provides an effective mechanism to…
Recent works show that adversarial examples exist for random neural networks [Daniely and Schacham, 2020] and that these examples can be found using a single step of gradient ascent [Bubeck et al., 2021]. In this work, we extend this line…