Unreasonable Effectiveness of Last Hidden Layer Activations for Adversarial Robustness

TL;DR

This paper demonstrates that using high-temperature activation functions in the output layer of DNNs can significantly improve adversarial robustness by nullifying gradients, thus hindering gradient-based attack methods.

Contribution

The study introduces a novel approach of applying high-temperature activation functions at the output layer to enhance adversarial robustness, supported by mathematical analysis and empirical validation.

Findings

High-temperature activations reduce gradients, preventing gradient-based attacks.

The approach improves robustness on MNIST and CIFAR10 datasets.

Enhanced non-linearity offers additional defense against certain attacks.

Abstract

In standard Deep Neural Network (DNN) based classifiers, the general convention is to omit the activation function in the last (output) layer and directly apply the softmax function on the logits to get the probability scores of each class. In this type of architectures, the loss value of the classifier against any output class is directly proportional to the difference between the final probability score and the label value of the associated class. Standard White-box adversarial evasion attacks, whether targeted or untargeted, mainly try to exploit the gradient of the model loss function to craft adversarial samples and fool the model. In this study, we show both mathematically and experimentally that using some widely known activation functions in the output layer of the model with high temperature values has the effect of zeroing out the gradients for both targeted and untargeted attack cases, preventing attackers from exploiting the model's loss function to craft adversarial samples. We've experimentally verified the efficacy of our approach on MNIST (Digit), CIFAR10 datasets. Detailed experiments confirmed that our approach substantially improves robustness against gradient-based targeted and untargeted attack threats. And, we showed that the increased non-linearity at the output layer has some additional benefits against some other attack methods like Deepfool attack.