Spectral Analysis of Hard-Constraint PINNs: The Spatial Modulation Mechanism of Boundary Functions

Physics-Informed Neural Networks with hard constraints (HC-PINNs) are increasingly favored for their ability to strictly enforce boundary conditions via a trial function ansatz $\tilde{u} = A + B \cdot N$, yet the theoretical mechanisms governing their training dynamics have remained unexplored. Unlike soft-constrained formulations where boundary terms act as additive penalties, this work reveals that the boundary function $B$ introduces a multiplicative spatial modulation that fundamentally alters the learning landscape. A rigorous Neural Tangent Kernel (NTK) framework for HC-PINNs is established, deriving the explicit kernel composition law. This relationship demonstrates that the boundary function $B(\vec{x})$ functions as a spectral filter, reshaping the eigenspectrum of the neural network's native kernel. Through spectral analysis, the effective rank of the residual kernel is identified as a deterministic predictor of training convergence, superior to classical condition numbers. It is shown that widely used boundary functions can inadvertently induce spectral collapse, leading to optimization stagnation despite exact boundary satisfaction. Validated across multi-dimensional benchmarks, this framework transforms the design of boundary functions from a heuristic choice into a principled spectral optimization problem, providing a solid theoretical foundation for geometric hard constraints in scientific machine learning.

GAT-COBO: Cost-Sensitive Graph Neural Network for Telecom Fraud Detection

Along with the rapid evolution of mobile communication technologies, such as 5G, there has been a drastically increase in telecom fraud, which significantly dissipates individual fortune and social wealth. In recent years, graph mining techniques are gradually becoming a mainstream solution for detecting telecom fraud. However, the graph imbalance problem, caused by the Pareto principle, brings severe challenges to graph data mining. This is a new and challenging problem, but little previous work has been noticed. In this paper, we propose a Graph ATtention network with COst-sensitive BOosting (GAT-COBO) for the graph imbalance problem. First, we design a GAT-based base classifier to learn the embeddings of all nodes in the graph. Then, we feed the embeddings into a well-designed cost-sensitive learner for imbalanced learning. Next, we update the weights according to the misclassification cost to make the model focus more on the minority class. Finally, we sum the node embeddings obtained by multiple cost-sensitive learners to obtain a comprehensive node representation, which is used for the downstream anomaly detection task. Extensive experiments on two real-world telecom fraud detection datasets demonstrate that our proposed method is effective for the graph imbalance problem, outperforming the state-of-the-art GNNs and GNN-based fraud detectors. In addition, our model is also helpful for solving the widespread over-smoothing problem in GNNs. The GAT-COBO code and datasets are available at https://github.com/xxhu94/GAT-COBO.

Cost Sensitive GNN-based Imbalanced Learning for Mobile Social Network Fraud Detection

With the rapid development of mobile networks, the people's social contacts have been considerably facilitated. However, the rise of mobile social network fraud upon those networks, has caused a great deal of distress, in case of depleting personal and social wealth, then potentially doing significant economic harm. To detect fraudulent users, call detail record (CDR) data, which portrays the social behavior of users in mobile networks, has been widely utilized. But the imbalance problem in the aforementioned data, which could severely hinder the effectiveness of fraud detectors based on graph neural networks(GNN), has hardly been addressed in previous work. In this paper, we are going to present a novel Cost-Sensitive Graph Neural Network (CSGNN) by creatively combining cost-sensitive learning and graph neural networks. We conduct extensive experiments on two open-source realworld mobile network fraud datasets. The results show that CSGNN can effectively solve the graph imbalance problem and then achieve better detection performance than the state-of-the-art algorithms. We believe that our research can be applied to solve the graph imbalance problems in other fields. The CSGNN code and datasets are publicly available at https://github.com/xxhu94/CSGNN.

CubemapSLAM: A Piecewise-Pinhole Monocular Fisheye SLAM System

We present a real-time feature-based SLAM (Simultaneous Localization and Mapping) system for fisheye cameras featured by a large field-of-view (FoV). Large FoV cameras are beneficial for large-scale outdoor SLAM applications, because they increase visual overlap between consecutive frames and capture more pixels belonging to the static parts of the environment. However, current feature-based SLAM systems such as PTAM and ORB-SLAM limit their camera model to pinhole only. To compensate for the vacancy, we propose a novel SLAM system with the cubemap model that utilizes the full FoV without introducing distortion from the fisheye lens, which greatly benefits the feature matching pipeline. In the initialization and point triangulation stages, we adopt a unified vector-based representation to efficiently handle matches across multiple faces, and based on this representation we propose and analyze a novel inlier checking metric. In the optimization stage, we design and test a novel multi-pinhole reprojection error metric that outperforms other metrics by a large margin. We evaluate our system comprehensively on a public dataset as well as a self-collected dataset that contains real-world challenging sequences. The results suggest that our system is more robust and accurate than other feature-based fisheye SLAM approaches. The CubemapSLAM system has been released into the public domain.