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.

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With distinguished performance in generating samples that resemble the observed data, diffusion models are widely used in image, video, and text synthesis nowadays. In recent years, the concept of diffusion has been extended to time-series applications, and many powerful models have been developed. Considering the deficiency of a methodical summary and discourse on these models, we provide this survey as an elementary resource for new researchers in this area and to provide inspiration to motivate future research. For better understanding, we include an introduction about the basics of diffusion models. Except for this, we primarily focus on diffusion-based methods for time-series forecasting, imputation, and generation, and present them, separately, in three individual sections. We also compare different methods for the same application and highlight their connections if applicable. Finally, we conclude with the common limitation of diffusion-based methods and highlight potential future research directions.

Graph data collected from the real world often contains noise, making it imperative to develop robust representation learning tools for graphs. While existing research has primarily focused on feature smoothing, the robustness of the underlying geometric structure is frequently overlooked. In addition, the prevalent use of the$\mathbb {L}_{2}$-norm for achieving global smoothness in graph neural networks shrinks many local characteristics, limiting their expressivity on a node's neighboring information. This paper introduces novel regularizers designed to address noise in both feature and structural aspects of graph data. We employ the alternating direction method of multipliers (ADMM) to optimize the objective function. Our proposed approach effectively prevents oversmoothing graph signal representations when applying multiple layers and ensures convergence to optimal solutions. Empirical results from our study demonstrate the superior performance of our proposedDoTover popular graph convolutions, especially in scenarios where the graph is heavily contaminated.

Recently, many works on Graph Neural Networks (GNNs) have been well developed for graph-level representation learning tasks and continuously improve graph classification accuracy. These works, however, mainly focus on the principle of different blocks of GNNs to strengthen their representation learning capability and pay less attention to the choice of a more appropriate loss function as learning objectives. In this paper, we aim to facilitate the representation learning process of any existing GNN frameworks by incorporating more task-oriented objectives. To this end, we propose approaches based on Laplacian eigenmaps to enhance the common-used cross-entropy loss, called LEELoss. Our study shows, with the property of Laplacian eigenmaps for classification problems, that utilizing the Laplacian eigenmaps as a regularizer in the original loss function can further enhance the performance of the graph-level learning tasks. Finally, via extensive experiments on popular benchmark datasets, we demonstrate that the proposed approach actually facilitates the classification performance on various GNN frameworks.