Despite their impressive performance in classification, neural networks are known to be vulnerable to adversarial attacks. These attacks are small perturbations of the input data designed to fool the model. Naturally, a question arises regarding the potential connection between the architecture, settings, or properties of the model and the nature of the attack. In this work, we aim to shed light on this problem by focusing on the implicit bias of the neural network, which refers to its inherent inclination to favor specific patterns or outcomes. Specifically, we investigate one aspect of the implicit bias, which involves the essential Fourier frequencies required for accurate image classification. We conduct tests to assess the statistical relationship between these frequencies and those necessary for a successful attack. To delve into this relationship, we propose a new method that can uncover non-linear correlations between sets of coordinates, which, in our case, are the aforementioned frequencies. By exploiting the entanglement between intrinsic dimension and correlation, we provide empirical evidence that the network bias in Fourier space and the target frequencies of adversarial attacks are closely tied.

Deep neural networks (DNNs) perform very well when trained on a large amount of data [1], but large SSVEP datasets are not commonly available for open use. Our way to overcome this problem was to employ data augmentation and transfer learning techniques to train the DNNs, as both are known to improve the performances of DNNs on smaller datasets [2]. We started with an open SSVEP dataset [3], which we consider to be large in comparison with other open databases. The electroencephalography (EEG) signals where transformed into images, specifically spectrograms, using the shorttime Fourier transform (STFT). By doing so, we take advantage of the ability of convolutional DNN in classifying images, which is well documented [1]. The neural network used in this study [4] is a DCNN based on the original VGG [5].