Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological features. In this paper, we formulates message passing as a system of hyperbolic partial differential equations (hyperbolic PDEs), constituting a dynamical system that explicitly maps node representations into a particular solution space. This solution space is spanned by a set of eigenvectors describing the topological structure of graphs. Within this system, for any moment in time, a node features can be decomposed into a superposition of the basis of eigenvectors. This not only enhances the interpretability of message passing but also enables the explicit extraction of fundamental characteristics about the topological structure. Furthermore, by solving this system of hyperbolic partial differential equations, we establish a connection with spectral graph neural networks (spectral GNNs), serving as a message passing enhancement paradigm for spectral GNNs.We further introduce polynomials to approximate arbitrary filter functions. Extensive experiments demonstrate that the paradigm of hyperbolic PDEs not only exhibits strong flexibility but also significantly enhances the performance of various spectral GNNs across diverse graph tasks.

Malware poses a significant threat to the security of cyberspace. For malware detection, utilizing machine learning or deep learning techniques to analyze API sequences has been proven to be effective. However, the existing methods fail in mitigating the interference caused by redundant information when processing excessively lengthy or behavior-masking sequences. To address this issue, we propose MalSE, a novel malware detection framework based on API call sensitivity estimation. MalSE aims to highlight key information in the sequence and minimize the interference of redundant information, thereby increasing detection performance. Firstly, MalSE uses a novel statistical-based method to annotate parameter sensitivity labels, which provide a foundation for subsequent module training. Secondly, MalSE employs a Bert-based estimator to transform the parameters into the semantic space and then predict the parameters’ sensitivities. Thirdly, MalSE assesses the sensitivity of each API call by aggregating the sensitivities of parameters, thus providing powerful features for detection tasks. Finally, MalSE employs an attention-based sequence model, which can concentrate on crucial information within the sequence to enhance the detection performance. We evaluate MalSE on 2 binary classification tasks and 1 multi-classification task. MalSE outperforms other methods across all tasks, demonstrating superior and robust detection capabilities under different scenarios.

Smart contracts control critical financial assets on blockchains, with potential weaknesses risking substantial losses. Thus, smart contract vulnerability detection is essential for maintaining blockchain ecosystem stability. Traditional methods depend extensively on expert-driven patterns, resulting in poor scalability. Although deep learning-based approaches have made significant progress, they still suffer from issues such as inflexible representations, insufficient feature modalities, and limited model capabilities. In this paper, we propose FSGDec, a novel smart contract vulnerability detection framework that fuses sequential information and structural features at the bytecode level. Firstly, an efficient node embedding method is developed for contract control flow graphs, flexibly processing node sequences and incorporating node-specific semantic information associated with weaknesses. Then, by modeling node features as time series signals, an adaptive graph wave network is introduced to automatically capture vulnerability-related structural features. Finally, a classifier is deployed to perform bug detection utilizing the extracted graph-level features that integrate semantic information. Evaluated on two real-world smart contract datasets, the experimental results demonstrate that FSGDec achieves superior performance compared to state-of-the-art baselines.

Dynamics modeling has been introduced as a novel paradigm in message passing (MP) of graph neural networks (GNNs). Existing methods consider MP between nodes as a heat diffusion process, and leverage heat equation to model the temporal evolution of nodes in the embedding space. However, heat equation can hardly depict the wave nature of graph signals in graph signal processing. Besides, heat equation is essentially a partial differential equation (PDE) involving a first partial derivative of time, whose numerical solution usually has low stability, and leads to inefficient model training. In this paper, we would like to depict more wave details in MP, since graph signals are essentially wave signals that can be seen as a superposition of a series of waves in the form of eigenvector. This motivates us to consider MP as a wave propagation process to capture the temporal evolution of wave signals in the space. Based on wave equation in physics, we innovatively develop a graph wave equation to leverage the wave propagation on graphs. In details, we demonstrate that the graph wave equation can be connected to traditional spectral GNNs, facilitating the design of graph wave networks (GWNs) based on various Laplacians and enhancing the performance of the spectral GNNs. Besides, the graph wave equation is particularly a PDE involving a second partial derivative of time, which has stronger stability on graphs than the heat equation that involves a first partial derivative of time. Additionally, we theoretically prove that the numerical solution derived from the graph wave equation are constantly stable, enabling to significantly enhance model efficiency while ensuring its performance. Extensive experiments show that GWNs achieve state-of-the-art and efficient performance on benchmark datasets, and exhibit outstanding performance in addressing challenging graph problems, such as over-smoothing and heterophily. Our code is available at https://github.com/YueAWu/Graph-Wave-Networks.

Smart contracts have been increasingly deployed and applied on various blockchain platforms. Nevertheless, vulnerabilities may cause significant financial losses due to the involvement of substantial funds in smart contracts. Traditional analysis tools heavily rely on manually predefined rules. Recent studies have demonstrated the promising potential of deep learning techniques in smart contract vulnerability detection. However, existing approaches often disregard cross-function and cross-contract vulnerability scenarios, focusing primarily on characterization or detection tasks at the function level. In this study, we propose CL-HGAN, a novel framework for smart contract vulnerability detection at the contract level. Firstly, we construct a contract-level heterogeneous graph to embody the relationships between contracts and functions. Specifically, we build the backbone of the heterogeneous graph based on the abstract syntax tree (AST) and multiple types of edges and then incorporate two additional categories of edges to augment its structural information. Subsequently, we design a two-phase feature learning method to automatically generate graph-level representations based on a heterogeneous graph attention network and meta-paths specific to the constructed graph. Finally, we employ a classifier to perform vulnerability detection tasks. In particular, the proposed CL-HGAN comprehensively captures vulnerability features and accurately identifies vulnerabilities at the contract level. Furthermore, we evaluate the CL-HGAN framework on an Ethereum smart contract dataset containing thirty types of vulnerabilities. The experimental results show that the average metrics of our approach outperform the state-of-the-art baselines.