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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 develop a new regularizer that is both more efficient than existing certified defenses, requiring only one additional forward propagation through a network, and can be used to train networks with similar certified accuracy. Through experiments on MNIST and CIFAR-10 we demonstrate improvements in training speed and comparable certified accuracy compared to state-of-the-art certified defenses.
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Modern neural networks have the capacity to overfit noisy labels frequently found in real-world datasets. Although great progress has been made, existing techniques are limited in providing theoretical guarantees for the performance of the neural networks trained with noisy labels. Here we propose a novel approach with strong theoretical guarantees for robust training of deep networks trained with noisy labels. The key idea behind our method is to select weighted subsets (coresets) of clean data points that provide an approximately low-rank Jacobian matrix. We then prove that gradient descent applied to the subsets do not overfit the noisy labels. Our extensive experiments corroborate our theory and demonstrate that deep networks trained on our subsets achieve a significantly superior performance compared to state-of-the art, e.g., 6% increase in accuracy on CIFAR-10 with 80% noisy labels, and 7% increase in accuracy on mini Webvision.
Metric learning is an important family of algorithms for classification and similarity search, but the robustness of learned metrics against small adversarial perturbations is less studied. In this paper, we show that existing metric learning algorithms, which focus on boosting the clean accuracy, can result in metrics that are less robust than the Euclidean distance. To overcome this problem, we propose a novel metric learning algorithm to find a Mahalanobis distance that is robust against adversarial perturbations, and the robustness of the resulting model is certifiable. Experimental results show that the proposed metric learning algorithm improves both certified robust errors and empirical robust errors (errors under adversarial attacks). Furthermore, unlike neural network defenses which usually encounter a trade-off between clean and robust errors, our method does not sacrifice clean errors compared with previous metric learning methods. Our code is available at https://github.com/wangwllu/provably_robust_metric_learning.
Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications. However, despite GNNs impressive performance, it has been observed that carefully crafted perturbations on graph structures (or nodes attributes) lead them to make wrong predictions. Presence of these adversarial examples raises serious security concerns. Most of the existing robust GNN design/training methods are only applicable to white-box settings where model parameters are known and gradient based methods can be used by performing convex relaxation of the discrete graph domain. More importantly, these methods are not efficient and scalable which make them infeasible in time sensitive tasks and massive graph datasets. To overcome these limitations, we propose a general framework which leverages the greedy search algorithms and zeroth-order methods to obtain robust GNNs in a generic and an efficient manner. On several applications, we show that the proposed techniques are significantly less computationally expensive and, in some cases, more robust than the state-of-the-art methods making them suitable to large-scale problems which were out of the reach of traditional robust training methods.
Differentially private stochastic gradient descent (DPSGD) is a variation of stochastic gradient descent based on the Differential Privacy (DP) paradigm which can mitigate privacy threats arising from the presence of sensitive information in training data. One major drawback of training deep neural networks with DPSGD is a reduction in the models accuracy. In this paper, we propose an alternative method for preserving data privacy based on introducing noise through learnable probability distributions, which leads to a significant improvement in the utility of the resulting private models. We also demonstrate that normalization layers have a large beneficial impact on the performance of deep neural networks with noisy parameters. In particular, we show that contrary to general belief, a large amount of random noise can be added to the weights of neural networks without harming the performance, once the networks are augmented with normalization layers. We hypothesize that this robustness is a consequence of the scale invariance property of normalization operators. Building on these observations, we propose a new algorithmic technique for training deep neural networks under very low privacy budgets by sampling weights from Gaussian distributions and utilizing batch or layer normalization techniques to prevent performance degradation. Our method outperforms previous approaches, including DPSGD, by a substantial margin on a comprehensive set of experiments on Computer Vision and Natural Language Processing tasks. In particular, we obtain a 20 percent accuracy improvement over DPSGD on the MNIST and CIFAR10 datasets with DP-privacy budgets of $varepsilon = 0.05$ and $varepsilon = 2.0$, respectively. Our code is available online: https://github.com/uds-lsv/SIDP.
We show new connections between adversarial learning and explainability for deep neural networks (DNNs). One form of explanation of the output of a neural network model in terms of its input features, is a vector of feature-attributions. Two desirable characteristics of an attribution-based explanation are: (1) $textit{sparseness}$: the attributions of irrelevant or weakly relevant features should be negligible, thus resulting in $textit{concise}$ explanations in terms of the significant features, and (2) $textit{stability}$: it should not vary significantly within a small local neighborhood of the input. Our first contribution is a theoretical exploration of how these two properties (when using attributions based on Integrated Gradients, or IG) are related to adversarial training, for a class of 1-layer networks (which includes logistic regression models for binary and multi-class classification); for these networks we show that (a) adversarial training using an $ell_infty$-bounded adversary produces models with sparse attribution vectors, and (b) natural model-training while encouraging stable explanations (via an extra term in the loss function), is equivalent to adversarial training. Our second contribution is an empirical verification of phenomenon (a), which we show, somewhat surprisingly, occurs $textit{not only}$ $textit{in 1-layer networks}$, $textit{but also DNNs}$ $textit{trained on }$ $textit{standard image datasets}$, and extends beyond IG-based attributions, to those based on DeepSHAP: adversarial training with $ell_infty$-bounded perturbations yields significantly sparser attribution vectors, with little degradation in performance on natural test data, compared to natural training. Moreover, the sparseness of the attribution vectors is significantly better than that achievable via $ell_1$-regularized natural training.
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