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Register a new userA single gradient step finds adversarial examples on random two-layers neural networks
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Added by
Gauthier Gidel
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Daniely and Schacham recently showed that gradient descent finds adversarial examples on random undercomplete two-layers ReLU neural networks. The term undercomplete refers to the fact that their proof only holds when the number of neurons is a vanishing fraction of the ambient dimension. We extend their result to the overcomplete case, where the number of neurons is larger than the dimension (yet also subexponential in the dimension). In fact we prove that a single step of gradient descent suffices. We also show this result for any subexponential width random neural network with smooth activation function.
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Adversarial examples have become one of the largest challenges that machine learning models, especially neural network classifiers, face. These adversarial examples break the assumption of attack-free scenario and fool state-of-the-art (SOTA) classifiers with insignificant perturbations to human. So far, researchers achieved great progress in utilizing adversarial training as a defense. However, the overwhelming computational cost degrades its applicability and little has been done to overcome this issue. Single-Step adversarial training methods have been proposed as computationally viable solutions, however they still fail to defend against iterative adversarial examples. In this work, we first experimentally analyze several different SOTA defense methods against adversarial examples. Then, based on observations from experiments, we propose a novel single-step adversarial training method which can defend against both single-step and iterative adversarial examples. Lastly, through extensive evaluations, we demonstrate that our proposed method outperforms the SOTA single-step and iterative adversarial training defense. Compared with ATDA (single-step method) on CIFAR10 dataset, our proposed method achieves 35.67% enhancement in test accuracy and 19.14% reduction in training time. When compared with methods that use BIM or Madry examples (iterative methods) on CIFAR10 dataset, it saves up to 76.03% in training time with less than 3.78% degeneration in test accuracy.
Adversarial examples (AEs) are images that can mislead deep neural network (DNN) classifiers via introducing slight perturbations into original images. This security vulnerability has led to vast research in recent years because it can introduce real-world threats into systems that rely on neural networks. Yet, a deep understanding of the characteristics of adversarial examples has remained elusive. We propose a new way of achieving such understanding through a recent development, namely, invertible neural models with Lipschitz continuous mapping functions from the input to the output. With the ability to invert any latent representation back to its corresponding input image, we can investigate adversarial examples at a deeper level and disentangle the adversarial examples latent representation. Given this new perspective, we propose a fast latent space adversarial example generation method that could accelerate adversarial training. Moreover, this new perspective could contribute to new ways of adversarial example detection.
Despite being popularly used in many applications, neural network models have been found to be vulnerable to adversarial examples, i.e., carefully crafted examples aiming to mislead machine learning models. Adversarial examples can pose potential risks on safety and security critical applications. However, existing defense approaches are still vulnerable to attacks, especially in a white-box attack scenario. To address this issue, we propose a new defense approach, named MulDef, based on robustness diversity. Our approach consists of (1) a general defense framework based on multiple models and (2) a technique for generating these multiple models to achieve high defense capability. In particular, given a target model, our framework includes multiple models (constructed from the target model) to form a model family. The model family is designed to achieve robustness diversity (i.e., an adversarial example successfully attacking one model cannot succeed in attacking other models in the family). At runtime, a model is randomly selected from the family to be applied on each input example. Our general framework can inspire rich future research to construct a desirable model family achieving higher robustness diversity. Our evaluation results show that MulDef (with only up to 5 models in the family) can substantially improve the target models accuracy on adversarial examples by 22-74% in a white-box attack scenario, while maintaining similar accuracy on legitimate examples.
The existence of adversarial examples underscores the importance of understanding the robustness of machine learning models. Bayesian neural networks (BNNs), due to their calibrated uncertainty, have been shown to posses favorable adversarial robustness properties. However, when approximate Bayesian inference methods are employed, the adversarial robustness of BNNs is still not well understood. In this work, we employ gradient-free optimization methods in order to find adversarial examples for BNNs. In particular, we consider genetic algorithms, surrogate models, as well as zeroth order optimization methods and adapt them to the goal of finding adversarial examples for BNNs. In an empirical evaluation on the MNIST and Fashion MNIST datasets, we show that for various approximate Bayesian inference methods the usage of gradient-free algorithms can greatly improve the rate of finding adversarial examples compared to state-of-the-art gradient-based methods.
We consider the phenomenon of adversarial examples in ReLU networks with independent gaussian parameters. For networks of constant depth and with a large range of widths (for instance, it suffices if the width of each layer is polynomial in that of any other layer), small perturbations of input vectors lead to large changes of outputs. This generalizes results of Daniely and Schacham (2020) for networks of rapidly decreasing width and of Bubeck et al (2021) for two-layer networks. The proof shows that adversarial examples arise in these networks because the functions that they compute are very close to linear. Bottleneck layers in the network play a key role: the minimal width up to some point in the network determines scales and sensitivities of mappings computed up to that point. The main result is for networks with constant depth, but we also show that some constraint on depth is necessary for a result of this kind, because there are suitably deep networks that, with constant probability, compute a function that is close to constant.
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