Enhancing Adversarial Robustness via Test-time Transformation Ensembling

Deep learning models are prone to being fooled by imperceptible perturbations known as adversarial attacks. In this work, we study how equipping models with Test-time Transformation Ensembling (TTE) can work as a reliable defense against such attacks. While transforming the input data, both at train and test times, is known to enhance model performance, its effects on adversarial robustness have not been studied. Here, we present a comprehensive empirical study of the impact of TTE, in the form of widely-used image transforms, on adversarial robustness. We show that TTE consistently improves model robustness against a variety of powerful attacks without any need for re-training, and that this improvement comes at virtually no trade-off with accuracy on clean samples. Finally, we show that the benefits of TTE transfer even to the certified robustness domain, in which TTE provides sizable and consistent improvements.

ANCER: Anisotropic Certification via Sample-wise Volume Maximization

Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification, which has the advantage of yielding certificates that can be easily compared among isotropic methods via $\ell_p$-norm radius. However, isotropic certification limits the region that can be certified around an input to worst-case adversaries, i.e., it cannot reason about other "close", potentially large, constant prediction safe regions. To alleviate this issue, (i) we theoretically extend the isotropic randomized smoothing $\ell_1$ and $\ell_2$ certificates to their generalized anisotropic counterparts following a simplified analysis. Moreover, (ii) we propose evaluation metrics allowing for the comparison of general certificates - a certificate is superior to another if it certifies a superset region - with the quantification of each certificate through the volume of the certified region. We introduce ANCER, a practical framework for obtaining anisotropic certificates for a given test set sample via volume maximization. Our empirical results demonstrate that ANCER achieves state-of-the-art $\ell_1$ and $\ell_2$ certified accuracy on both CIFAR-10 and ImageNet at multiple radii, while certifying substantially larger regions in terms of volume, thus highlighting the benefits of moving away from isotropic analysis. Code used in our experiments is available in https://github.com/MotasemAlfarra/ANCER.

DeformRS: Certifying Input Deformations with Randomized Smoothing

Deep neural networks are vulnerable to input deformations in the form of vector fields of pixel displacements and to other parameterized geometric deformations e.g. translations, rotations, etc. Current input deformation certification methods either (i) do not scale to deep networks on large input datasets, or (ii) can only certify a specific class of deformations, e.g. only rotations. We reformulate certification in randomized smoothing setting for both general vector field and parameterized deformations and propose DeformRS-VF and DeformRS-Par, respectively. Our new formulation scales to large networks on large input datasets. For instance, DeformRS-Par certifies rich deformations, covering translations, rotations, scaling, affine deformations, and other visually aligned deformations such as ones parameterized by Discrete-Cosine-Transform basis. Extensive experiments on MNIST, CIFAR10 and ImageNet show that DeformRS-Par outperforms existing state-of-the-art in certified accuracy, e.g. improved certified accuracy of 6% against perturbed rotations in the set [-10,10] degrees on ImageNet.

Combating Adversaries with Anti-Adversaries

Deep neural networks are vulnerable to small input perturbations known as adversarial attacks. Inspired by the fact that these adversaries are constructed by iteratively minimizing the confidence of a network for the true class label, we propose the anti-adversary layer, aimed at countering this effect. In particular, our layer generates an input perturbation in the opposite direction of the adversarial one, and feeds the classifier a perturbed version of the input. Our approach is training-free and theoretically supported. We verify the effectiveness of our approach by combining our layer with both nominally and robustly trained models, and conduct large scale experiments from black-box to adaptive attacks on CIFAR10, CIFAR100 and ImageNet. Our anti-adversary layer significantly enhances model robustness while coming at no cost on clean accuracy.

Data Dependent Randomized Smoothing

Randomized smoothing is a recent technique that achieves state-of-art performance in training certifiably robust deep neural networks. While the smoothing family of distributions is often connected to the choice of the norm used for certification, the parameters of the distributions are always set as global hyper parameters independent of the input data on which a network is certified. In this work, we revisit Gaussian randomized smoothing where we show that the variance of the Gaussian distribution can be optimized at each input so as to maximize the certification radius for the construction of the smoothed classifier. This new approach is generic, parameter-free, and easy to implement. In fact, we show that our data dependent framework can be seamlessly incorporated into 3 randomized smoothing approaches, leading to consistent improved certified accuracy. When this framework is used in the training routine of these approaches followed by a data dependent certification, we get 9% and 6% improvement over the certified accuracy of the strongest baseline for a radius of 0.5 on CIFAR10 and ImageNet, respectively.

ClusTR: Clustering Training for Robustness

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 correlate with human perception. Inspired by this connection from robustness to semantics, we study the complementary connection: from semantics to robustness. To do so, we provide a tight robustness certificate for distance-based classification models (clustering-based classifiers), which we leverage to propose ClusTR (Clustering Training for Robustness), a clustering-based and adversary-free training framework to learn robust models. Interestingly, ClusTR outperforms adversarially-trained networks by up to 4\% under strong PGD attacks. Moreover, it can be equipped with simple and fast adversarial training to improve the current state-of-the-art in robustness by 16\%-29\% on CIFAR10, SVHN, and CIFAR100.

ClustTR: Clustering Training for Robustness

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 correlate with human perception. Inspired by this connection from robustness to semantics, we study the complementary connection: from semantics to robustness. To do so, we provide a tight robustness certificate for distance-based classification models (clustering-based classifiers), which we leverage to propose \emph{ClusTR} (Clustering Training for Robustness), a clustering-based and adversary-free training framework to learn robust models. Interestingly, \textit{ClusTR} outperforms adversarially-trained networks by up to $4\%$ under strong PGD attacks. Moreover, it can be equipped with simple and fast adversarial training to improve the current state-of-the-art in robustness by $16\%$-$29\%$ on CIFAR10, SVHN, and CIFAR100.

Adaptive Learning of the Optimal Mini-Batch Size of SGD

Recent advances in the theoretical understandingof SGD (Qian et al., 2019) led to a formula for the optimal mini-batch size minimizing the number of effective data passes, i.e., the number of iterations times the mini-batch size. However, this formula is of no practical value as it depends on the knowledge of the variance of the stochastic gradients evaluated at the optimum. In this paper we design a practical SGD method capable of learning the optimal mini-batch size adaptively throughout its iterations. Our method does this provably, and in our experiments with synthetic and real data robustly exhibits nearly optimal behaviour; that is, it works as if the optimal mini-batch size was known a-priori. Further, we generalize our method to several new mini-batch strategies not considered in the literature before, including a sampling suitable for distributed implementations.

On the Decision Boundaries of Deep Neural Networks: A Tropical Geometry Perspective

This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations. We use tropical geometry, a new development in the area of algebraic geometry, to characterize the decision boundaries of a simple neural network of the form (Affine, ReLU, Affine). Our main finding is that the decision boundaries are a subset of a tropical hypersurface, which is intimately related to a polytope formed by the convex hull of two zonotopes. The generators of these zonotopes are functions of the neural network parameters. This geometric characterization provides new perspective to three tasks. Specifically, we propose a new tropical perspective to the lottery ticket hypothesis, where we see the effect of different initializations on the tropical geometric representation of a network's decision boundaries. Moreover, we use this characterization to propose a new set of tropical regularizers, which directly deal with the decision boundaries of a network. We investigate the use of these regularizers in neural network pruning (by removing network parameters that do not contribute to the tropical geometric representation of the decision boundaries) and in generating adversarial input attacks (by producing input perturbations that explicitly perturb the decision boundaries' geometry and ultimately change the network's prediction).