### Robust Detection of Adversarial Attacks by Modeling the Intrinsic Properties of Deep Neural Networks

It has been shown that deep neural network (DNN) based classifiers are vulnerable to human-imperceptive adversarial perturbations which can cause DNN classifiers to output wrong predictions with high confidence. We propose an unsupervised learning approach to detect adversarial inputs without any knowledge of attackers. Our approach tries to capture the intrinsic properties of a DNN classifier and uses them to detect adversarial inputs. The intrinsic properties used in this study are the output distributions of the hidden neurons in a DNN classifier presented with natural images. Our approach can be easily applied to any DNN classifiers or combined with other defense strategies to improve robustness. Experimental results show that our approach demonstrates state-of-the-art robustness in defending black-box and gray-box attacks.

### Robust Detection of Adversarial Attacks by Modeling the Intrinsic Properties of Deep Neural Networks

It has been shown that deep neural network (DNN) based classifiers are vulnerable to human-imperceptive adversarial perturbations which can cause DNN classifiers to output wrong predictions with high confidence. We propose an unsupervised learning approach to detect adversarial inputs without any knowledge of attackers. Our approach tries to capture the intrinsic properties of a DNN classifier and uses them to detect adversarial inputs. The intrinsic properties used in this study are the output distributions of the hidden neurons in a DNN classifier presented with natural images. Our approach can be easily applied to any DNN classifiers or combined with other defense strategies to improve robustness. Experimental results show that our approach demonstrates state-of-the-art robustness in defending black-box and gray-box attacks.

### Lower bounds on the robustness to adversarial perturbations

The input-output mappings learned by state-of-the-art neural networks are significantly discontinuous.It is possible to cause a neural network used for image recognition to misclassify its input by applying very specific, hardly perceptible perturbations to the input, called adversarial perturbations. Many hypotheses have been proposed to explain the existence of these peculiar samples as well as several methods to mitigate them, but a proven explanation remains elusive. In this work, we take steps towards a formal characterization of adversarial perturbations by deriving lower bounds on the magnitudes of perturbations necessary to change the classification of neural networks. The proposed bounds can be computed efficiently, requiring time at most linear in the number of parameters and hyperparameters of the model for any given sample. This makes them suitable for use in model selection, when one wishes to find out which of several proposed classifiers is most robust to adversarial perturbations. They may also be used as a basis for developing techniques to increase the robustness of classifiers, since they enjoy the theoretical guarantee that no adversarial perturbation could possibly be any smaller than the quantities provided by the bounds. We experimentally verify the bounds on the MNIST and CIFAR-10 data sets and find no violations. Additionally, the experimental results suggest that very small adversarial perturbations may occur with nonzero probability on natural samples.

### Enhancing ML Robustness Using Physical-World Constraints

Recent advances in Machine Learning (ML) have demonstrated that neural networks can exceed human performance in many tasks. While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs -an input that is similar'' to the original input, but misclassified by the model. Existing defenses focus on Lp-norm bounded adversaries that perturb ML inputs in the digital space. In the real world, however, attackers can generate adversarial perturbations that have a large Lp-norm in the digital space. Additionally, these defenses also come at a cost to accuracy, making their applicability questionable in the real world. To defend models against such a powerful adversary, we leverage one constraint on its power: the perturbation should not change the human's perception of the physical information; the physical world places some constraints on the space of possible attacks. Two questions follow: how to extract and model these constraints? and how to design a classification paradigm that leverages these constraints to improve robustness accuracy trade-off? We observe that an ML model is typically a part of a larger system with access to different input modalities. Utilizing these modalities, we introduce invariants that limit the attacker's action space. We design a hierarchical classification paradigm that enforces these invariants at inference time. As a case study, we implement and evaluate our proposal in the context of the real-world application of road sign classification because of its applicability to autonomous driving. With access to different input modalities, such as LiDAR, camera, and location we show how to extract invariants and develop a hierarchical classifier. Our results on the KITTI and GTSRB datasets show that we can improve the robustness against physical attacks at minimal harm to accuracy.

### Reject Illegal Inputs with Generative Classifier Derived from Any Discriminative Classifier

Generative classifiers have been shown promising to detect illegal inputs including adversarial examples and out-of-distribution samples. Supervised Deep Infomax~(SDIM) is a scalable end-to-end framework to learn generative classifiers. In this paper, we propose a modification of SDIM termed SDIM-\emph{logit}. Instead of training generative classifier from scratch, SDIM-\emph{logit} first takes as input the logits produced any given discriminative classifier, and generate logit representations; then a generative classifier is derived by imposing statistical constraints on logit representations. SDIM-\emph{logit} could inherit the performance of the discriminative classifier without loss. SDIM-\emph{logit} incurs a negligible number of additional parameters, and can be efficiently trained with base classifiers fixed. We perform \emph{classification with rejection}, where test samples whose class conditionals are smaller than pre-chosen thresholds will be rejected without predictions. Experiments on illegal inputs, including adversarial examples, samples with common corruptions, and out-of-distribution~(OOD) samples show that allowed to reject a portion of test samples, SDIM-\emph{logit} significantly improves the performance on the left test sets.