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arxiv: 2605.03550 · v1 · submitted 2026-05-05 · 💻 cs.SI

Recognition: unknown

PDSL: Propagation Dynamics Aware Framework for Source Localization

Yansong Wang , Qisen Chai , Longlong Lin , Tao Jia
Authors on Pith no claims yet

Pith reviewed 2026-05-07 12:41 UTC · model grok-4.3

classification 💻 cs.SI
keywords source localizationpropagation dynamicsgraph neural ODEsdeep generative modelsinformation diffusionnetwork analysisstochastic processescontinuous dynamics
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The pith

Modeling continuous diffusion dynamics with graph neural differential equations allows generative models to locate propagation sources despite random spreading.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to solve source localization by directly addressing the randomness in how information or influence travels through networks, rather than treating spreads as fixed once the network structure is known. Existing generative approaches map observed results back to sources mainly via topology but leave out the extra uncertainty created by stochastic diffusion steps. PDSL combines a deep generative model with continuous-time modeling to generate a distribution over possible sources while accounting for that randomness. Graph Neural Ordinary Differential Equations serve as the tool to evolve the process forward in continuous time without assuming any particular diffusion rule in advance. A separate matching step pulls in relevant historical blocks to make the generated sources more consistent with the observed outcome.

Core claim

PDSL integrates a deep generative model with propagation dynamics to approximate the source distribution and explicitly mitigate uncertainty arising from diffusion stochasticity. Graph Neural Ordinary Differential Equations model the continuous dynamics of diffusion processes without relying on a predefined diffusion mechanism. A matching mechanism extracts relevant data blocks that enhance source generation reliability. Experiments on synthetic and real-world diffusion datasets show superior performance across diverse scenarios.

What carries the argument

Graph Neural Ordinary Differential Equations that evolve node states continuously over time, paired with a deep generative model that outputs a distribution over candidate sources and a matching mechanism that selects supporting data blocks.

If this is right

  • Source localization becomes feasible in settings where the underlying spreading rule is unknown or changes over time.
  • The framework produces a full distribution over possible sources instead of a single point estimate, quantifying remaining uncertainty.
  • Performance gains appear on both synthetic graphs with controlled randomness and real diffusion traces from social or information networks.
  • The matching mechanism increases consistency between generated sources and observed propagation patterns.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same continuous modeling step could be reused for related inverse tasks such as identifying the start of an epidemic from partial case reports.
  • If the ODE component generalizes, the approach might support online source tracking as new observations arrive incrementally.
  • Applications in misinformation tracing on platforms could benefit from the reduced reliance on hand-crafted diffusion assumptions.

Load-bearing premise

Graph neural differential equations can capture the random fluctuations of spreading processes well enough to improve source estimates even when no fixed diffusion rule is supplied.

What would settle it

If the method shows no accuracy gain over topology-only generative baselines on multiple high-stochasticity datasets where spreading variance is independently measured and large, the benefit of adding continuous dynamics modeling would be refuted.

Figures

Figures reproduced from arXiv: 2605.03550 by Longlong Lin, Qisen Chai, Tao Jia, Yansong Wang.

Figure 1
Figure 1. Figure 1: Different source nodes leading to the same propagation result. view at source ↗
Figure 2
Figure 2. Figure 2: The architectural overview of our framework. During the training phase, the proposed framework takes graph topology view at source ↗
Figure 3
Figure 3. Figure 3: An illustration of the VAE variant. samples, often a consequence of noise introduction, CVAE [71] employs additional conditionality for conditional gen￾eration. With this idea, we design a VAE variant that uses propagation dynamics as encoding and generation conditions. As illustrated in view at source ↗
Figure 2
Figure 2. Figure 2: Algorithm 2 Inference Phase Require: propagation dynamics: Yt ∈ R (T −1)×n, propagation result: YT ∈ R n, adjacency matrix of graph G: A ∈ R n×n, parameters: θ, ϕ, ψ, learning rate: α Ensure: predicted source vector: sˆ ∈ R n 1: sb ← Div(YT (train), YT (test)) ▷ Identify similar batch 2: Sampling latent variables z ▷ ¯ Equation(15) 3: se ∗ ← fϕ(Yt, A, z¯) ▷ Generate an initial source se ∗ 4: for each epoch… view at source ↗
Figure 4
Figure 4. Figure 4: The performance with different snapshot vectors under the SI diffusion mechanism. view at source ↗
Figure 5
Figure 5. Figure 5: The performance with different time step sizes under the SI diffusion view at source ↗
Figure 6
Figure 6. Figure 6: Visualizations of Jazz dataset for all methods and the ground truth. The correctly predicted sources are marked in blue, while the incorrectly predicted view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of runtime and F1-score performance on CollegeMsg (SI view at source ↗
read the original abstract

Source localization is a representative inverse inference task in information propagation, aiming to identify the source node or node set that triggers the propagation results based on the observed information. A primary challenge is quantifying the inherent uncertainty between observed outcomes and potential sources. Although deep generative models have partially mitigated this issue, most existing approaches primarily focus on uncertainty induced by network topology, attempting to learn a direct mapping from propagation outcomes to sources based on network structure, while overlooking the additional uncertainty stemming from the highly stochastic nature of the propagation process. To address this limitation, we propose a Propagation Dynamics aware framework for Source Localization (PDSL), a novel method that integrates a deep generative model with propagation dynamics to approximate the source distribution and explicitly mitigate uncertainty arising from diffusion stochasticity. Moreover, we employ Graph Neural Ordinary Differential Equations to model the continuous dynamics of diffusion processes without relying on a predefined diffusion mechanism. Additionally, a matching mechanism is designed to extract relevant data blocks that enhance source generation reliability. Comprehensive experiments on both synthetic and real-world diffusion datasets demonstrate the superior performance of the proposed framework across diverse application scenarios.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes PDSL, a Propagation Dynamics aware framework for Source Localization that integrates a deep generative model with Graph Neural Ordinary Differential Equations (GNN-ODEs) to model continuous diffusion dynamics without predefined mechanisms such as Independent Cascade or Linear Threshold. It introduces a matching mechanism to extract relevant data blocks and mitigate uncertainty arising from the stochastic nature of propagation, with the goal of better approximating the source distribution. Experiments on synthetic and real-world diffusion datasets are reported to demonstrate superior performance across application scenarios.

Significance. If the technical claims are substantiated, the work could advance source localization by explicitly incorporating propagation dynamics via continuous ODE modeling rather than relying solely on topology-based mappings, addressing a gap in prior deep generative approaches. The parameter-free modeling of dynamics and the matching mechanism offer potential for improved generalizability if they demonstrably capture stochastic effects.

major comments (2)
  1. [Proposed Method] The core claim that GNN-ODEs model continuous dynamics without a predefined diffusion mechanism while mitigating uncertainty from propagation stochasticity is load-bearing. Standard GNN-ODE formulations integrate deterministic vector fields via message passing, yielding a single trajectory for given initial conditions. The manuscript must specify (in the methods description of the GNN-ODE component and its integration with the generative model) how stochasticity is injected—e.g., via explicit noise, SDE extensions, or variational sampling over trajectories—otherwise the approach risks approximating only mean behavior rather than the required posterior over sources.
  2. [Proposed Method] The matching mechanism is described as enhancing source generation reliability by extracting relevant data blocks, but its interaction with the GNN-ODE dynamics and generative model is not shown to be sufficient for recovering variance in the source distribution. A concrete derivation or ablation showing how this block interacts with the ODE integration to address stochasticity (rather than just topology uncertainty) is needed to support the central claim.
minor comments (2)
  1. [Abstract] The abstract is dense and would benefit from explicit separation of the three main contributions (generative model + dynamics, GNN-ODE formulation, matching mechanism) for improved readability.
  2. [Experiments] Ensure that all performance claims in the experiments section are accompanied by quantitative metrics, baseline comparisons, and error bars or statistical tests, as these are referenced but not visible in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback, which highlights important aspects of our proposed framework that require further clarification. We address each major comment below and will revise the manuscript to strengthen the presentation of the technical details.

read point-by-point responses

  1. Referee: [Proposed Method] The core claim that GNN-ODEs model continuous dynamics without a predefined diffusion mechanism while mitigating uncertainty from propagation stochasticity is load-bearing. Standard GNN-ODE formulations integrate deterministic vector fields via message passing, yielding a single trajectory for given initial conditions. The manuscript must specify (in the methods description of the GNN-ODE component and its integration with the generative model) how stochasticity is injected—e.g., via explicit noise, SDE extensions, or variational sampling over trajectories—otherwise the approach risks approximating only mean behavior rather than the required posterior over sources.

    Authors: We agree that the integration of stochasticity requires more explicit specification in the manuscript. In PDSL, the deep generative model approximates the posterior over sources via variational sampling of initial conditions and latent variables, which are then fed into the GNN-ODE to evolve continuous trajectories. This ensemble of sampled trajectories captures the stochasticity of the diffusion process, while the GNN-ODE itself provides a deterministic but continuous evolution for each sample without assuming a discrete mechanism such as IC or LT. We will revise the methods section to include a precise description of this sampling-based integration, along with relevant equations and pseudocode, to clarify that the posterior approximation arises from the generative sampling rather than from stochasticity within the ODE solver. revision: yes

  2. Referee: [Proposed Method] The matching mechanism is described as enhancing source generation reliability by extracting relevant data blocks, but its interaction with the GNN-ODE dynamics and generative model is not shown to be sufficient for recovering variance in the source distribution. A concrete derivation or ablation showing how this block interacts with the ODE integration to address stochasticity (rather than just topology uncertainty) is needed to support the central claim.

    Authors: The matching mechanism selects and aligns observed data blocks with the continuous dynamics simulated by the GNN-ODE, providing dynamics-conditioned inputs to the generative model that help recover variance attributable to stochastic propagation paths. This goes beyond topology by focusing on temporal consistency with the ODE-evolved states. We acknowledge that the original manuscript does not include a dedicated derivation or ablation isolating this interaction. We will add an ablation study in the experiments section that quantifies the contribution to source distribution variance, and include a concise derivation in the methods section showing how the matching output modulates the ODE integration and generative sampling. revision: yes

Circularity Check

0 steps flagged

No circularity; claims introduce independent modeling components without reduction to inputs or self-citations.

full rationale

The provided abstract and text describe PDSL as integrating a deep generative model with Graph Neural ODEs to model continuous diffusion dynamics without predefined mechanisms, plus a matching mechanism for reliability. No equations, derivations, or self-citations are quoted that would make any 'prediction' equivalent to fitted inputs by construction, nor does the text invoke uniqueness theorems or ansatzes from prior self-work as load-bearing. The framework's central elements (GNN-ODE integration and matching) are presented as novel proposals rather than renamings or self-definitional reductions. The skeptic concern about deterministic ODEs vs. stochastic diffusion is a question of modeling adequacy, not circularity in the derivation chain. The paper's description remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based solely on abstract; no specific free parameters, axioms, or invented entities are detailed in the text. The framework itself is presented as new but without explicit ledger entries.

axioms (1)
  • domain assumption Deep generative models can approximate source distributions from observed propagation outcomes when combined with dynamics modeling.
    Implicit in the proposal to address uncertainty from diffusion stochasticity.

pith-pipeline@v0.9.0 · 5487 in / 1253 out tokens · 35207 ms · 2026-05-07T12:41:18.359655+00:00 · methodology

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Reference graph

Works this paper leans on

86 extracted references · 3 canonical work pages · 1 internal anchor

  1. [1]

    Spreading dynamics of information on online social networks,

    F. Meng, J. Xie, J. Sun, C. Xu, Y . Zeng, X. Wang, T. Jia, S. Huang, Y . Deng, and Y . Hu, “Spreading dynamics of information on online social networks,”Proceedings of the National Academy of Sciences, vol. 122, no. 4, p. e2410227122, 2025

    2025

  2. [2]

    The science of fake news,

    D. M. Lazer, M. A. Baum, Y . Benkler, A. J. Berinsky, K. M. Greenhill, F. Menczer, M. J. Metzger, B. Nyhan, G. Pennycook, D. Rothschild et al., “The science of fake news,”Science, vol. 359, no. 6380, pp. 1094–1096, 2018

    2018

  3. [3]

    The spread of true and false news online,

    S. V osoughi, D. Roy, and S. Aral, “The spread of true and false news online,”science, vol. 359, no. 6380, pp. 1146–1151, 2018

    2018

  4. [4]

    The so- cial media context interferes with truth discernment,

    Z. Epstein, N. Sirlin, A. Arechar, G. Pennycook, and D. Rand, “The so- cial media context interferes with truth discernment,”Science Advances, vol. 9, no. 9, p. eabo6169, 2023

    2023

  5. [5]

    Adam: an adaptive ddos attack mitigation scheme in software-defined cyber-physical system,

    T. Cai, T. Jia, S. Adepu, Y . Li, and Z. Yang, “Adam: an adaptive ddos attack mitigation scheme in software-defined cyber-physical system,” IEEE Transactions on Industrial Informatics, vol. 19, no. 6, pp. 7802– 7813, 2023

    2023

  6. [6]

    Modeling and analyzing malware propagation over wireless networks based on hypergraphs,

    J. Chen, S. Sun, C. Xia, D. Shi, and G. Chen, “Modeling and analyzing malware propagation over wireless networks based on hypergraphs,” IEEE Transactions on Network Science and Engineering, vol. 10, no. 6, pp. 3767–3778, 2023

    2023

  7. [7]

    Modeling and predicting malware propagation in double-layer computer networks,

    D. Duan, X. Yang, C. Lv, and Z. Cai, “Modeling and predicting malware propagation in double-layer computer networks,”IEEE Transactions on Network Science and Engineering, 2025

    2025

  8. [8]

    Modeling the uncer- tainty of information propagation for rumor detection: A neuro-fuzzy approach,

    L. Wei, D. Hu, W. Zhou, X. Wang, and S. Hu, “Modeling the uncer- tainty of information propagation for rumor detection: A neuro-fuzzy approach,”IEEE transactions on neural networks and learning systems, vol. 35, no. 2, pp. 2522–2533, 2022

    2022

  9. [9]

    Modality percep- tion learning-based determinative factor discovery for multimodal fake news detection,

    B. Wang, G. Wu, X. Li, J. Gao, Y . Hu, and B. Yin, “Modality percep- tion learning-based determinative factor discovery for multimodal fake news detection,”IEEE Transactions on Neural Networks and Learning Systems, 2024

    2024

  10. [10]

    Defense strategy for social network fake news under non-real-time data collection and disjointed decision making,

    Z. Liu, H. Zhang, J. Sun, and L. Wang, “Defense strategy for social network fake news under non-real-time data collection and disjointed decision making,”IEEE Transactions on Network Science and Engi- neering, 2025

    2025

  11. [11]

    Locating the source of diffusion in large-scale networks,

    P. C. Pinto, P. Thiran, and M. Vetterli, “Locating the source of diffusion in large-scale networks,”Physical review letters, vol. 109, no. 6, p. 068702, 2012

    2012

  12. [12]

    Mul- tiple rumor source detection with graph convolutional networks,

    M. Dong, B. Zheng, N. Quoc Viet Hung, H. Su, and G. Li, “Mul- tiple rumor source detection with graph convolutional networks,” in Proceedings of the 28th ACM international conference on information and knowledge management, 2019, pp. 569–578

    2019

  13. [13]

    Deciphering the overtaking phenomenon ini- tiated by low-centrality nodes in spreading processes,

    W. He, C. Gao, and T. Jia, “Deciphering the overtaking phenomenon ini- tiated by low-centrality nodes in spreading processes,”Communications Physics, vol. 8, no. 1, p. 266, 2025

    2025

  14. [14]

    Rumors in a network: Who’s the culprit?

    D. Shah and T. Zaman, “Rumors in a network: Who’s the culprit?”IEEE Transactions on information theory, vol. 57, no. 8, pp. 5163–5181, 2011

    2011

  15. [15]

    Estimating infection sources in a network with incomplete observations,

    W. Luo and W. P. Tay, “Estimating infection sources in a network with incomplete observations,” in2013 IEEE Global Conference on Signal and Information Processing. IEEE, 2013, pp. 301–304

    2013

  16. [16]

    K-center: An approach on the multi-source identification of information diffusion,

    J. Jiang, S. Wen, S. Yu, Y . Xiang, and W. Zhou, “K-center: An approach on the multi-source identification of information diffusion,” IEEE Transactions on Information Forensics and Security, vol. 10, no. 12, pp. 2616–2626, 2015

    2015

  17. [17]

    Information source detection in networks: Pos- sibility and impossibility results,

    K. Zhu and L. Ying, “Information source detection in networks: Pos- sibility and impossibility results,” inIEEE INFOCOM 2016-The 35th Annual IEEE International Conference on Computer Communications. IEEE, 2016, pp. 1–9

    2016

  18. [18]

    Maximum a posteriori estimation for information source detection,

    B. Chang, E. Chen, F. Zhu, Q. Liu, T. Xu, and Z. Wang, “Maximum a posteriori estimation for information source detection,”IEEE Trans- actions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 6, pp. 2242–2256, 2018

    2018

  19. [19]

    Multiple-source localization from a single-snapshot observation using graph bayesian optimization,

    Z. Zhang, Z. Zhang, and Z. Chen, “Multiple-source localization from a single-snapshot observation using graph bayesian optimization,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38, no. 20, 2024, pp. 22 538–22 546

    2024

  20. [20]

    A general framework for sensor placement in source localization,

    B. Spinelli, L. E. Celis, and P. Thiran, “A general framework for sensor placement in source localization,”IEEE Transactions on Network Science and Engineering, vol. 6, no. 2, pp. 86–102, 2017

    2017

  21. [21]

    Rank-one semidefinite programming solutions for mobile source localization in sensor networks,

    X. Wu, H. Qi, and N. Xiong, “Rank-one semidefinite programming solutions for mobile source localization in sensor networks,”IEEE Transactions on Network Science and Engineering, vol. 8, no. 1, pp. 638–650, 2020

    2020

  22. [22]

    Lightweight source localization for large-scale social networks,

    Z. Wang, D. Hou, C. Gao, X. Li, and X. Li, “Lightweight source localization for large-scale social networks,” inProceedings of the ACM Web Conference 2023, 2023, pp. 286–294

    2023

  23. [23]

    A comprehensive survey on multi-view clustering,

    U. Fang, M. Li, J. Li, L. Gao, T. Jia, and Y . Zhang, “A comprehensive survey on multi-view clustering,”IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 12, pp. 12 350–12 368, 2023

    2023

  24. [24]

    Coata: Effective co-augmentation of topology and attribute for graph neural networks,

    T. Liu, L. Lin, Y . Yu, X. Ou, Y . Zhang, Z. Ye, and T. Jia, “Coata: Effective co-augmentation of topology and attribute for graph neural networks,” inProceedings of the 2025 International Conference on Multimedia Retrieval, 2025, pp. 851–860. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 17

    2025

  25. [25]

    Information source estimation with multi-channel graph neural network,

    X. Shu, B. Yu, Z. Ruan, Q. Zhang, and Q. Xuan, “Information source estimation with multi-channel graph neural network,”Graph Data Mining: Algorithm, Security and Application, pp. 1–27, 2021

    2021

  26. [26]

    Diffusion model for graph inverse problems: Towards effective source localization on complex networks,

    X. Yan, H. Fang, and Q. He, “Diffusion model for graph inverse problems: Towards effective source localization on complex networks,” Advances in Neural Information Processing Systems, vol. 36, 2024

    2024

  27. [27]

    Learning deep generative clustering via mutual information maximization,

    X. Yang, J. Yan, Y . Cheng, and Y . Zhang, “Learning deep generative clustering via mutual information maximization,”IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 9, pp. 6263–6275, 2022

    2022

  28. [28]

    Gen-graphex: Generative in-distribution graph explanations for time-efficient model-level in- terpretability of gnns,

    S. Saha, M. Das, and S. Bandyopadhyay, “Gen-graphex: Generative in-distribution graph explanations for time-efficient model-level in- terpretability of gnns,”IEEE Transactions on Neural Networks and Learning Systems, 2025

    2025

  29. [29]

    Source localization of graph diffusion via variational autoencoders for graph inverse problems,

    C. Ling, J. Jiang, J. Wang, and Z. Liang, “Source localization of graph diffusion via variational autoencoders for graph inverse problems,” inProceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining, 2022, pp. 1010–1020

    2022

  30. [30]

    Pgsl: A probabilistic graph diffusion model for source localization,

    X. Xu, T. Qian, Z. Xiao, N. Zhang, J. Wu, and F. Zhou, “Pgsl: A probabilistic graph diffusion model for source localization,”Expert Systems with Applications, vol. 238, p. 122028, 2024

    2024

  31. [31]

    How to identify an infection source with limited observations,

    W. Luo, W. P. Tay, and M. Leng, “How to identify an infection source with limited observations,”IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 4, pp. 586–597, 2014

    2014

  32. [32]

    Rumor source localization in social networks based on infection potential energy,

    W. Li, C. Guo, Y . Liu, X. Zhou, Q. Jin, and M. Xin, “Rumor source localization in social networks based on infection potential energy,” Information Sciences, vol. 634, pp. 172–188, 2023

    2023

  33. [33]

    Dislpsi: A framework for source localization in signed social networks with structural balance,

    Z.-W. Ma, H.-j. Wang, Z.-L. Hu, X.-B. Zhu, Y .-Z. Huang, and F. Huang, “Dislpsi: A framework for source localization in signed social networks with structural balance,”Physics Letters A, vol. 523, p. 129772, 2024

    2024

  34. [34]

    Source localization in signed networks based on dynamic message passing algorithm,

    Z.-X. Jiang, Z.-L. Hu, and F. Huang, “Source localization in signed networks based on dynamic message passing algorithm,”Chaos, Solitons & Fractals, vol. 188, p. 115532, 2024

    2024

  35. [35]

    Diffusion source identification on networks with statistical confidence,

    Q. E. Dawkins, T. Li, and H. Xu, “Diffusion source identification on networks with statistical confidence,” inInternational Conference on Machine Learning. PMLR, 2021, pp. 2500–2509

    2021

  36. [36]

    Hmsl: Source localization based on higher-order markov propagation,

    C. Gong, J. Li, L. Qian, S. Li, Z. Yang, and K. Yang, “Hmsl: Source localization based on higher-order markov propagation,”Chaos, Solitons & Fractals, vol. 182, p. 114765, 2024

    2024

  37. [37]

    Multi-source localization based on graph representation learning and bayesian optimization,

    Z. Zhou, Y . Wang, Q. Zhai, and J. Yan, “Multi-source localization based on graph representation learning and bayesian optimization,”IEEE Transactions on Network Science and Engineering, vol. 13, pp. 4815– 4832, 2025

    2025

  38. [38]

    Two-stage denoising diffusion model for source localization in graph inverse problems,

    B. Huang, W. Yu, R. Xie, J. Xiao, and J. Huang, “Two-stage denoising diffusion model for source localization in graph inverse problems,” inJoint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, 2023, pp. 325–340

    2023

  39. [39]

    A generalized diffusion framework with learnable propagation dynamics for source localization,

    D. Hou, Y . Wang, C. Gao, and X. Li, “A generalized diffusion framework with learnable propagation dynamics for source localization,” inPro- ceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, 2025, pp. 2919–2927

    2025

  40. [40]

    Structure-prior informed diffusion model for graph source localization with limited data,

    H. Chen, J. Ding, X. Liang, Y . Li, and X.-P. Zhang, “Structure-prior informed diffusion model for graph source localization with limited data,” inProceedings of the 34th ACM International Conference on Information and Knowledge Management, 2025, pp. 250–259

    2025

  41. [41]

    Path-based multi- sources localization in multiplex networks,

    L. Cheng, X. Li, Z. Han, T. Luo, L. Ma, and P. Zhu, “Path-based multi- sources localization in multiplex networks,”Chaos, Solitons & Fractals, vol. 159, p. 112139, 2022

    2022

  42. [42]

    Random full-order-coverage based rapid source localization with limited observations for large-scale networks,

    D. Hou, C. Gao, Z. Wang, X. Li, and X. Li, “Random full-order-coverage based rapid source localization with limited observations for large-scale networks,”IEEE Transactions on Network Science and Engineering, vol. 11, no. 5, pp. 4213–4226, 2024

    2024

  43. [43]

    Enhanced epidemic control: Community- based observer placement and source tracing,

    J. Zhao and K. H. Cheong, “Enhanced epidemic control: Community- based observer placement and source tracing,”IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2025

    2025

  44. [44]

    Locating multi-sources in social networks with a low infection rate,

    P. Zhu, L. Cheng, C. Gao, Z. Wang, and X. Li, “Locating multi-sources in social networks with a low infection rate,”IEEE Transactions on Network Science and Engineering, vol. 9, no. 3, pp. 1853–1865, 2022

    2022

  45. [45]

    An invertible graph diffusion neural network for source localization,

    J. Wang, J. Jiang, and L. Zhao, “An invertible graph diffusion neural network for source localization,” inProceedings of the ACM Web Conference 2022, 2022, pp. 1058–1069

    2022

  46. [46]

    New localization frameworks: User-centric approaches to source localization in real-world propagation scenarios,

    D. Hou, Y . Wang, C. Gao, X. Li, and Z. Wang, “New localization frameworks: User-centric approaches to source localization in real-world propagation scenarios,” inProceedings of the 33rd ACM International Conference on Information and Knowledge Management, 2024, pp. 839– 848

    2024

  47. [47]

    Graph contrastive learn- ing for source localization in social networks,

    Q. Bao, Y . Jiang, W. Zhang, P. Jiao, and J. Su, “Graph contrastive learn- ing for source localization in social networks,”Information Sciences, vol. 679, p. 121090, 2024

    2024

  48. [48]

    Trace: Structural riemannian bridge matching for transferable source localization in information propagation,

    L. Sun, S. Zhou, B. Fang, H. Zhang, J. Ye, Y . Ye, and P. S. Yu, “Trace: Structural riemannian bridge matching for transferable source localization in information propagation,” inProceedings of IJCAI, 2025

    2025

  49. [49]

    Finding patient zero: Learning contagion source with graph neural networks,

    C. Shah, N. Dehmamy, N. Perra, M. Chinazzi, A.-L. Barab ´asi, A. Vespignani, and R. Yu, “Finding patient zero: Learning contagion source with graph neural networks,”arXiv preprint arXiv:2006.11913, 2020

    work page arXiv 2006

  50. [50]

    Inferring patient zero on temporal networks via graph neural networks,

    X. Ru, J. M. Moore, X.-Y . Zhang, Y . Zeng, and G. Yan, “Inferring patient zero on temporal networks via graph neural networks,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 37, no. 8, 2023, pp. 9632–9640

    2023

  51. [51]

    Multiple location profiling for users and relationships from social network and content,

    R. Li, S. Wang, and K. Chen-Chuan, “Multiple location profiling for users and relationships from social network and content,”Proceedings of the VLDB Endowment, vol. 5, no. 11, 2012

    2012

  52. [52]

    Topic-aware source locating in social networks,

    W. Zang, C. Zhou, L. Guo, and P. Zhang, “Topic-aware source locating in social networks,” inProceedings of the 24th International Conference on World Wide Web, 2015, pp. 141–142

    2015

  53. [53]

    Source localization in signed networks with effective distance,

    Z.-W. Ma, L. Sun, Z.-G. Ding, Y .-Z. Huang, and Z.-L. Hu, “Source localization in signed networks with effective distance,”Chinese Physics B, vol. 33, no. 2, p. 028902, 2024

    2024

  54. [54]

    Talk of the network: A complex systems look at the underlying process of word-of-mouth,

    J. Goldenberg, B. Libai, and E. Muller, “Talk of the network: A complex systems look at the underlying process of word-of-mouth,”Marketing letters, vol. 12, pp. 211–223, 2001

    2001

  55. [55]

    Information sources estimation in time- varying networks,

    Y . Chai, Y . Wang, and L. Zhu, “Information sources estimation in time- varying networks,”IEEE Transactions on Information Forensics and Security, vol. 16, pp. 2621–2636, 2021

    2021

  56. [56]

    Back to the source: an online approach for sensor placement and source localization,

    B. Spinelli, L. E. Celis, and P. Thiran, “Back to the source: an online approach for sensor placement and source localization,” inProceedings of the 26th international conference on world wide web, 2017, pp. 1151– 1160

    2017

  57. [57]

    Optimizing sensors placement in complex networks for localization of hidden signal source: A review,

    R. Paluch, Ł. G. Gajewski, J. A. Hołyst, and B. K. Szymanski, “Optimizing sensors placement in complex networks for localization of hidden signal source: A review,”Future Generation Computer Systems, vol. 112, pp. 1070–1092, 2020

    2020

  58. [58]

    Mase: Multi-attribute source estimator for epidemic transmission in complex networks,

    J. Zhao and K. H. Cheong, “Mase: Multi-attribute source estimator for epidemic transmission in complex networks,”IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 54, no. 6, pp. 3308–3320, 2024

    2024

  59. [59]

    Community partition- based source localization with adaptive observers deployment,

    J. Shi, Y . Fang, Z. Tan, X. Zhang, and X. Zhao, “Community partition- based source localization with adaptive observers deployment,” inPro- ceedings of the 34th ACM International Conference on Information and Knowledge Management, 2025, pp. 2663–2673

    2025

  60. [60]

    A rapid source lo- calization method in the early stage of large-scale network propagation,

    Z. Wang, D. Hou, C. Gao, J. Huang, and Q. Xuan, “A rapid source lo- calization method in the early stage of large-scale network propagation,” inProceedings of the ACM web conference 2022, 2022, pp. 1372–1380

    2022

  61. [61]

    Diffusion source inference for large-scale complex networks based on network percola- tion,

    Y . Liu, X. Wang, X. Wang, Z. Wang, and J. Kurths, “Diffusion source inference for large-scale complex networks based on network percola- tion,”IEEE Transactions on Neural Networks and Learning Systems, 2023

    2023

  62. [62]

    Joint source localization in different platforms via implicit propagation characteristics of similar top- ics,

    Z. Wang, D. Hou, S. Yin, C. Gao, and X. Li, “Joint source localization in different platforms via implicit propagation characteristics of similar top- ics,” inProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, IJCAI-24, Kate Larson (Ed.). International Joint Conferences on Artificial Intelligence Organization, 2024,...

    2024

  63. [63]

    Fgssi: a feature-enhanced framework with transferability for sequential source identification,

    D. Hou, C. Gao, Z. Wang, and X. Li, “Fgssi: a feature-enhanced framework with transferability for sequential source identification,” IEEE Transactions on Dependable and Secure Computing, 2025

    2025

  64. [64]

    Rumor source localization in social networks based on the propagation direction of observers,

    Z.-W. Ma, H.-J. Wang, Z.-L. Hu, X.-B. Zhu, H. Peng, L.-Y . L ¨u, Y .-Z. Huang, and M. Li, “Rumor source localization in social networks based on the propagation direction of observers,”Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 36, no. 1, 2026

    2026

  65. [65]

    Dis- tinguishing simple and complex contagion processes on networks,

    G. Cencetti, D. A. Contreras, M. Mancastroppa, and A. Barrat, “Dis- tinguishing simple and complex contagion processes on networks,” Physical Review Letters, vol. 130, no. 24, p. 247401, 2023

    2023

  66. [66]

    The simple rules of social contagion,

    N. O. Hodas and K. Lerman, “The simple rules of social contagion,” Scientific reports, vol. 4, no. 1, p. 4343, 2014

    2014

  67. [67]

    Algorithmic aspects of inverse problems using generative models,

    C. Hegde, “Algorithmic aspects of inverse problems using generative models,” in2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2018, pp. 166–172

    2018

  68. [68]

    Auto-Encoding Variational Bayes

    D. P. Kingma and M. Welling, “Auto-encoding variational bayes,”arXiv preprint arXiv:1312.6114, 2013

    work page internal anchor Pith review arXiv 2013

  69. [69]

    Generating diverse structure for image inpainting with hierarchical vq-vae,

    J. Peng, D. Liu, S. Xu, and H. Li, “Generating diverse structure for image inpainting with hierarchical vq-vae,” inProceedings of the JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 18 IEEE/CVF conference on computer vision and pattern recognition, 2021, pp. 10 775–10 784

    2015

  70. [70]

    Qarv: Quantization-aware resnet vae for lossy image compression,

    Z. Duan, M. Lu, J. Ma, Y . Huang, Z. Ma, and F. Zhu, “Qarv: Quantization-aware resnet vae for lossy image compression,”IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023

    2023

  71. [71]

    Learning structured output represen- tation using deep conditional generative models,

    K. Sohn, H. Lee, and X. Yan, “Learning structured output represen- tation using deep conditional generative models,”Advances in neural information processing systems, vol. 28, 2015

    2015

  72. [72]

    Neural ordinary differential equations,

    R. T. Chen, Y . Rubanova, J. Bettencourt, and D. K. Duvenaud, “Neural ordinary differential equations,”Advances in neural information pro- cessing systems, vol. 31, 2018

    2018

  73. [73]

    arXiv preprint arXiv:1911.07532 , year=

    M. Poli, S. Massaroli, J. Park, A. Yamashita, H. Asama, and J. Park, “Graph neural ordinary differential equations,”arXiv preprint arXiv:1911.07532, 2019

    work page arXiv 1911

  74. [74]

    Continuous graph neural net- works,

    L.-P. Xhonneux, M. Qu, and J. Tang, “Continuous graph neural net- works,” inInternational conference on machine learning. PMLR, 2020, pp. 10 432–10 441

    2020

  75. [75]

    Grand: Graph neural diffusion,

    B. Chamberlain, J. Rowbottom, M. I. Gorinova, M. Bronstein, S. Webb, and E. Rossi, “Grand: Graph neural diffusion,” inInternational confer- ence on machine learning. PMLR, 2021, pp. 1407–1418

    2021

  76. [76]

    ¨Uber die numerische aufl¨osung von differentialgleichungen,

    C. Runge, “ ¨Uber die numerische aufl¨osung von differentialgleichungen,” Mathematische Annalen, vol. 46, no. 2, pp. 167–178, 1895

  77. [77]

    The network data repository with interactive graph analytics and visualization,

    R. Rossi and N. Ahmed, “The network data repository with interactive graph analytics and visualization,” inProceedings of the AAAI confer- ence on artificial intelligence, vol. 29, no. 1, 2015

    2015

  78. [78]

    Patterns and dynamics of users’ behavior and interaction: Network analysis of an online community,

    P. Panzarasa, T. Opsahl, and K. M. Carley, “Patterns and dynamics of users’ behavior and interaction: Network analysis of an online community,”Journal of the American Society for Information Science and Technology, vol. 60, no. 5, pp. 911–932, 2009

    2009

  79. [79]

    Emergence of scaling in random net- works,

    A.-L. Barab ´asi and R. Albert, “Emergence of scaling in random net- works,”science, vol. 286, no. 5439, pp. 509–512, 1999

    1999

  80. [80]

    Comsoc: adaptive transfer of user behaviors over composite social network,

    E. Zhong, W. Fan, J. Wang, L. Xiao, and Y . Li, “Comsoc: adaptive transfer of user behaviors over composite social network,” inProceed- ings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining, 2012, pp. 696–704

    2012

Showing first 80 references.