A significant challenge for Graph Neural Networks (GNNs) lies in accurately performing node classification tasks on heterophilous graphs. Traditional GNN models, which largely rely on the assumption of homophily, often struggle under heterophilous conditions due to the inherent low-pass filtering nature during message-passing among neighboring nodes. Motivated by these limitations, our research explores the dendritic structures found in real neurons, which dynamically amplify and inhibit signals. We demonstrate how the biophysical properties of dendrites enable GNNs to adaptively modulate the Dirichlet energy of graph representations based on the specific context, providing a theoretical justification for integrating neural dendrites into GNNs to improve learning on heterophilous graphs. In this work, we introduce the GDendrite framework, which dynamically adjusts GNN's output response to the various contexts. Our empirical studies, conducted across 13 homophilous and heterophilous benchmark datasets, show that our framework significantly enhances the performance of traditional GNNs in heterophilous settings and outperforms state-of-the-art models in most cases.

Graph Neural Networks (GNNs) have become a cornerstone in multivariate time series forecasting by addressing the challenge of modeling inter-series dependencies often overlooked by traditional temporal approaches. However, real-world temporal dependencies (inter- and intra-dependencies) are inherently intertwined, making it difficult to treat them as separate processes. Recent pure graph paradigms attempt to capture these dependencies holistically by transforming time series into fully connected graphs. While effective, these methods suffer from prohibitive computational complexity O (( NT ) 2 ), limiting their scalability for large-scale data and long-term forecasting. To address these challenges, we propose UFGTime, a novel framework that leverages spectral signals to construct a "spectral-variate graph," embedding multivariate temporal dependencies in a compact spectral representation and modeling inter- and intra-signal connections through frequency similarities. Empowered by our proposed graph framelet message-passing function, UFGTime efficiently aggregates global information, avoids over-smoothing, and achieves near-linear complexity O ( kNT ). Extensive experiments on diverse datasets demonstrate that UFG-Time consistently outperforms state-of-the-art baselines, offering a scalable, accurate, and resource-efficient pure graph solution for multivariate time series forecasting.

Anomalous node detection in a static graph faces significant challenges due to the rarity of anomalies and the substantial cost of labeling their deviant structure and attribute patterns. These challenges give rise to data-centric problems, including extremely imbalanced data distributions and intricate graph learning, which significantly impede machine learning and deep learning methods from discerning the patterns of graph anomalies with few labels. While these issues remain crucial, much of the current research focuses on addressing the induced technical challenges, treating the shortage of labeled data as a given. Distinct from previous efforts, this work focuses on tackling the data-centric problems by generating auxiliary training nodes that conform to the original graph topology and attribute distribution. We categorize this approach as data-centric, aiming to enhance existing anomaly detectors by training them on our synthetic data. However, the methods for generating nodes and the effectiveness of utilizing synthetic data for graph anomaly detection remain unexplored in the realm. To answer these questions, we thoroughly investigate the denoising diffusion model. Drawing from our observations on the diffusion process, we illuminate the shifts in graph energy distribution and establish two principles for designing denoising neural networks tailored to graph anomaly generation. From the insights, we propose a diffusion-based graph generation method to synthesize training nodes, which can be promptly integrated to work with existing anomaly detectors. The empirical results on eight widely-used datasets demonstrate our generated data can effectively enhance the nine state-of-the-art graph detectors' performance.