Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ polynomial approximation to construct the filters, whereas another superior option, namely ration approximation, remains underexplored. Although a handful of prior works have attempted to deploy the rational approximation, their implementations often involve intensive computational demands or still resort to polynomial approximations, hindering full potential of the rational graph filters. To address the issues, this paper introduces ERGNN, a novel spectral GNN with explicitly-optimized rational filter. ERGNN adopts a unique two-step framework that sequentially applies the numerator filter and the denominator filter to the input signals, thus streamlining the model paradigm while enabling explicit optimization of both numerator and denominator of the rational filter. Extensive experiments validate the superiority of ERGNN over state-of-the-art methods, establishing it as a practical solution for deploying rational-based GNNs.

Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by k-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility. Code is available with the Github repository: https://github.com/vasile-paskardlgm/CPF.

Spectral graph neural networks are proposed to harness spectral information inherent in graph-structured data through the application of polynomial-defined graph filters, recently achieving notable success in graph-based web applications. Existing studies reveal that various polynomial choices greatly impact spectral GNN performance, underscoring the importance of polynomial selection. However, this selection process remains a critical and unresolved challenge. Although prior work suggests a connection between the approximation capabilities of polynomials and the efficacy of spectral GNNs, there is a lack of theoretical insights into this relationship, rendering polynomial selection a largely heuristic process.

Recently, multi-layer perceptron-based implicit representations have achieved remarkable successes in hand modeling. Compared with previous explicit mesh-based representation methods, implicit methods are more compact shape representations. However, it is expensive to obtain explicit geometry surfaces from implicit functions with Marching Cubes, which limits the real-time performance in surface reconstruction applications. To explore a more effective and efficient hand representation, we present a skeleton-driven method to represent a human hand with a point cloud. To achieve this goal, we propose a Tri-Axis Modeling method to model the motion pattern of the xyz coordinate of a patch of point cloud, and an Order Encoding strategy to construct a parameter-sharing and geometry-disentangled network. These two effective strategies make our method run in real-time and has super-high fidelity close to implicit methods. Qualitative and quantitative experiments on public datasets demonstrate the efficiency, effectiveness, and robustness of our method against state-of-the-art approaches.

Multiview 3-D reconstruction holds considerable promise across a wide applications in social manufacturing. Conducting in-depth research on precise and robust multiview 3-D reconstruction holds the potential to significantly empower the domain of social manufacturing. Recently, there has been a burgeoning interest in the domain of neural implicit surfaces learning through volume rendering for the purpose of multiview reconstruction without 3-D supervision. Conventional approaches often overlook explicit multiview geometry constraints, resulting in shortcomings in generating consistent surface reconstructions and recovering fine details. To solve this, we propose geometry-guided neural implicit surface (GG-NeuS), a geometry-guided neural implicit surfaces learning method for multiview surface reconstruction. Our model places a stronger emphasis on maintaining geometry consistency, significantly enhancing the quality of reconstruction. First, we enforce multiview geometry constraints on the surface points by locating the zero-level set of signed distance function (SDF). Second, we incorporate normal cues, predicted by general-purpose monocular estimators, to substantially recover fine geometric details. Additionally, we introduce a voxel-based surface reconstruction methodology that strikes an optimal balance between training time and reconstruction quality. Through comprehensive qualitative and quantitative experiments and analyses, we demonstrate thatGG-NeuSsuccessfully reconstructs fine-grained surface details and achieves superior surface reconstruction quality than state-of-the-art approaches.

Radio resource management (RRM), which aims to satisfy the requirements of both mobile users and service providers, can be seen as one of the typical issues of cyber-physical-social system since the social factors, that is, the requirements and priorities of users are extremely important in heterogeneous networks. In this paper, we propose a novel resource allocation and access control mechanism based on parallel network architecture, which provides a high-bandwidth connectivity with guaranteed quality of service (QoS) for mobile users in a seamless manner. In this mechanism, multiple users are classified into several types according to their social property such as priorities and bandwidth requirements of different users. Compared with the general received signal strength (RSS)-based method, the proposed user priority (UP)-based method achieves three main advantages as follows: 1) it further balances the load of base stations (BSs) when the resource is sufficient; 2) it provides a mechanism called high priority users higher QoS when the network is heavily loaded compared to the RSS-based method; and 3) it hands over a few users from a heavily loaded BS to a lightly loaded one to allow more users to access this network. The simulation results confirm the advantages of the proposed UP-based mechanism and show that the simulation results of the Q-learning method are consistent with its theoretical analysis.