Predicting the future popularity of information in online social networks is a crucial yet challenging task, due to the complex spatiotemporal dynamics underlying information diffusion. Existing methods typically use structural or sequential patterns within the observation window as direct inputs for subsequent popularity prediction. However, most approaches lack the ability to explicitly model the overall trend of popularity up to the prediction time, which leads to limited predictive capability. To address these limitations, we propose VNOIP, a novel method based on variational neural Ordinary Differential Equations (ODEs) for information popularity prediction. Specifically, VNOIP introduces bidirectional jump ODEs with attention mechanisms to capture long-range dependencies and bidirectional context within cascade sequences. Furthermore, by jointly considering both cascade patterns and overall trend temporal patterns, VNOIP explicitly models the continuous-time dynamics of popularity trend trajectories with variational neural ODEs. Additionally, a knowledge distillation loss is employed to align the evolution of prior and posterior latent variables. Extensive experiments on real-world datasets demonstrate that VNOIP is highly competitive in both prediction accuracy and efficiency compared to state-of-the-art baselines.

Source localization has attracted increasing attention in recent years due to its vital role in governing the harmful propagation. However, existing localization methods do not fully consider the temporal characteristics in propagation and struggle to leverage the continuous-time information of real-world propagation scenarios. Moreover, the aggregation ability of GNN based localization models is limited by the structural noise commonly present in complicated real-world topologies. To address these challenges, a Spectral Neural Ordinary Differential Equation (SNODE) is proposed to infer the source in real-world continuous-time scenarios. First, the forward propagation is formulated as a flow based ODE system, and the source localization problem is transformed into an inverse ODE modeling task. Second, a neural process based on a graph variational autoencoder is introduced to encode global latent propagation patterns as a conditioning variable for the ODE system. Third, a spectral graph optimization is performed to suppress topological noise by filtering out high-frequency components that degrade the quality of graph aggregation in the neural process. Comprehensive experiments demonstrate that SNODE not only outperforms the optimal baseline in real-world continuous-time propagation scenarios with an average performance improvement of 43.8%, but also achieves consistently superior performance in synthetic discrete-time datasets with an improvement of 4.5%, highlighting its strong generalization ability in different propagation settings. Our code is available at https://github.com/cgao-comp/SNODE.

Diffusion probabilistic models (DPMs) have recently demonstrated impressive generative capabilities. There is emerging evidence that their sample reconstruction ability can yield meaningful representations for recognition tasks. In this paper, we demonstrate that the objectives underlying generation and representation learning are not perfectly aligned. Through a spectral analysis, we find that minimizing the mean squared error (MSE) between the original graph and its reconstructed counterpart does not necessarily optimize representations for downstream tasks. Instead, focusing on reconstructing a small subset of features, specifically those capturing global information, proves to be more effective for learning powerful representations. Motivated by these insights, we propose a novel framework, the Smooth Diffusion Model for Graphs (SDMG), which introduces a multi-scale smoothing loss and low-frequency information encoders to promote the recovery of global, low-frequency details, while suppressing irrelevant high-frequency noise. Extensive experiments validate the effectiveness of our method, suggesting a promising direction for advancing diffusion models in graph representation learning.

Graph generation is essential in social network analysis, particularly for modeling information flow and user interactions. However, existing probabilistic diffusion models face challenges when applied to social propagation graphs. The continuous noise does not apply to the discrete nature of graph generation tasks, and the random Gaussian initialization in the reverse process can introduce biases that deviate from real-world propagation patterns. To address these issues, this paper introduces a Prior-based Discrete Diffusion Model (PDDM) for social graph generation. PDDM redefines the forward process as a discrete process for node denoising and edge generation, and the task of the denoising module is transformed into the connection probability learning of node-level tasks. Further, PDDM employs a new starting point of the reverse process by incorporating user similarity as the probability matrix, which can better leverage the social context. These developments mitigate reverse-starting bias and enhance model robustness. Moreover, PDDM integrates lightweight deep graph networks such as GAT, demonstrating both scalability and applicability to graph generation scenarios. Comprehensive experiments on real-world social network datasets demonstrate PDDM’s superiority in terms of the MMD metric and downstream tasks. The code is available at https://github.com/cgao-comp/PDDM.

Source localization has been widely studied in recent years due to its crucial role in controlling the spread of harmful information. Existing methods only achieve satisfactory performance within a specific propagation model, which restricts their applicability and generalizability across different scenarios. To address this, we propose a Generalized Diffusion Framework for Source Localization (GDFSL), which enhances probabilistic diffusion models to flexibly capture the underlying dynamics of various propagation scenarios. By redefining the forward diffusion process, GDFSL ensures convergence to a real distribution of infected states that accurately represents the targeted dynamics, enabling the model to learn unbiased noise in a self-supervised manner that encodes fine-grained propagation characteristics. A closed-form reverse diffusion process is then derived to trace the propagation back to the source. The process does not rely on an explicit source label term, facilitating direct inference of sources from observed data. Experimental results show that GDFSL outperforms SOTA methods in various propagation models, particularly in scenarios where historical training data is limited or unavailable. The code is available at https://github.com/cgao-comp/GDFSL.

With the rapid development of AI large model technology, large language models (LLMs) provide a new solution for source localization tasks due to the deep linguistic understanding and generation capabilities. However, it is difficult to understand complex propagation patterns and network structures when LLMs are directly applied to source localization, resulting in limited accuracy of source localization. Meanwhile, the high-dimensional embedding of the textual representation introduces significant amounts of redundant features, which also reduces its efficiency in source localization task to some extent. To solve the above problems, this paper proposes a multi-modal fusion framework for rumor source localization, namely Contrastive Rumor Source Localization via LLM (CRSLL), based on the idea of contrastive learning. Specifically, the framework constructs propagation embeddings by comprehensively capturing both propagation dynamics and user profile features, adopts a contrastive learning approach to enhance the representation ability of comment embeddings of rumor cascades by differentiating them from non-rumor cascade comments, filters out invalid features through a differentiable masking strategy, and fuses comment modality embeddings with propagation embeddings through an attention mechanism, so as to better capture the multi-modal data interactions. It is worth mentioning that the framework uses LLM as a good ``advisor'' to provide a rich deep semantic representation, which improves the accuracy of rumor source localization. The code is available at https://github.com/cgao-comp/CRSLL.

Multivariate Temporal Point Processes (MTPPs) play an important role in diverse domains such as social networks and finance for predicting event sequence data. In recent years, MTPPs based on Ordinary Differential Equations (ODEs) and Stochastic Differential Equations (SDEs) have demonstrated their strong modeling capabilities. However, these models have yet to thoroughly consider the underlying relationships among different event types to enhance their modeling capacity. Therefore, this paper introduces a method that uses neural SDEs with a jump process guided by the latent graph. Firstly, our proposed method employs multi-dimensional SDEs to capture the dynamics of the intensity function for each event type. Subsequently, a latent graph structure is integrated into the jump process without any encoder, aiming to enhance the modeling and predictive capabilities for MTPPs. Theoretical analysis guarantees the existence and uniqueness of the solution for our proposed method. The experiments conducted on multiple real-world datasets show that our approaches demonstrate significant competitiveness when compared to state-of-the-art neural point processes. Meanwhile, the trainable parameters of the latent graph also improve the model interpretability without any prior knowledge. Our code is available at https://github.com/cgao-comp/LNJSDE.

Source localization based on snapshot observations has gained popularity owing to its low cost and accessibility. However, current methods do not adequately address the impact of user interaction in time-varying infection scenarios, leading to reduced accuracy in heterogeneous interaction environments. To address these issues and ensure transferability and applicability in different scenarios, this paper proposes an inductive localization framework based on sequence-to-sequence architecture, named Feature-representation-based Graph Sequential Source Identification (FGSSI). Particularly, FGSSI employs a user-feature-construction-based encoder to construct low-dimensional embeddings of each individual by evaluating their dynamic and static behavioral attributes at different timestamps. Additionally, FGSSI uses a graph-GRU based decoder with temporal attention to infer the source by incorporating graph topology information into the sequential model and handling imbalanced infection information under temporal characteristics. It is worth mentioning that FGSSI can detect sources in new scenarios without prior knowledge owing to the proposed inductive learning approach. Comprehensive experiments using SOTA methods demonstrate FGSSI's superior detection performance and transferability.

Propagation models in social networks are critical, with extensive applications across various fields and downstream tasks. However, existing propagation models are often oversimplified, scenario-specific, and lack real-world user social attributes. These limitations detaching from real-world analysis lead to inaccurate representations of the propagation process in social networks. To address these issues, we propose a User Features Attention-based DAG-Aware Variational Autoencoder (DAVA) for propagation graph generation. First, nearly 1 million pieces of user attributes data are collected. Then DAVA can integrate the analysis of propagation graph topology and corresponding user attributes as prior knowledge. By leveraging a lightweight attention-based framework and a sliding window mechanism based on BFS permutations weighted by user influence, DAVA significantly enhances the ability to generate realistic, large-scale propagation data, yielding graph scales ten times greater than those produced by existing SOTA methods. Every module of DAVA has flexibility and extension that allows for easy substitution to suit other generation tasks. Additionally, we provide a comprehensive evaluation of DAVA, one focus is the effectiveness of generated data in improving the performance of downstream tasks. During the generation process, we discover the Credibility Erosion Effect by modifying the generation rules, revealing a social phenomenon in social network propagation.

Source localization in social platforms is critical for managing and controlling the misinformation spreading. Despite all the recent advancements, existing methods do not consider the dynamic and heterogeneous propagation behaviors of users and are developed based on simulated data with strong model assumptions, limiting the application in real-world scenarios. This research addresses this limitation by presenting a novel framework for source localization, grounded in real-world propagation cascades from platforms like Weibo and Twitter. What's more, recognizing the user-driven nature of users in information spread, we systematically crawl and integrate user-specific profiles, offering a realistic understanding of user-driven propagation dynamics. In summary, by developing datasets derived from real-world propagation cascades, we set a precedent in enhancing the authenticity and practice of source identification for social media. Our comprehensive experiments not only validate the feasibility and rationale of our novel user-centric localization approaches but also emphasize the significance of considering user profiles in real-world propagation scenarios. The code is available at https://github.com/cgao-comp/NFSL.

The topology of diffusion networks plays an essential role in understanding information propagation dynamics and conducting social network analysis. However, diffusion networks are often unobservable in practical applications, leading to wide research on network inference from information cascades over the past decade. At present, novel cascades-based methods have been further developed to recover temporal dynamics and network topology by exploring the utilization of node temporal information, resulting in notable advancements. However, it requires high costs to acquire extensive temporal information, and the performance of network inference may decrease due to potential observational errors. Therefore, this paper specifically focuses on the time-independent scenario to address these limitations. Firstly, this paper models the node statuses of each diffusion process by leveraging the assumption of propagation trees based on the well-known independent cascade model. Subsequently, a gradient-based approach is developed to estimate the influences between nodes, facilitating the inference of network structure. Furthermore, this paper proposes a Monte Carlo EM-based approach to enhance the efficiency of network inference while maintaining comparable accuracy. Extensive experiments are conducted to verify the efficiency and effectiveness of our approaches on both synthetic and real-world networks.

Snapshot observation based source localization has been widely studied due to its accessibility and low cost. However, the interaction of users in existing methods does not be addressed in time-varying infection scenarios. So these methods have a decreased accuracy in heterogeneous interaction scenarios. To solve this critical issue, this paper proposes a sequence-to-sequence based localization framework called Temporal-sequence based Graph Attention Source Identification (TGASI) based on an inductive learning idea. More specifically, the encoder focuses on generating multiple features by estimating the influence probability between two users, and the decoder distinguishes the importance of prediction sources in different timestamps by a designed temporal attention mechanism. It's worth mentioning that the inductive learning idea ensures that TGASI can detect the sources in new scenarios without knowing other prior knowledge, which proves the scalability of TGASI. Comprehensive experiments with the SOTA methods demonstrate the higher detection performance and scalability in different scenarios of TGASI.

The rapid diffusion of hazardous information in large-flow-based social media causes great economic losses and potential threats to society. It is crucial to infer the inner information source as early as possible to prevent further losses. However, existing localization methods wait until all deployed sensors obtain propagation information before starting source inference within a network, and hence the best opportunity to control propagation is missed. In this paper, we propose a new localization strategy based on finite deployed sensors, named Greedy-coverage-based Rapid Source Localization (GRSL), to rapidly, flexibly and accurately infer the source in the early propagation stage of large-scale networks. There are two phases in GRSL. In the first phase, the Greedy-based Strategy (GS) greedily deploys sensors to rapidly achieve wide area coverage at a low cost. In the second phase, when a propagation event within a network is observed by a part of the sensors, the Inference Strategy (IS) with an earlier response mechanism begins executing the source inference task in an earlier small infected area. Comprehensive experiments with the SOTA methods demonstrate the superior performance and robustness of GRSL in various application scenarios.

Recently, the rapid diffusion of malicious information in online social networks causes great harm to our society. Therefore, it is of great significance to localize diffusion sources as early as possible to stem the spread of malicious information. This paper proposes a novel sensor-based method, called greedy full-order neighbor localization (denoted as GFNL), to solve this problem under a low infection propagation in line with the real world. More specifically, GFNL includes two main components, i.e., the greedy-based sensor deployment strategy (DS) and direction-path-based source estimation strategy (ES). In more detail, to ensure sensors can observe a propagation information as early as possible, a set of sensors is deployed in a network to minimize the geodesic distance (i.e., the distance of the shortest path) between the candidate set and the sensor set based on DS. Then when a fraction of sensors observe a propagation, ES infers the source based on the idea that the distance of the actual propagation path is proportional to the observed time. Compared with some state-of-the-art methods, comprehensive experiments have proved the superiority and robustness of our proposed GFNL.