Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are critical. However, theoretical understanding of algorithms that are robust to adversarial perturbations is limited. In this work we focus on Principal Component Analysis (PCA), a ubiquitous algorithmic primitive in machine learning. We formulate a natural robust variant of PCA where the goal is to find a low dimensional subspace to represent the given data with minimum projection error, that is in addition robust to small perturbations measured in $\ell_q$ norm (say $q=\infty$). Unlike PCA which is solvable in polynomial time, our formulation is computationally intractable to optimize as it captures a variant of the well-studied sparse PCA objective as a special case. We show the following results: -Polynomial time algorithm that is constant factor competitive in the worst-case with respect to the best subspace, in terms of the projection error and the robustness criterion. -We show that our algorithmic techniques can also be made robust to adversarial training-time perturbations, in addition to yielding representations that are robust to adversarial perturbations at test time. Specifically, we design algorithms for a strong notion of training-time perturbations, where every point is adversarially perturbed up to a specified amount. -We illustrate the broad applicability of our algorithmic techniques in addressing robustness to adversarial perturbations, both at training time and test time. In particular, our adversarially robust PCA primitive leads to computationally efficient and robust algorithms for both unsupervised and supervised learning problems such as clustering and learning adversarially robust classifiers.
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An established way to improve the transferability of black-box evasion attacks is to craft the adversarial examples on a surrogate ensemble model to increase diversity. We argue that transferability is fundamentally related to epistemic uncertainty. Based on a state-of-the-art Bayesian Deep Learning technique, we propose a new method to efficiently build a surrogate by sampling approximately from the posterior distribution of neural network weights, which represents the belief about the value of each parameter. Our extensive experiments on ImageNet and CIFAR-10 show that our approach improves the transfer rates of four state-of-the-art attacks significantly (up to 62.1 percentage points), in both intra-architecture and inter-architecture cases. On ImageNet, our approach can reach 94% of transfer rate while reducing training computations from 11.6 to 2.4 exaflops, compared to an ensemble of independently trained DNNs. Our vanilla surrogate achieves 87.5% of the time higher transferability than 3 test-time techniques designed for this purpose. Our work demonstrates that the way to train a surrogate has been overlooked although it is an important element of transfer-based attacks. We are, therefore, the first to review the effectiveness of several training methods in increasing transferability. We provide new directions to better understand the transferability phenomenon and offer a simple but strong baseline for future work.
The majority of adversarial machine learning research focuses on additive attacks, which add adversarial perturbation to input data. On the other hand, unlike image recognition problems, only a handful of attack approaches have been explored in the video domain. In this paper, we propose a novel attack method against video recognition models, Multiplicative Adversarial Videos (MultAV), which imposes perturbation on video data by multiplication. MultAV has different noise distributions to the additive counterparts and thus challenges the defense methods tailored to resisting additive adversarial attacks. Moreover, it can be generalized to not only Lp-norm attacks with a new adversary constraint called ratio bound, but also different types of physically realizable attacks. Experimental results show that the model adversarially trained against additive attack is less robust to MultAV.
In this article, we develop and analyse a new spectral method to solve the semi-classical Schr\"odinger equation based on the Gaussian wave-packet transform (GWPT) and Hagedorn's semi-classical wave-packets (HWP). The GWPT equivalently recasts the highly oscillatory wave equation as a much less oscillatory one (the $w$ equation) coupled with a set of ordinary differential equations governing the dynamics of the so-called GWPT parameters. The Hamiltonian of the $ w $ equation consists of a quadratic part and a small non-quadratic perturbation, which is of order $ \mathcal{O}(\sqrt{\varepsilon }) $, where $ \varepsilon\ll 1 $ is the rescaled Planck's constant. By expanding the solution of the $ w $ equation as a superposition of Hagedorn's wave-packets, we construct a spectral method while the $ \mathcal{O}(\sqrt{\varepsilon}) $ perturbation part is treated by the Galerkin approximation. This numerical implementation of the GWPT avoids imposing artificial boundary conditions and facilitates rigorous numerical analysis. For arbitrary dimensional cases, we establish how the error of solving the semi-classical Schr\"odinger equation with the GWPT is determined by the errors of solving the $ w $ equation and the GWPT parameters. We prove that this scheme has the spectral convergence with respect to the number of Hagedorn's wave-packets in one dimension. Extensive numerical tests are provided to demonstrate the properties of the proposed method.
We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This gives rise to a new definition of disentanglement, and to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.
Generating high-quality and interpretable adversarial examples in the text domain is a much more daunting task than it is in the image domain. This is due partly to the discrete nature of text, partly to the problem of ensuring that the adversarial examples are still probable and interpretable, and partly to the problem of maintaining label invariance under input perturbations. In order to address some of these challenges, we introduce sparse projected gradient descent (SPGD), a new approach to crafting interpretable adversarial examples for text. SPGD imposes a directional regularization constraint on input perturbations by projecting them onto the directions to nearby word embeddings with highest cosine similarities. This constraint ensures that perturbations move each word embedding in an interpretable direction (i.e., towards another nearby word embedding). Moreover, SPGD imposes a sparsity constraint on perturbations at the sentence level by ignoring word-embedding perturbations whose norms are below a certain threshold. This constraint ensures that our method changes only a few words per sequence, leading to higher quality adversarial examples. Our experiments with the IMDB movie review dataset show that the proposed SPGD method improves adversarial example interpretability and likelihood (evaluated by average per-word perplexity) compared to state-of-the-art methods, while suffering little to no loss in training performance.
Deep neural networks are susceptible to adversarial attacks. In computer vision, well-crafted perturbations to images can cause neural networks to make mistakes such as identifying a panda as a gibbon or confusing a cat with a computer. Previous adversarial examples have been designed to degrade performance of models or cause machine learning models to produce specific outputs chosen ahead of time by the attacker. We introduce adversarial attacks that instead reprogram the target model to perform a task chosen by the attacker---without the attacker needing to specify or compute the desired output for each test-time input. This attack is accomplished by optimizing for a single adversarial perturbation, of unrestricted magnitude, that can be added to all test-time inputs to a machine learning model in order to cause the model to perform a task chosen by the adversary when processing these inputs---even if the model was not trained to do this task. These perturbations can be thus considered a program for the new task. We demonstrate adversarial reprogramming on six ImageNet classification models, repurposing these models to perform a counting task, as well as two classification tasks: classification of MNIST and CIFAR-10 examples presented within the input to the ImageNet model.
Despite of the success of Generative Adversarial Networks (GANs) for image generation tasks, the trade-off between image diversity and visual quality are an well-known issue. Conventional techniques achieve either visual quality or image diversity; the improvement in one side is often the result of sacrificing the degradation in the other side. In this paper, we aim to achieve both simultaneously by improving the stability of training GANs. A key idea of the proposed approach is to implicitly regularizing the discriminator using a representative feature. For that, this representative feature is extracted from the data distribution, and then transferred to the discriminator for enforcing slow updates of the gradient. Consequently, the entire training process is stabilized because the learning curve of discriminator varies slowly. Based on extensive evaluation, we demonstrate that our approach improves the visual quality and diversity of state-of-the art GANs.
Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.
Unsupervised learning is of growing interest because it unlocks the potential held in vast amounts of unlabelled data to learn useful representations for inference. Autoencoders, a form of generative model, may be trained by learning to reconstruct unlabelled input data from a latent representation space. More robust representations may be produced by an autoencoder if it learns to recover clean input samples from corrupted ones. Representations may be further improved by introducing regularisation during training to shape the distribution of the encoded data in latent space. We suggest denoising adversarial autoencoders, which combine denoising and regularisation, shaping the distribution of latent space using adversarial training. We introduce a novel analysis that shows how denoising may be incorporated into the training and sampling of adversarial autoencoders. Experiments are performed to assess the contributions that denoising makes to the learning of representations for classification and sample synthesis. Our results suggest that autoencoders trained using a denoising criterion achieve higher classification performance, and can synthesise samples that are more consistent with the input data than those trained without a corruption process.
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for high-dimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have state-of-the-art performance and suddenly make high-dimensional robust estimation a realistic possibility.
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