Machine learning models are vulnerable to adversarial attacks. One approach to addressing this vulnerability is certification, which focuses on models that are guaranteed to be robust for a given perturbation size. A drawback of recent certified models is that they are stochastic: they require multiple computationally expensive model evaluations with random noise added to a given input. In our work, we present a deterministic certification approach which results in a certifiably robust model. This approach is based on an equivalence between training with a particular regularized loss, and the expected values of Gaussian averages. We achieve certified models on ImageNet-1k by retraining a model with this loss for one epoch without the use of label information.

We present a deterministic method to compute the Gaussian average of neural networks used in regression and classification. Our method is based on an equivalence between training with a particular regularized loss, and the expected values of Gaussian averages. We use this equivalence to certify models which perform well on clean data but are not robust to adversarial perturbations. In terms of certified accuracy and adversarial robustness, our method is comparable to known stochastic methods such as randomized smoothing, but requires only a single model evaluation during inference.

We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This formulation allows us to train a dual objective comprised only of the scalar potential functions, and removes the burden of explicitly computing normalizing flows during training. After training, the normalizing flow is easily recovered from the potential functions.

Deep neural networks are vulnerable to adversarial perturbations: small changes in the input easily lead to misclassification. In this work, we propose an attack methodology catered not only for cases where the perturbations are measured by $\ell_p$ norms, but in fact any adversarial dissimilarity metric with a closed proximal form. This includes, but is not limited to, $\ell_1$, $\ell_2$, $\ell_\infty$ perturbations, and the $\ell_0$ counting "norm", i.e. true sparseness. Our approach to generating perturbations is a natural extension of our recent work, the LogBarrier attack, which previously required the metric to be differentiable. We demonstrate our new algorithm, ProxLogBarrier, on the MNIST, CIFAR10, and ImageNet-1k datasets. We attack undefended and defended models, and show that our algorithm transfers to various datasets with little parameter tuning. In particular, in the $\ell_0$ case, our algorithm finds significantly smaller perturbations compared to multiple existing methods

Input gradient regularization is not thought to be an effective means for promoting adversarial robustness. In this work we revisit this regularization scheme with some new ingredients. First, we derive new per-image theoretical robustness bounds based on local gradient information, and curvature information when available. These bounds strongly motivate input gradient regularization. Second, we implement a scaleable version of input gradient regularization which avoids double backpropagation: adversarially robust ImageNet models are trained in 33 hours on four consumer grade GPUs. Finally, we show experimentally that input gradient regularization is competitive with adversarial training.

Adversarial attacks for image classification are small perturbations to images that are designed to cause misclassification by a model. Adversarial attacks formally correspond to an optimization problem: find a minimum norm image perturbation, constrained to cause misclassification. A number of effective attacks have been developed. However, to date, no gradient-based attacks have used best practices from the optimization literature to solve this constrained minimization problem. We design a new untargeted attack, based on these best practices, using the established logarithmic barrier method. On average, our attack distance is similar or better than all state-of-the-art attacks on benchmark datasets (MNIST, CIFAR10, ImageNet-1K). In addition, our method performs significantly better on the most challenging images, those which normally require larger perturbations for misclassification. We employ the LogBarrier attack on several adversarially defended models, and show that it adversarially perturbs all images more efficiently than other attacks: the distance needed to perturb all images is significantly smaller with the LogBarrier attack than with other state-of-the-art attacks.

How well can we estimate the probability that the classification, $C(f(x))$, predicted by a deep neural network is correct (or in the Top 5)? We consider the case of a classification neural network trained with the KL divergence which is assumed to generalize, as measured empirically by the test error and test loss. We present conditional probabilities for predictions based on the histogram of uncertainty metrics, which have a significant Bayes ratio. Previous work in this area includes Bayesian neural networks. Our metric is twice as predictive, based on the expected Bayes ratio, on ImageNet compared to our best tuned implementation of Bayesian dropout~\cite{gal2016dropout}. Our method uses just the softmax values and a stored histogram so it is essentially free to compute, compared to many times inference cost for Bayesian dropout.

Adversarial training is an effective method for improving robustness to adversarial attacks. We show that adversarial training using the Fast Signed Gradient Method can be interpreted as a form of regularization. We implemented a more effective form of adversarial training, which in turn can be interpreted as regularization of the loss in the 2-norm, $\|\nabla_x \ell(x)\|_2$. We obtained further improvements to adversarial robustness, as well as provable robustness guarantees, by augmenting adversarial training with Lipschitz regularization.