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Title: Instance adaptive adversarial training: Improved accuracy tradeoffs in neural nets

Paper content:
Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks.
Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test set.
We hypothesize that this poor generalization is a consequence of adversarial training with uniform perturbation radius around every training sample.
Samples close to decision boundary can be morphed into a different class under a small perturbation budget, and enforcing large margins around these samples produce poor decision boundaries that generalize poorly.
Motivated by this hypothesis, we propose instance adaptive adversarial training -- a technique that enforces sample-specific perturbation margins around every training sample.
We show that using our approach, test accuracy on unperturbed samples improve with a marginal drop in robustness.
Extensive experiments on CIFAR-10, CIFAR-100 and Imagenet datasets demonstrate the effectiveness of our proposed approach.
A key challenge when deploying neural networks in safety-critical applications is their poor stability to input perturbations.
Extremely tiny perturbations to network inputs may be imperceptible to the human eye, and yet cause major changes to outputs.
One of the most effective and widely used methods for hardening networks to small perturbations is "adversarial training" (Madry et al., 2018) , in which a network is trained using adversarially perturbed samples with a fixed perturbation size.
By doing so, adversarial training typically tries to enforce that the output of a neural network remains nearly constant within an p ball of every training input.
Despite its ability to increase robustness, adversarial training suffers from poor accuracy on clean (natural) test inputs.
The drop in clean accuracy can be as high as 10% on CIFAR-10, and 15% on Imagenet (Madry et al., 2018; Xie et al., 2019) , making robust models undesirable in some industrial settings.
The consistently poor performance of robust models on clean data has lead to the line of thought that there may be a fundamental trade-off between robustness and accuracy (Zhang et al., 2019; Tsipras et al., 2019) , and recent theoretical results characterized this tradeoff (Fawzi et al., 2018; Shafahi et al., 2018; Mahloujifar et al., 2019) .
In this work, we aim to understand and optimize the tradeoff between robustness and clean accuracy.
More concretely, our objective is to improve the clean accuracy of adversarial training for a chosen level of adversarial robustness.
Our method is inspired by the observation that the constraints enforced by adversarial training are infeasible; for commonly used values of , it is not possible to achieve label consistency within an -ball of each input image because the balls around images of different classes overlap.
This is illustrated on the left of Figure 1 , which shows that the -ball around a "bird" (from the CIFAR-10 training set) contains images of class "deer" (that do not appear in the training set).
If adversarial training were successful at enforcing label stability in an = 8 ball around the "bird" training image, doing so would come at the unavoidable cost of misclassifying the nearby "deer" images that come along at test time.
At the same time, when training images lie far from the decision boundary (eg., the deer image on the right in Fig 1) , it is possible to enforce stability with large with no compromise in clean accuracy.
When adversarial training on CIFAR-10, we see that = 8 is too large for some images, causing accuracy loss, while being unnecessarily small for others, leading to sub-optimal robustness.
In this work, we focus on improving the robustness-accuracy tradeoff in adversarial training.
We first show that realizable robustness is a sample-specific attribute: samples close to the decision boundary can only achieve robustness within a small ball, as they contain samples from a different class beyond this radius.
On the other hand samples far from the decision boundary can be robust on a relatively large perturbation radius.
Motivated by this observation, we develop instance adaptive adversarial training, in which label consistency constraints are imposed within sample-specific perturbation radii, which are in-turn estimated.
Our proposed algorithm has empirically been shown to improve the robustness-accuracy tradeoff in CIFAR-10, CIFAR-100 and Imagenet datasets.
A recent paper that addresses the problem of improving natural accuracy in adversarial training is mixup adversarial training (Lamb et al., 2019) , where adversarially trained models are optimized using mixup loss instead of the standard cross-entropy loss.
In this paper, natural accuracy was shown to improve with no drop in adversarial robustness.
However, the robustness experiments were not evaluated on strong attacks (experiments were reported only on PGD-20).
We compare our implementation of mixup adversarial training with IAAT on stronger attacks in Table.
8.
We observe that while natural accuracy improves for mixup, drop in adversarial accuracy is much higher than IAAT.

assistant: text: Instance adaptive adversarial training for improving robustness-accuracy tradeoff