Brain Programming is Immune to Adversarial Attacks: Towards Accurate and Robust Image Classification using Symbolic Learning

Abstract: In recent years, the security concerns about the vulnerability of Deep Convolutional Neural Networks (DCNN) to Adversarial Attacks (AA) in the form of small modifications to the input image almost invisible to human vision make their predictions untrustworthy. Therefore, it is necessary to provide robustness to adversarial examples in addition to an accurate score when developing a new classifier. In this work, we perform a comparative study of the effects of AA on the complex problem of art media categorization, which involves a sophisticated analysis of features to classify a fine collection of artworks. We tested a prevailing bag of visual words approach from computer vision, four state-of-the-art DCNN models (AlexNet, VGG, ResNet, ResNet101), and the Brain Programming (BP) algorithm. In this study, we analyze the algorithms' performance using accuracy. Besides, we use the accuracy ratio between adversarial examples and clean images to measure robustness. Moreover, we propose a statistical analysis of each classifier's predictions' confidence to corroborate the results. We confirm that BP predictions' change was below 2\% using adversarial examples computed with the fast gradient sign method. Also, considering the multiple pixel attack, BP obtained four out of seven classes without changes and the rest with a maximum error of 4\% in the predictions. Finally, BP also gets four categories using adversarial patches without changes and for the remaining three classes with a variation of 1\%. Additionally, the statistical analysis showed that the predictions' confidence of BP were not significantly different for each pair of clean and perturbed images in every experiment. These results prove BP's robustness against adversarial examples compared to DCNN and handcrafted features methods, whose performance on the art media classification was compromised with the proposed perturbations.