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We propose a principled framework that combines adversarial training and provable robustness verification for training certifiably robust neural networks. We formulate the training problem as a joint optimization problem with both empirical…
Local robustness verification can verify that a neural network is robust wrt. any perturbation to a specific input within a certain distance. We call this distance Robustness Radius. We observe that the robustness radii of correctly…
Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We…
Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees.…
The success of neural networks across most machine learning tasks and the persistence of adversarial examples have made the verification of such models an important quest. Several techniques have been successfully developed to verify…
For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial…
We propose a method to learn deep ReLU-based classifiers that are provably robust against norm-bounded adversarial perturbations on the training data. For previously unseen examples, the approach is guaranteed to detect all adversarial…
In the past two decades we have seen the popularity of neural networks increase in conjunction with their classification accuracy. Parallel to this, we have also witnessed how fragile the very same prediction models are: tiny perturbations…
While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are…
Recent work has demonstrated that deep neural networks are vulnerable to adversarial examples---inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings…
Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness…
Formal verification provides critical security assurances for neural networks, yet its practical application suffers from the long verification time. This work introduces a novel method for training verification-friendly neural networks,…
This paper proposes a new algorithmic framework, predictor-verifier training, to train neural networks that are verifiable, i.e., networks that provably satisfy some desired input-output properties. The key idea is to simultaneously train…
We focus on the robustness of neural networks for classification. To permit a fair comparison between methods to achieve robustness, we first introduce a standard based on the mensuration of a classifier's degradation. Then, we propose…
With the proliferation of Deep Machine Learning into real-life applications, a particular property of this technology has been brought to attention: robustness Neural Networks notoriously present low robustness and can be highly sensitive…
Reinforcement learning often uses neural networks to solve complex control tasks. However, neural networks are sensitive to input perturbations, which makes their deployment in safety-critical environments challenging. This work lifts…
Deep neural networks have proven remarkably effective at solving many classification problems, but have been criticized recently for two major weaknesses: the reasons behind their predictions are uninterpretable, and the predictions…
Neural Networks (NNs) are vulnerable to adversarial examples. Such inputs differ only slightly from their benign counterparts yet provoke misclassifications of the attacked NNs. The required perturbations to craft the examples are often…
We give a formal verification procedure that decides whether a classifier ensemble is robust against arbitrary randomized attacks. Such attacks consist of a set of deterministic attacks and a distribution over this set. The…