pith. sign in

arxiv: 2604.24811 · v1 · submitted 2026-04-27 · 💻 cs.LG · cs.AI

Time-varying Interaction Graph ODE for Dynamic Graph Representation Learning

Xiaoyi Wang , Zhiqiang Wang , Jianqing Liang , Xingwang Zhao , Chuangyin Dang , Zhen Jin , Jiye Liang This is my paper

Pith reviewed 2026-05-08 04:33 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords dynamic graphsgraph neural ODEtime-varying interactionscontinuous-time modelinggraph representation learningattribute predictionmodel robustness
0
0 comments X

The pith

TI-ODE decomposes graph ODE evolution into learnable interaction basis functions mixed by time-dependent weights to capture shifting node interactions.

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

Existing graph neural ODEs rely on one fixed message-passing rule that applies uniformly to all node pairs at all times, which cannot reflect how real interactions diversify and change. TI-ODE instead writes the ODE right-hand side as a sum of several distinct learnable basis functions, each standing for a different interaction style, and lets time-dependent weights decide how much each basis contributes at each moment. This structure lets the continuous dynamics adapt without retraining or switching discrete layers. A reader would care because social, biological, and traffic networks routinely exhibit exactly these time-varying interaction patterns, so a model that tracks them should produce better forecasts of node attributes over long horizons.

Core claim

The central claim is that the evolution function of a graph ODE can be decomposed into a fixed set of learnable interaction basis functions that are then combined at each instant by time-dependent learnable weights. This decomposition directly addresses the limitation of a single unified message-passing mechanism and enables the interaction pattern itself to evolve continuously. Experiments on six dynamic graph datasets show consistent outperformance and state-of-the-art accuracy on attribute prediction, while the Covid dataset illustrates interpretability; both theory and experiments confirm greater robustness than unified baselines.

What carries the argument

The decomposition of the graph ODE right-hand side into learnable interaction basis functions that are scaled by time-dependent weights.

If this is right

  • TI-ODE achieves state-of-the-art attribute prediction accuracy on six different dynamic graph datasets.
  • The model exhibits superior robustness compared with unified message-passing graph ODEs, both in theoretical analysis and in experiments.
  • Training on the Covid dataset yields interpretable time weights that reveal how interaction styles shift during the pandemic period.
  • The same architecture generalizes across multiple dynamic graph tasks without requiring per-task redesign of the message function.

Where Pith is reading between the lines

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

  • Inspecting the learned basis functions after training could identify a small vocabulary of recurring interaction motifs that recur across different time windows.
  • The time-dependent weights themselves might serve as a compact signature for detecting regime shifts, such as the onset of a new community structure in a social network.
  • Because the bases are learned rather than hand-specified, the same trained model could be fine-tuned on a new dynamic graph whose interaction types overlap only partially with the original training distribution.
  • In domains such as traffic or epidemic forecasting, the explicit time weights could be aligned with external event logs to test whether the model recovers known changes in contact or flow patterns.

Load-bearing premise

Diverse and time-varying inter-node interactions can be expressed as combinations of a small fixed set of basis functions whose relative strengths change smoothly with time.

What would settle it

On a dynamic graph dataset engineered so that interaction types appear and disappear in ways that cannot be approximated by any small number of fixed bases, TI-ODE would cease to outperform a standard graph ODE that uses a single message-passing function.

Figures

Figures reproduced from arXiv: 2604.24811 by Chuangyin Dang, Jianqing Liang, Jiye Liang, Xiaoyi Wang, Xingwang Zhao, Zhen Jin, Zhiqiang Wang.

Figure 1
Figure 1. Figure 1: An overview of the proposed TI-ODE. Our TI-ODE first constructs temporal graphs from historical dynamic graph sequences and employs an attention-driven spatio-temporal encoder to obtain node sequence representations through message passing and temporal aggregation, thereby inferring the primary posterior distribution. We then introduce a random mapping network to generate multiple auxiliary posterior distr… view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of the Spring dataset under two different prediction lengths. • AGCRN (Bai et al., 2020): An adaptive graph convolutional recurrent network that learns hidden graph structures through node embeddings. • TTS-AMP (Cini et al., 2023): A “Temporal-Then-Spatial (TTS)” architecture that first employs a GRU to extract temporal features, and then applies an Anisotropic Message Passing (AMP) mechanism… view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of the Spring dataset (24-step ahead). 5.4. Empirical Performance The experimental results are shown in view at source ↗
Figure 4
Figure 4. Figure 4: Sensitivity analysis on the Spring dataset. (a) MSE results (12-step ahead). (b) MAE results (12-step ahead). (c)Training time per epoch under different configurations (12-step ahead). (d) MSE results (24-step ahead). (e) MAE results (24-step ahead). (f)Training time per epoch under different configurations (24-step ahead). (a) (b) (c) (d) view at source ↗
Figure 5
Figure 5. Figure 5: Sensitivity analysis on the Charged dataset. (a) MSE results (12-step ahead). (b) MAE results (12-step ahead). (c) MSE results (24-step ahead). (d) MAE results (24-step ahead). First Author et al.: Preprint submitted to Elsevier Page 13 of 25 view at source ↗
Figure 6
Figure 6. Figure 6: Performance under different condition lengths. 5.6. Parameter Sensitivity To assess the impact of the number of basis functions and RandNet on model performance, we conducted a parameter sensitivity experiment in the combination space of basis function 𝐾 ∈ {2, 3, 4, 5, 6} and RandNet numbers 𝐾𝑟 ∈ {1, 2, 3, 4, 5}. The results on the Spring and Charged dataset are shown in view at source ↗
Figure 7
Figure 7. Figure 7: Visualization of the learned bias weights. (a) Daily new confirmed COVID-19 cases in Jilin and Tianjin from March 1 to May 31, 2022. (b) Weight visualization for the period from March 18 to April 9, 2022. (c) Weight visualization for the period from April 23 to May 15, 2022 and transportation restriction measures. In contrast, the epidemic situation in Tianjin remained relatively stable, while inter-provin… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of training times for different methods on the all datasets. The training durations are presented in units of 𝑙𝑜𝑔10(seconds/epoch). To validate the computational efficiency of TI-ODE, we compared the training time of TI-ODE with other graph neural ODE methods (LG-ODE, CG-ODE, PG-ODE and CSG-ODE). All experiments were run on a Titan RTX GPU, and we compared the time cost per training epoch. As shown in view at source ↗
Figure 9
Figure 9. Figure 9: Temporal Evolution of Absolute Error under Initial State Perturbations across Different Models. basis functions and increases the parameter count, its impact on the overall training time is negligible. Compared to other graph neural ODE methods such as CSG-ODE and PG-ODE, TI-ODE achieves superior property prediction performance while maintaining comparable training efficiency. These results indicate that T… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of Total Cumulative Error across Different Models. We investigate whether TI-ODE exhibits a lower perturbation growth rate and smaller cumulative error compared to models with a unified message passing mechanism, such as CSG-ODE and PG-ODE. The core logic of this experiment is to validate model robustness by introducing infinitesimal perturbations to the initial state and observing the resultin… view at source ↗
read the original abstract

Graph neural Ordinary Differential Equations (ODE) combine neural ODE with the message passing mechanism of Graph Neural Networks (GNN), providing a continuous-time modeling method for graph representation learning. However, in dynamic graph scenarios, existing graph neural ODEs typically employ a unified message passing mechanism, assuming that inter-node interactions share the same message passing function at any time, which makes it challenging to capture the diversity and time-varying nature of inter-node interaction patterns. To address this, we propose Time-varying Interaction Graph Ordinary Differential Equations (TI-ODE). The core idea of TI-ODE is to decompose the evolution function of a graph ODE into a set of learnable interaction basis functions, where each basis function corresponds to a distinct type of inter-node interaction. These basis functions are dynamically combined through time-dependent learnable weights, enabling inter-node interaction patterns to adaptively evolve over time. Experimental results on six dynamic graph datasets demonstrate that TI-ODE consistently outperforms existing methods and achieves state-of-the-art performance on attribute prediction tasks, and experiments on the \textit{Covid} dataset further verify the interpretability and generalizability of our TI-ODE. Furthermore, we demonstrate both theoretically and empirically that TI-ODE exhibits superior robustness compared to models utilizing a unified message-passing mechanism.

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

4 major / 2 minor

Summary. The manuscript proposes Time-varying Interaction Graph Ordinary Differential Equations (TI-ODE) to model dynamic graphs. Existing graph neural ODEs are critiqued for using a single unified message-passing function at all times; TI-ODE instead decomposes the ODE right-hand side into a fixed collection of learnable interaction basis functions that are linearly combined by time-dependent weights, allowing interaction patterns to evolve continuously. The authors report state-of-the-art results on attribute prediction across six dynamic-graph benchmarks and claim both theoretical and empirical robustness advantages over unified-message-passing baselines, with additional interpretability experiments on the Covid dataset.

Significance. If the decomposition is shown to capture genuinely time-varying interaction structure rather than simply increasing capacity, the approach would supply a principled continuous-time mechanism for evolving graphs and could influence downstream tasks such as epidemic modeling or temporal link prediction. The combination of a new architectural primitive with robustness analysis is potentially valuable, provided the empirical gains are reproducible and the theoretical claims are fully substantiated.

major comments (4)
  1. [Model description (§3–4)] Model description (likely §3–4): the central construction decomposes the ODE vector field into static basis functions f_k combined by w(t), yet no explicit constraints (linear independence of the f_k, Lipschitz conditions on w(t), or separation of timescales) are stated; without them the construction can collapse to a standard unified GNN-ODE under gradient descent, undermining the claim that the time-varying mechanism itself drives the reported gains.
  2. [Theoretical robustness (§5)] Theoretical robustness section (likely §5): the abstract asserts a theoretical demonstration of superior robustness, but the provided text supplies neither the statement of the theorem nor the key assumptions (e.g., bounds on the weight functions or properties of the basis span); this derivation is load-bearing for the robustness claim and must be supplied with all intermediate steps.
  3. [Experimental results (§6)] Experimental results (likely §6 and tables): SOTA performance is asserted on six datasets for attribute prediction, yet no error bars, number of random seeds, statistical significance tests, or ablation on the number of basis functions are referenced; without these controls it is impossible to determine whether improvements stem from the proposed time-varying interaction mechanism or from increased parameter count.
  4. [§4] §4, interaction basis functions: the modeling assumption that arbitrary time-varying inter-node interactions can be spanned by a small fixed set of learnable bases plus flexible w(t) is stated without a supporting lemma or capacity argument; if the chosen bases are redundant or insufficiently expressive, the performance advantage may be illusory.
minor comments (2)
  1. [Abstract] Abstract: the sentence beginning 'Furthermore, we demonstrate both theoretically and empirically' should cite the specific theorem or subsection so readers can locate the supporting material.
  2. [Experiments] The Covid-dataset interpretability experiment is mentioned but lacks a quantitative metric (e.g., alignment with known epidemiological phases) or visualization details.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments have helped us clarify key aspects of the model, strengthen the theoretical claims, and improve the experimental rigor. We have revised the manuscript accordingly and address each major comment point by point below.

read point-by-point responses

  1. Referee: [Model description (§3–4)] Model description (likely §3–4): the central construction decomposes the ODE vector field into static basis functions f_k combined by w(t), yet no explicit constraints (linear independence of the f_k, Lipschitz conditions on w(t), or separation of timescales) are stated; without them the construction can collapse to a standard unified GNN-ODE under gradient descent, undermining the claim that the time-varying mechanism itself drives the reported gains.

    Authors: We agree that the absence of explicit constraints leaves open the possibility of collapse under optimization. In the revised manuscript we have added a dedicated paragraph in Section 3.2 that states three constraints: (i) the basis functions are kept approximately linearly independent by a diversity regularizer added to the loss, (ii) the weight network uses bounded activations that guarantee a uniform Lipschitz constant on w(t), and (iii) we assume a mild separation of timescales between the slowly varying bases and the faster weights. A short proposition in the appendix shows that, under these conditions, any collapse to a single unified function incurs a measurable expressivity penalty. These additions make the time-varying mechanism the operative source of the reported gains. revision: yes

  2. Referee: [Theoretical robustness (§5)] Theoretical robustness section (likely §5): the abstract asserts a theoretical demonstration of superior robustness, but the provided text supplies neither the statement of the theorem nor the key assumptions (e.g., bounds on the weight functions or properties of the basis span); this derivation is load-bearing for the robustness claim and must be supplied with all intermediate steps.

    Authors: We apologize for the omission. The revised Section 5 now contains the complete statement of Theorem 1 together with all intermediate steps. The theorem states that, when the weight functions satisfy ||w(t)||_∞ ≤ 1 and the K basis functions span a subspace whose minimal angle is bounded away from zero, the sensitivity of the TI-ODE trajectory to input perturbations is bounded by a factor of O(1/√K) relative to a unified GNN-ODE. The proof proceeds by applying Gronwall’s inequality to the decomposed vector field and then using the linear-combination structure to bound perturbation propagation. The full set of assumptions is listed at the start of the section and the complete derivation appears in the main text. revision: yes

  3. Referee: [Experimental results (§6)] Experimental results (likely §6 and tables): SOTA performance is asserted on six datasets for attribute prediction, yet no error bars, number of random seeds, statistical significance tests, or ablation on the number of basis functions are referenced; without these controls it is impossible to determine whether improvements stem from the proposed time-varying interaction mechanism or from increased parameter count.

    Authors: We thank the referee for this important observation. All tables in the revised Section 6 now report mean ± standard deviation over five independent random seeds. We added paired t-tests and report p-values < 0.05 for every improvement over the strongest baseline. A new ablation table (Table 7) varies the number of basis functions K from 1 to 8 while keeping total parameter count fixed by adjusting hidden dimensions; performance peaks at K = 4 and the K = 1 case (which reduces to a unified model) is strictly inferior, confirming that the gains arise from the time-varying mechanism rather than capacity alone. revision: yes

  4. Referee: [§4] §4, interaction basis functions: the modeling assumption that arbitrary time-varying inter-node interactions can be spanned by a small fixed set of learnable bases plus flexible w(t) is stated without a supporting lemma or capacity argument; if the chosen bases are redundant or insufficiently expressive, the performance advantage may be illusory.

    Authors: We acknowledge that a formal capacity argument is needed. In the revised Section 4 we have inserted Lemma 1: any continuous time-varying interaction function that is Lipschitz in time can be approximated to within O(1/K) error by a linear combination of K learnable bases whose weights are produced by a universal-approximator network. The proof combines the density of neural networks for the weight functions with a covering argument over the basis span. We also added a short discussion and an appendix figure showing that the learned bases remain diverse (measured by cosine similarity) throughout training, addressing concerns about redundancy. revision: yes

Circularity Check

0 steps flagged

No circularity: architectural proposal with independent empirical and theoretical support

full rationale

The paper's core contribution is an architectural change: decomposing the graph ODE right-hand side into a fixed set of learnable basis functions combined by time-dependent weights. This is presented as a modeling choice to capture time-varying interactions, not as a derivation that reduces to its own fitted outputs or prior self-citations. Performance claims rest on experiments across six datasets plus separate robustness arguments, without any equation shown that equates a 'prediction' to a parameter fit by construction. No load-bearing step collapses to self-definition, renaming, or an unverified self-citation chain; the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

Review limited to abstract; full derivation and experimental protocol unavailable.

free parameters (2)
  • interaction basis functions
    Learnable components that represent distinct inter-node interaction types; number and form chosen during training.
  • time-dependent combination weights
    Learnable scalars or vectors that mix the basis functions at each time step.
axioms (2)
  • domain assumption Graph neural ODEs combine neural ODEs with GNN message passing
    Stated as the starting point for the extension.
  • ad hoc to paper Inter-node interactions admit a decomposition into a small set of reusable basis functions
    Core modeling choice introduced to capture time-varying diversity.
invented entities (1)
  • time-varying interaction basis functions no independent evidence
    purpose: To represent distinct types of node interactions that can be recombined over time
    Newly postulated construct not present in standard graph ODE formulations

pith-pipeline@v0.9.0 · 5536 in / 1349 out tokens · 32837 ms · 2026-05-08T04:33:37.601051+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages · 1 internal anchor

  1. [1]

    17804–17815

    Adaptive graph convolutional recurrent network for traffic forecasting, in: Proceedings of the 34nd International Conference on Neural Information Processing Systems (NeurIPS 2020), pp. 17804–17815. Butcher, J.C.,

    work page 2020

  2. [2]

    Neural ordinary differential equations, in: Proceedings of the 32nd International Conference on Neural Information Processing Systems (NeurIPS 2018), Curran Associates, Inc. pp. 6572–6583. Cini, A., Marisca, I., Zambon, D., Alippi, C., et al.,

    work page 2018

  3. [3]

    Taming local effects in graph-based spatiotemporal forecasting, in: Proceedings of the 37th Conferenceon Neural Information Processing Systems (NeurIPS 2023), pp. 1–19. CMU,

    work page 2023

  4. [4]

    Exploiting edge features for graph neural networks, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR 2019), IEEE. pp. 9211–9219. Gravina, A., Lovisotto, G., Gallicchio, C., Bacciu, D., Grohnfeldt, C.,

    work page 2019

  5. [5]

    16206–16225

    Long range propagation on continuous-time dynamic graphs, in: Proceedings of the 41st International Conference on Machine Learning (ICML 2024), pp. 16206–16225. Hartman, P.,

    work page 2024

  6. [6]

    Society for Industrial and Applied Mathematics

    Ordinary differential equations. Society for Industrial and Applied Mathematics. ISBN:978-0-89871-510-1. He,K.,Zhang,X.,Ren,S.,Sun,J.,2016. Deepresiduallearningforimagerecognition,in:ProceedingsoftheIEEEconferenceonComputerVision and Pattern Recognition (CVPR 2016), pp. 770–778. Huang, Z., Sun, Y., Wang, W.,

    work page 2016

  7. [7]

    Learning continuous system dynamics from irregularly-sampled partial observations, in: Proceedings of the 34th International Conference on Neural Information Processing Systems (NeurIPS 2020), Curran Associates, Inc. pp. 16177–16187. Huang, Z., Sun, Y., Wang, W.,

    work page 2020

  8. [8]

    Coupled graph ode for learning interacting system dynamics, in: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2021), Association for Computing Machinery. pp. 705–715. Huang, Z., Zhao, W., Gao, J., Hu, Z., Luo, X., Cao, Y., Chen, Y., Sun, Y., Wang, W.,

    work page 2021

  9. [9]

    Physics-informed regularization for domain-agnostic dynamical system modeling, in: Proceedings of the 38th International Conference on Neural Information Processing Systems (NeurIPS 2024), pp. 739–774. Jiao, P., Chen, S., Guo, X., He, D., Liu, D.,

    work page 2024

  10. [10]

    Journal of Computer Research and Development 61, 2045–2066

    Survey on graph neural ordinary differential equations. Journal of Computer Research and Development 61, 2045–2066. (in Chinese). Karia, R., Gupta, I., Khandait, H., Yadav, A., Yadav, A.,

    work page 2045

  11. [11]

    Auto-Encoding Variational Bayes

    Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 . Kipf, T., Fetaya, E., Wang, K.C., Welling, M., Zemel, R.,

    work page internal anchor Pith review arXiv

  12. [12]

    Neural relational inference for interacting systems, in: Proceedings of the 35th International Conference on Machine Learning (ICML 2018), PMLR. pp. 2688–2697. Kumar, S., Zhang, X., Leskovec, J.,

    work page 2018

  13. [13]

    Predicting dynamic embedding trajectory in temporal interaction networks, in: Proceedings of the 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2019), Association for Computing Machinery. pp. 1269–1278. Lebl, J.,

    work page 2019

  14. [14]

    Liu, J., Liu, M., Liang, W.,

    Diffusion convolutional recurrent neural network: Data-driven traffic forecasting, in: Proceedings of the 6th International Conference on Learning Representations (ICLR 2018). Liu, J., Liu, M., Liang, W.,

    work page 2018

  15. [15]

    Graph odes and beyond: A comprehensive survey on integrating differential equationswithgraphneuralnetworks,in:Proceedingsofthe31stACMSIGKDDConferenceonKnowledgeDiscoveryandDataMining(KDD 2025), Association for Computing Machinery. pp. 6118–6128. Luo,X.,Gu,Y.,Jiang,H.,Zhou,H.,Huang,J.,Ju,W.,Xiao,Z.,Zhang,M.,Sun,Y.,2024. Pgode:Towardshigh-qualitysystemdynam...

    work page 2025

  16. [16]

    Hope: High-order graph ode for modeling interacting dynamics, in: Proceedings of the 40th International Conference on Machine Learning (ICML 2023), PMLR. pp. 23124–23139. Manessi, F., Rozza, A., Manzo, M.,

    work page 2023

  17. [17]

    Frontiers in public health 10, 949594

    Comparison of epidemiological characteristicsandtransmissibilityofdifferentstrainsofcovid-19basedontheincidencedataofalllocaloutbreaksinchinaasofmarch1,2022. Frontiers in public health 10, 949594. Pareja, A., Domeniconi, G., Chen, J., Ma, T., Suzumura, T., Kanezashi, H., Kaler, T., Schardl, T., Leiserson, C.,

    work page 2022

  18. [18]

    Latent ordinary differential equations for irregularly-sampled time series, in: Proceedings of the 33rd International Conference on Neural Information Processing Systems (NeurIPS 2019), Curran Associates, Inc. pp. 5320–5330. Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.,

    work page 2019

  19. [19]

    Thompson, B

    On evaluation metrics for graph generative models. arXiv preprint arXiv:2201.09871 . Thorgren, E., Mohammadinodooshan, A., Carlsson, N.,

    work page arXiv

  20. [20]

    Temporal dynamics of user engagement on instagram: A comparative analysis of album, photo, and video interactions, in: Proceedings of the 16th ACM Web Science Conference (WEBSCI 2024), Association for Computing Machinery. pp. 224–234. Trivedi,R.,Farajtabar,M.,Biswal,P.,Zha,H.,2019. Dyrep:Learningrepresentationsoverdynamicgraphs,in:Proceedingsofthe7thInter...

    work page 2024

  21. [21]

    Wang,X.,Jin,Z.,2025

    One Health 16, 100475. Wang,X.,Jin,Z.,2025. Multi-regioninfectiousdiseasepredictionmodelingbasedonspatio-temporalgraphneuralnetworkandthedynamicmodel. PLOS Computational Biology 21, e1012738. Wang, Z., Wang, X., Liang, J.,

    work page 2025

  22. [22]

    CSG-ODE: ControlSynth graph ODE for modeling complex evolution of dynamic graphs, in: Proceedings of the 42nd International Conference on Machine Learning (ICML 2025), PMLR. pp. 64670–64689. Wen,S.,Wang,H.,Metaxas,D.,2022. Socialode:Multi-agenttrajectoryforecastingwithneuralordinarydifferentialequations,in:Proceedingsof the 17th European Conference on Com...

    work page 2025

  23. [23]

    1907–1913

    Graph wavenet for deep spatial-temporal graph modeling, in: Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI 2019), pp. 1907–1913. Xin, X., Li, S.f., Cheng, L., Liu, C.y., Xin, Y.j., Huang, H.l., Beejadhursing, R., Wang, S.s., Feng, L.,

    work page 2019

  24. [24]

    Inductive repre- sentation learning on temporal graphs,

    Government intervention measures effectively control covid-19 epidemic in wuhan, china. Current Medical Science 41, 77–83. Xu,D.,Ruan,C.,Korpeoglu,E.,Kumar,S.,Achan,K.,2020.Inductiverepresentationlearningontemporalgraphs.arXivpreprintarXiv:2002.07962 . Yang, L., Chatelain, C., Adam, S.,

    work page arXiv 2020

  25. [25]

    IEEE Transactions on Knowledge and Data Engineering 38, 1159–1173

    Learnable game-theoretic policy optimization for data-centric self-explanation rationalization. IEEE Transactions on Knowledge and Data Engineering 38, 1159–1173. doi:10.1109/TKDE.2025.3638864. Zheng, Y., Yi, L., Wei, Z.,

    work page doi:10.1109/tkde.2025.3638864 2025