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Title: Calibration of neural network logit vectors to combat adversarial attacks

Paper content:
Adversarial examples remain an issue for contemporary neural networks.
This paper draws on Background Check (Perello-Nieto et al., 2016), a technique in model calibration, to assist two-class neural networks in detecting adversarial examples, using the one dimensional difference between logit values as the underlying measure.
This method interestingly tends to achieve the highest average recall on image sets that are generated with large perturbation vectors, which is unlike the existing literature on adversarial attacks (Cubuk et al., 2017).
The proposed method does not need knowledge of the attack parameters or methods at training time, unlike a great deal of the literature that uses deep learning based methods to detect adversarial examples, such as Metzen et al. (2017), imbuing the proposed method with additional flexibility.
Adversarial examples are specially crafted input instances generated by adversarial attacks.
The term was introduced by BID23 in the context of image classification.
These attacks generate, or manipulate data, to achieve poor performance when classified by neural networks, which poses existential questions about their usage in high stakes security critical applications.
Since they were introduced, there have been many papers that have introduced novel attack methods and other papers that attempt to combat those attacks.
For instance, BID5 introduces the fast gradient sign method (FGSM), and BID20 proposes a method based on modifying the gradient of the softmax function as a defence.Adversarial attacks can be identified into various classes such as white box and black box, where in the former, the attack has full knowledge of all model parameters.
Examples created by these attacks can be false positives or false negatives.
In the case of images, they can be nonsensical data (e.g. noise classified as a road sign) or clear cut (e.g. a visually clear cat, classified as a road sign).
These attacks can be non-targeted or targeted such that the classifier chooses a specific class for the adversarial example.
Various adversarial defences exist, some based on deep learning techniques and others on purely distributional techniques.
Similar work on adversarial defences has been done by BID6 , in which the network is trained on specific attack types and parameters with an additional outlier class for adversarial examples.
A multi-dimensional statistical test over the maximum mean discrepancy and the energy distance on input features is then used to classify instances as adversarial.
Other work has been done by BID0 , where Gaussian Processes are placed on top of conventional convolutional neural network architectures, with radial basis kernels, imbuing the neural network with a way of understanding its own perceptual limits.
The authors find that the network becomes more resistant to adversarial attack.
The work that follows continues in a similar vein to both of these methods.
Some methods such as BID14 use sub-units of deep learning architectures to detect adversarial instances.Calibration is a technique of converting model scores, normally, through application of a post processing function, to probability estimates.
Background Check is a method to yield probability estimates, via a set of explicit assumptions, in regions of space where no data has been observed.
In this work, Background Check is useful in producing calibrated probabilities for adversarial data that often exists in regions where no training and test data has been seen.
Reliable probability estimates can then be measured by calibration and refinement loss.
Various calibrating procedures exist such as binning, logistic regression, isotonic regression and softmax.
BID8 demonstrates the logistic function is optimal when the class-conditional densities are Gaussians with unit variance.
Softmax extends this to multi-variate Gaussian densities with unit variance.Calibration of neural network models has been performed by BID7 , using a method called Temperature Scaling, that modifies the gradient of the softmax function allowing softmax to calibrate densities with non-unit variance.
The authors perform this calibration after noticing that calibration loss for neural networks has increased in recent years.
When adversarial attacks against neural networks are brought into perspective, a problem arises for existing calibration techniques, which is the question of mapping adversarial logit scores to reliable probability estimates (which should be zero for a successful adversarial attack).
In this work, a method is demonstrated that uses Background Check to identify adversarial attacks.
A novel approach to defending neural networks against adversarial attacks has been established.
This approach intersects two previously unrelated fields of machine learning, calibration and adversarial defences, using the principles underlying Background Check.
This work demonstrates that adversarial attacks, produced as a result of large perturbations of various forms, can be detected and assigned to an adversarial class.
The larger the perturbation, the easier it was for the attacks to be detected.

assistant: text: This paper uses principles from the field of calibration in machine learning on the logits of a neural network to defend against adversarial attacks