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Title: Stochastic Quantized Activation: To prevent Overfitting in Fast Adversarial Training

Paper content:
Existing neural networks are vulnerable to "adversarial examples"---created by adding maliciously designed small perturbations in inputs to induce a misclassification by the networks.
The most investigated defense strategy is adversarial training which augments training data with adversarial examples.
However, applying single-step adversaries in adversarial training does not support the robustness of the networks, instead, they will even make the networks to be overfitted.
In contrast to the single-step, multi-step training results in the state-of-the-art performance on MNIST and CIFAR10, yet it needs a massive amount of time.
Therefore, we propose a method, Stochastic Quantized Activation (SQA) that solves overfitting problems in single-step adversarial training and fastly achieves the robustness comparable to the multi-step.
SQA attenuates the adversarial effects by providing random selectivity to activation functions and allows the network to learn robustness with only single-step training.
Throughout the experiment, our method demonstrates the state-of-the-art robustness against one of the strongest white-box attacks as PGD training, but with much less computational cost.
Finally, we visualize the learning process of the network with SQA to handle strong adversaries, which is different from existing methods.
As Convolutional Neural Networks (CNNs) stand out as a solution to many real world computer vision tasks BID17 BID0 BID18 BID20 , achieving a certain level of robustness has become indispensable for security-sensitive systems, such as autonomous driving, robot vision, and identity authentication.
However, recent studies BID26 BID10 have shown that the existing CNNs are vulnerable to small perturbations of the input that are intentionally or adversarially designed to fool the system.
The adversarial attack is a serious problem since these maliciously designed attacks have shown effective in physical world scenarios, where inputs are obtained from signals of cameras and other sensors BID15 BID8 .
Another disconcerting feature about adversarial examples is their transferability across different models BID26 BID23 BID21 ) that enables black-box attacks.
In other words, adversarial examples can be designed from a different model without having the information about the target network.The most studied defense strategy against adversarial attacks is adversarial training BID10 BID16 BID28 BID22 , which increases robustness by augmenting training data with adversarial examples.
Since adversarial training requires the model to train adversarial examples in addition to training data, the model consumes extra time to learn features of the examples via fine-tuning.
Even though the model is trained on more examples, it still might be defenseless to new examples generated by different attack due to the overfitting problem.
Recently, BID22 have found that adversarial training on examples created via gradient descent with random restarts, Projected Gradient Descent (PGD) training, results in a universally and partially unbreakable model on MNIST and CIFAR-10.
This method shows the state-of-the-art performance on MNIST and CIFAR-10 to the best of our knowledge, but the examples are created iteratively and the time increases proportionally to the number of steps.
For instance, in our CIFAR-10 training, FGSM training on ResNet18 took less than 2 hours for 30 epochs; however, PGD training took about 30 hours for the same epochs.
Thus, it is essential to find the universal method that is resistant against all of the attacks, with less computational cost.Since high dimensional representations of the neural networks give extreme complexity to the boundary of trained manifolds BID27 BID7 , we start from the idea that is to reduce degrees of freedom available to the adversary.
In this sense, we propose a Stochastic Quantized Activation (SQA) that provides stochastic randomness to the output of an original activation and reduces the opportunity for the attacker to make adversaries.
The best advantage of SQA is that SQA with fast adversarial training, training with only FGSM examples, allows the model to have robustness comparable to PGD training with less computational cost.
In particular, although SQA is one of the obfuscated gradients defined by BID1 , iterative optimization-based methods does not successfully circumvent our defense.
Besides, SQA can be combined with any deep learning models with a few lines of code but guarantees a certain level of robustness against adversarial attacks.In this paper, we first explain existing methods for adversarial attacks and defenses we refer in Section 2.
We separate the existing defense strategies into two categories and analyze the strengths and weaknesses.
In Section 3, we introduce the procedure of SQA, with an algorithm described in 1.
In Section 4, we show our experimental results on MNIST and CIFAR-10 and compare with existing defense systems.
Lastly, we visualize the penultimate layer of our networks and compare how SQA with fast adversarial training, learns differently from the existing methods.
Section 5 concludes the work and contributions of this paper are as follows:• We propose a Stochastic Quantized Activation (SQA) which achieves a significant level of robustness combined with FGSM training, comparable to state-of-the-art PGD adversarial training with much less computational cost.•
Due to the efficiency and the flexibility of the proposed method, it can be fastly and widely applied to any existing deep neural networks and combine with other types of defense strategies.•
We analytically demonstrate how SQA makes the model robust against adversaries in highlevel and low-level by using t-SNE, and plotting activation maps.
In this paper, we have found that SQA, a stochastic quantization in an activation function, make existing neural networks prevent overfitting to FGSM training.
It provides stochastic randomness in quantization to learn a robust decision boundary against adversarial attacks with FGSM training.
Our method not only shows dramatic improvements against one of the strongest white-box attacks, comparable to state-of-the-art PGD training but also significantly reduces the computational cost.
Throughout visualizing the penultimate layers of our network, we demonstrate that the network learns strong adversaries without overfitting.
We expect that SQA could be fastly and widely applied to other defense strategies because of its efficiency and flexibility.
In the future work, we plan to experiment on large scale image datasets.

assistant: text: This paper proposes Stochastic Quantized Activation that solves overfitting problems in FGSM adversarial training and fastly achieves the robustness comparable to multi-step training.