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Register a new userAdversarial Examples in Multi-Layer Random ReLU Networks
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Added by
Yeshwanth Cherapanamjeri
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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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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.
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.
We present a mechanism for detecting adversarial examples based on data representations taken from the hidden layers of the target network. For this purpose, we train individual autoencoders at intermediate layers of the target network. This allows us to describe the manifold of true data and, in consequence, decide whether a given example has the same characteristics as true data. It also gives us insight into the behavior of adversarial examples and their flow through the layers of a deep neural network. Experimental results show that our method outperforms the state of the art in supervised and unsupervised settings.
We consider the dynamic of gradient descent for learning a two-layer neural network. We assume the input $xinmathbb{R}^d$ is drawn from a Gaussian distribution and the label of $x$ satisfies $f^{star}(x) = a^{top}|W^{star}x|$, where $ainmathbb{R}^d$ is a nonnegative vector and $W^{star} inmathbb{R}^{dtimes d}$ is an orthonormal matrix. We show that an over-parametrized two-layer neural network with ReLU activation, trained by gradient descent from random initialization, can provably learn the ground truth network with population loss at most $o(1/d)$ in polynomial time with polynomial samples. On the other hand, we prove that any kernel method, including Neural Tangent Kernel, with a polynomial number of samples in $d$, has population loss at least $Omega(1 / d)$.
We introduce two challenging datasets that reliably cause machine learning model performance to substantially degrade. The datasets are collected with a simple adversarial filtration technique to create datasets with limited spurious cues. Our datasets real-world, unmodified examples transfer to various unseen models reliably, demonstrating that computer vision models have shared weaknesses. The first dataset is called ImageNet-A and is like the ImageNet test set, but it is far more challenging for existing models. We also curate an adversarial out-of-distribution detection dataset called ImageNet-O, which is the first out-of-distribution detection dataset created for ImageNet models. On ImageNet-A a DenseNet-121 obtains around 2% accuracy, an accuracy drop of approximately 90%, and its out-of-distribution detection performance on ImageNet-O is near random chance levels. We find that existing data augmentation techniques hardly boost performance, and using other public training datasets provides improvements that are limited. However, we find that improvements to computer vision architectures provide a promising path towards robust models.
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