Detection of adversarial examples through chaos quantification in time-series analysis

Abstract In the realm of deep learning, deep neural networks (DNNs) have recently propelled significant advancements in image classification applications. However, these DNN models are vulnerable to adversarial examples (AE), which are crafted by introducing imperceptible perturbations to legitimate samples, leading the models to make incorrect predictions. Time-series (TS) data are prevalent in real-world applications and naturally occurring phenomena. To recover and infer missing information, TS analysis has been extensively explored as a foundational research problem. The introduction of imperceptible perturbations induces irregularities in TS, resulting in chaotic behavior. Chaos, marked by a lack of organization and structure, is expected to play diverse functional roles in dynamical systems when analyzed through TS. By applying chaos theory to TS analysis, we aim to identify chaotic behavior to detect the subtle input perturbations added by the adversarial attacks. Chaos theory faces significant challenges when applied to the analysis or computation of chaotic systems due to the minimal and subtle nature of the perturbations introduced by adversarial attacks. Nonetheless, detecting chaos amidst adversarial perturbations is crucial for defending against such attacks. In this paper, we utilize features derived from ordinal patterns (OP) through TS analysis to detect the presence or absence of chaos, even under sophisticated attack methods. As an initial application of our pipeline, we exploit the edge-preserving capabilities of the guided filter (GF) and the spatial proximity properties of the Hilbert space-filling curve (HSFC) to represent the TS of input images. Experimental results show that our proposed method effectively identifies adversarial perturbations across various attacks on diverse datasets, including MNIST, Fashion-MNIST (FMNIST), CIFAR-10 and CIFAR-100.