Frank R. Schmidt

Eric Wong, Frank R. Schmidt, J. Zico Kolter

A rapidly growing area of work has studied the existence of adversarial examples, datapoints which have been perturbed to fool a classifier, but the vast majority of these works have focused primarily on threat models defined by $\ell_p$ norm-bounded perturbations. In this paper, we propose a new threat model for adversarial attacks based on the Wasserstein distance. In the image classification setting, such distances measure the cost of moving pixel mass, which naturally cover "standard" image manipulations such as scaling, rotation, translation, and distortion (and can potentially be applied to other settings as well). To generate Wasserstein adversarial examples, we develop a procedure for projecting onto the Wasserstein ball, based upon a modified version of the Sinkhorn iteration. The resulting algorithm can successfully attack image classification models, bringing traditional CIFAR10 models down to 3% accuracy within a Wasserstein ball with radius 0.1 (i.e., moving 10% of the image mass 1 pixel), and we demonstrate that PGD-based adversarial training can improve this adversarial accuracy to 76%. In total, this work opens up a new direction of study in adversarial robustness, more formally considering convex metrics that accurately capture the invariances that we typically believe should exist in classifiers. Code for all experiments in the paper is available at https://github.com/locuslab/projected_sinkhorn.

Eric Wong, Frank R. Schmidt, Jan Hendrik Metzen et al.

Recent work has developed methods for learning deep network classifiers that are provably robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this paper, in an effort to scale these approaches to substantially larger models, we extend previous work in three main directions. First, we present a technique for extending these training procedures to much more general networks, with skip connections (such as ResNets) and general nonlinearities; the approach is fully modular, and can be implemented automatically (analogous to automatic differentiation). Second, in the specific case of $\ell_\infty$ adversarial perturbations and networks with ReLU nonlinearities, we adopt a nonlinear random projection for training, which scales linearly in the number of hidden units (previous approaches scaled quadratically). Third, we show how to further improve robust error through cascade models. On both MNIST and CIFAR data sets, we train classifiers that improve substantially on the state of the art in provable robust adversarial error bounds: from 5.8% to 3.1% on MNIST (with $\ell_\infty$ perturbations of $ε=0.1$), and from 80% to 36.4% on CIFAR (with $\ell_\infty$ perturbations of $ε=2/255$). Code for all experiments in the paper is available at https://github.com/locuslab/convex_adversarial/.

Eric Wong, Tim Schneider, Joerg Schmitt et al.

Recent work has shown that it is possible to learn neural networks with provable guarantees on the output of the model when subject to input perturbations, however these works have focused primarily on defending against adversarial examples for image classifiers. In this paper, we study how these provable guarantees can be naturally applied to other real world settings, namely getting performance specifications for robust virtual sensors measuring fuel injection quantities within an engine. We first demonstrate that, in this setting, even simple neural network models are highly susceptible to reasonable levels of adversarial sensor noise, which are capable of increasing the mean relative error of a standard neural network from 6.6% to 43.8%. We then leverage methods for learning provably robust networks and verifying robustness properties, resulting in a robust model which we can provably guarantee has at most 16.5% mean relative error under any sensor noise. Additionally, we show how specific intervals of fuel injection quantities can be targeted to maximize robustness for certain ranges, allowing us to train a virtual sensor for fuel injection which is provably guaranteed to have at most 10.69% relative error under noise while maintaining 3% relative error on non-adversarial data within normalized fuel injection ranges of 0.6 to 1.0.

Juncheng Li, Frank R. Schmidt, J. Zico Kolter

Recent work has documented the susceptibility of deep learning systems to adversarial examples, but most such attacks directly manipulate the digital input to a classifier. Although a smaller line of work considers physical adversarial attacks, in all cases these involve manipulating the object of interest, e.g., putting a physical sticker on an object to misclassify it, or manufacturing an object specifically intended to be misclassified. In this work, we consider an alternative question: is it possible to fool deep classifiers, over all perceived objects of a certain type, by physically manipulating the camera itself? We show that by placing a carefully crafted and mainly-translucent sticker over the lens of a camera, one can create universal perturbations of the observed images that are inconspicuous, yet misclassify target objects as a different (targeted) class. To accomplish this, we propose an iterative procedure for both updating the attack perturbation (to make it adversarial for a given classifier), and the threat model itself (to ensure it is physically realizable). For example, we show that we can achieve physically-realizable attacks that fool ImageNet classifiers in a targeted fashion 49.6% of the time. This presents a new class of physically-realizable threat models to consider in the context of adversarially robust machine learning. Our demo video can be viewed at: https://youtu.be/wUVmL33Fx54

Emanuel Laude, Jan-Hendrik Lange, Jonas Schüpfer et al.

This paper introduces a novel algorithm for transductive inference in higher-order MRFs, where the unary energies are parameterized by a variable classifier. The considered task is posed as a joint optimization problem in the continuous classifier parameters and the discrete label variables. In contrast to prior approaches such as convex relaxations, we propose an advantageous decoupling of the objective function into discrete and continuous subproblems and a novel, efficient optimization method related to ADMM. This approach preserves integrality of the discrete label variables and guarantees global convergence to a critical point. We demonstrate the advantages of our approach in several experiments including video object segmentation on the DAVIS data set and interactive image segmentation.

Lena Gorelick, Ismail BenAyed, Frank R. Schmidt et al.

High-order (non-linear) functionals have become very popular in segmentation, stereo and other computer vision problems. Level sets is a well established general gradient descent framework, which is directly applicable to optimization of such functionals and widely used in practice. Recently, another general optimization approach based on trust region methodology was proposed for regional non-linear functionals. Our goal is a comprehensive experimental comparison of these two frameworks in regard to practical efficiency, robustness to parameters, and optimality. We experiment on a wide range of problems with non-linear constraints on segment volume, appearance and shape.