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# Robustness of Bayesian Neural Networks to Gradient-Based Attacks

NIPS 2020, (2020)

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摘要

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian N...更多

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简介

- Adversarial attacks are small, potentially imperceptible pertubations of test inputs that can lead to catastrophic misclassifications in high-dimensional classifiers such as deep Neural Networks (NN).
- Many attack strategies are based on identifying directions of high variability in the loss function by evaluating gradients w.r.t. input points
- Since such variability can be intuitively linked to uncertainty in the prediction, Bayesian Neural Networks (BNNs) [27] have been recently suggested as a more robust deep learning paradigm, a claim that has found some empirical support [15, 16, 3, 22].
- Neither the source of this robustness, nor its general applicability are well understood mathematically

重点内容

- Adversarial attacks are small, potentially imperceptible pertubations of test inputs that can lead to catastrophic misclassifications in high-dimensional classifiers such as deep Neural Networks (NN)
- In Section 5.1, we experimentally verify the validity of the zero-averaging property of gradients implied by Theorem 1, and discuss its implications on the behaviours of Fast Gradient Sign Method (FGSM) and Projected Gradient Descent method (PGD) attacks on Bayesian Neural Networks (BNNs) in Section 5.2
- Details on the experimental settings and BNN training parameters can be find in the Supplementary Material
- We investigate the vanishing behavior of input gradients - established by Theorem 1 for the thermodynamic limit regime - in the finite, practical settings, that is with a finite number of training data and with finite-width BNNs
- We look at an array of more than 1000 different BNN architectures trained with Hamiltonian Monte Carlo (HMC) and Variational Inference (VI) on MNIST and Fashion-MNIST. We experimentally evaluate their accuracy/robustness trade-off on FGSM attacks as compared to that obtained with deterministic NNs trained via Stochastic Gradient Descent (SGD) based methods
- We believe that the fact that Bayesian ensembles of NNs can evade a broad class of adversarial attacks will be of great relevance

方法

- BNNs that utilise pointwise uncertainty have been introduced in [21, 15, 30]
- Most of these approaches have largely relied on Monte Carlo dropout as a posterior inference [11].
- Bayesian inference combines likelihood and prior via Bayes theorem to obtain a posterior measure on the space of weights p (w|D) ∝ p (D|w) p (w)

结果

- The authors empirically investigate the theoretical findings on different BNNs. The authors train a variety of BNNs on the MNIST and Fashion MNIST [37] datasets, and evaluate their posterior distributions using HMC and VI approximate inference methods.
- In Section 5.3 the authors analyse the relationship between robustness and accuracy on thousands of different NN architectures, comparing the results obtained by Bayesian and by deterministic training.
- Details on the experimental settings and BNN training parameters can be find in the Supplementary Material

结论

- The quest for robust, data-driven models is an essential component towards the construction of AI-based technologies
- In this respect, the authors believe that the fact that Bayesian ensembles of NNs can evade a broad class of adversarial attacks will be of great relevance.
- While in the hands cheaper approximations such as VI enjoyed a degree of adversarial robustness, albeit reduced, there are no guarantees that this will hold in general
- To this end, the authors hope that this result will spark renewed interest in the pursuit of efficient Bayesian inference algorithms.
- Evaluating the robustness of BNNs against these attacks would be interesting

- Table1: Table 1
- Table2: Hyperparameters for training BNNs using HMC in Figures 2 and 3
- Table3: Hyperparameters for training BNNs using VI in Figures 2 and 3
- Table4: Hyperparameters for training BNNs with HMC in Figure 4. * indicates the parameters used in Table 1 of the main text
- Table5: Hyperparameters for training BNNs with SGD in Figure 4. * indicates the parameters used in Table 1 of the main text
- Table6: Hyperparameters for training BNNs with SGD in Figure 4

相关工作

**Related Work The robustess of**

BNNs to adversarial examples has been already observed by Gal and Smith [16], Bekasov and Murray [3]. In particular, in [3] the authors define Bayesian adversarial spheres and empirically show that, for BNNs trained with HMC, adversarial examples tend to have high uncertanity, while in [16] sufficient conditions for idealised BNNs to avoid adversarial examples are derived. However, it is unclear how such conditions could be checked in practice, as it would require one to check that the BNN architecture is invariant under all the symmetries of the data.

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