Finding the proper depth d of a graph convolutional network (GCN) that provides strong representation ability has drawn significant attention, yet nonetheless largely remains an open problem for the graph learning community. Although noteworthy progress has been made, the depth or the number of layers of a corresponding GCN is realized by a series of graph convolution operations, which naturally makes da positive integer (d N+). An interesting question is whether breaking the constraint of N+ by making d a real number (d R) can bring new insights into graph learning mechanisms. In this work, by redefining GCN's depth d as a trainable parameter continuously adjustable within (,+), we open a new door of controlling its signal processing capability to model graph homophily/heterophily (nodes with similar/dissimilar labels/attributes tend to be inter-connected). A simple and powerful GCN model TEDGCN, is proposed to retain the simplicity of GCN and meanwhile automatically search for the optimal d without the prior knowledge regarding whether the input graph is homophilic or heterophilic. Negative-valued dintrinsically enables high-pass frequency filtering functionality via augmented topology for graph heterophily. Extensive experiments demonstrate the superiority of TEDGCN on node classification tasks for a variety of homophilic and heterophilic graphs.

Pre-training on time series poses a unique challenge due to the potential mismatch between pre-training and target domains, such as shifts in temporal dynamics, fast-evolving trends, and long-range and short-cyclic effects, which can lead to poor downstream performance. While domain adaptation methods can mitigate these shifts, most methods need examples directly from the target domain, making them suboptimal for pre-training. To address this challenge, methods need to accommodate target domains with different temporal dynamics and be capable of doing so without seeing any target examples during pre-training. Relative to other modalities, in time series, we expect that time-based and frequencybased representations of the same example are located close together in the timefrequency space. To this end, we posit that time-frequency consistency (TF-C) -- embedding a time-based neighborhood of an example close to its frequency-based neighborhood -- is desirable for pre-training. Motivated by TF-C, we define a decomposable pre-training model, where the self-supervised signal is provided by the distance between time and frequency components, each individually trained by contrastive estimation. We evaluate the new method on eight datasets, including electrodiagnostic testing, human activity recognition, mechanical fault detection, and physical status monitoring. Experiments against eight state-of-the-art methods show that TF-C outperforms baselines by 15.4% (F1 score) on average in one-toone settings (e.g., fine-tuning an EEG-pretrained model on EMG data) and by 8.4% (precision) in challenging one-to-many settings (e.g., fine-tuning an EEG-pretrained model for either hand-gesture recognition or mechanical fault prediction), reflecting the breadth of scenarios that arise in real-world applications.

Then we give more experimental results on CIFAR-100 and stability analysis of Shapley value (Appendix B). Finally, we add properties of the Shapley value and proof of decomposition of CNNs in frequency domain (Appendix D). In this section, we introduce the details of the Shapley value sampling. A.1 Details of the Model for the Shapley Value Sampling We sample the Shapley value for models trained on CIFAR10, CIFAR100 and ImageNet. For CIFAR10 and CIFAR100, we employ ResNet-18 and train them ourselves.

The existence of adversarial examples poses concerns for the robustness of convolutional neural networks (CNN), for which a popular hypothesis is about the frequency bias phenomenon: CNNs rely more on high-frequency components (HFC) for classification than humans, which causes the brittleness of CNNs. However, most previous works manually select and roughly divide the image frequency spectrum and conduct qualitative analysis. In this work, we introduce Shapley value, a metric of cooperative game theory, into the frequency domain and propose to quantify the positive (negative) impact of every frequency component of data on CNNs. Based on the Shapley value, we quantify the impact in a fine-grained way and show intriguing instance disparity. Statistically, we investigate adversarial training(AT) and the adversarial attack in the frequency domain. The observations motivate us to perform an in-depth analysis and lead to multiple novel hypotheses about i) the cause of adversarial robustness of the AT model; ii) the fairness problem of AT between different classes in the same dataset; iii) the attack bias on different frequency components. Finally, we propose a Shapley-value guided data augmentation technique for improving the robustness. Experimental results on image classification benchmarks show its effectiveness. The code for this paper is at https://github.com/Ytchen981/CSA

Generating synthetic fake faces, known as pseudo-fake faces, is an effective way to improve the generalization of DeepFake detection. Existing methods typically generate these faces by blending real or fake faces in spatial domain. While these methods have shown promise, they overlook the simulation of frequency distribution in pseudo-fake faces, limiting the learning of generic forgery traces in-depth. To address this, this paper introduces {\em FreqBlender}, a new method that can generate pseudo-fake faces by blending frequency knowledge. Concretely, we investigate the major frequency components and propose a Frequency Parsing Network to adaptively partition frequency components related to forgery traces. Then we blend this frequency knowledge from fake faces into real faces to generate pseudo-fake faces. Since there is no ground truth for frequency components, we describe a dedicated training strategy by leveraging the inner correlations among different frequency knowledge to instruct the learning process. Experimental results demonstrate the effectiveness of our method in enhancing DeepFake detection, making it a potential plug-and-play strategy for other methods.

A widely discussed hypothesis regarding the cause of visual models' lack of robustness is that they can exploit human-imperceptible high-frequency components