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Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution

T0 review · 2 major / 4 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read TGN predictions can be traced to specific past events once memory updates themselves are attributed, not treated as fixed black boxes.

desk verdict Solid first explainer that actually opens TGN memory updates with conserved LRP trees; the gate heuristic is a soft spot but does not sink the claim. read the letter →

arxiv 2607.07716 v1 pith:PL3OZGZB submitted 2026-07-04 cs.LG cs.AI

Yazheng Liu , Xi Zhang , Sihong Xie , Hui Xiong This is my paper · ORCID
classification cs.LGcs.AI
keywords temporalgraphnetworksexplainabilitylayer-wiserelevancepropagationmemorybacktrackingtopologyattributionlinkpredictionfidelity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Temporal Graph Networks store each node’s history in a memory vector that is updated by every interaction. Existing explainers freeze that memory and therefore miss the long-range causal path from early events to the final prediction. This paper builds two trees that reverse those paths: a topology tree that splits a node embedding into contributions from its current neighbors and their memories, and a memory-backtracking tree that further decomposes each memory into the historical events that wrote it. Layer-wise Relevance Propagation is applied so that the sum of all event contributions exactly equals the model’s logit. Because the mapping from logit to probability is nonlinear, a small optimization problem then selects the sparsest set of events that preserves the original probability. On nine datasets covering link prediction, node property prediction and action classification, the resulting explanations are more faithful than four prior methods.

What carries the argument

The topology attribution tree plus the memory backtracking tree, together with LRP redistribution rules that enforce exact conservation of the logit across both trees.

What would settle it

On any of the nine datasets, replace the LRP-derived contributions with uniform or random scores that still sum to the same logit; if the subsequent optimization still yields equally low Fidelity_KL and Fidelity_prob, the claim that the backtracking trees supply the decisive causal signal fails.

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Extended reading notes

Core claim

Faithful explanations of Temporal Graph Networks require jointly attributing both the spatial neighborhood and the temporal memory-update chain; once Layer-wise Relevance Propagation is applied so that the sum of event contributions equals the logit, an optimization problem can recover a sparse set of historical events that preserves the model’s predicted probability better than methods that freeze memory.

Load-bearing premise

The particular LRP rules chosen for GRU gates and attention products correctly isolate each past event’s true causal share; if those rules systematically mis-allocate relevance inside the memory updater, the later selection step will still pick the wrong events even though the numbers still sum to the logit.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper proposes MemExplainer for explaining Temporal Graph Networks by attributing predictions to both neighboring events and historical events that update node memories. It builds a topology attribution tree (via LRP on the embedding module, Prop. 4.2 and App. A.3–A.4) that decomposes node embeddings into neighbor-event and memory contributions, then a memory backtracking tree (via LRP on GRU/RNN updates, Prop. 4.3 and App. A.5–A.6) that further attributes memory relevance to past events, preserving conservation so that summed event contributions equal the model logits. An optimization objective derived from the KL divergence between original and sparsified predictions (Eqs. 15, 33, 34) selects a sparse set of important events. Experiments on nine datasets across link prediction, node property prediction, and pose-based graph classification show lower Fidelity_KL and Fidelity_prob than TGNNExplainer, TempME, GNNExplainer, PGExplainer, and three ablations, with reported statistical significance in most settings.

Significance. If the results hold, the work fills a clear gap: prior TGN explainers fix final memory vectors and therefore cannot credit the historical events that actually shape those memories. The dual-tree LRP construction with explicit conservation, the KL-based selection that accounts for the nonlinear logit-to-probability map, the multi-task evaluation (including skeleton-graph action classification), and the public code are concrete strengths. The method is of practical interest for high-stakes TGN applications (fraud, healthcare) where users need to know which past interactions drive a decision.

major comments (2)
  1. The LRP rules for the memory updater (Prop. 4.3, App. A.5) adopt the signal-take-all heuristic for GRU gates and the AttnLRP half-and-half split for attention bilinears (App. A.4). Conservation of the scalar logit still holds, but these redistribution choices are heuristics; if they systematically mis-attribute relevance inside the memory module, the subsequent optimization (Eq. 15) can select the wrong events even while fidelity numbers look good. A short sensitivity study that replaces signal-take-all with an alternative gate rule (or reports results under pure RNN updates only) would strengthen the claim that the selected events are causally faithful rather than merely conservation-preserving.
  2. The combinatorial selection problem (Eq. 15 / 33) is stated as an exact argmin over binary vectors of fixed cardinality. Section 4.5 quotes O(d_c^3) complexity, yet the manuscript never states how the integer program is solved in practice (exact MIP, greedy, continuous relaxation, etc.). Because the reported fidelity gains rest on this selection step (and the w/o-selection ablation is weaker), the solver and any approximation guarantees should be specified so that the results are reproducible and the optimality claim can be assessed.
minor comments (4)
  1. Figures 5–6 and the corresponding tables in App. A.17 would be easier to read if the y-axis scales were consistent within each task family and if the sparsity axis were labeled with the exact |E*| values used.
  2. Notation for contribution matrices (C_t^u, M_t^{p0 o u}) is dense; a short glossary or a single running example that carries the same numerical values from topology tree through memory tree to the final logit would help readers follow the conservation proofs.
  3. The case-study tables (App. A.20) are informative but the caption should state the global edge budget explicitly so that the visual comparison across methods is fair.
  4. A few typographical issues remain (e.g., “unfaithful due to the nonlinear mapping” in the abstract; occasional missing spaces around math). A light copy-edit pass would suffice.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LRP conservation and the selection objective are algebraic consequences of the chosen redistribution rules, not tautologies that force the claimed event ranking.

full rationale

The paper's central derivation is self-contained. Topology attribution (Prop. 4.2 / Eq. 11–13) and memory backtracking (Prop. 4.3 / Eq. 27–29) apply standard LRP matrix forms (Lemma 4.1) to the TGN embedding and GRU/RNN update equations; the conservation identities 1⊤Ct = logits follow algebraically from the proportional matrices P that satisfy 1⊤P = 1⊤ by construction of LRP, not by fitting to fidelity. The subsequent selection objectives (Eq. 15 for link prediction, Eq. 33 for node property prediction) minimize a KL derived from that conserved logit under a cardinality constraint; they do not re-fit free parameters to the evaluation metrics FidelityKL / Fidelityprob. Empirical gains are measured against external baselines (TGNNExplainer, TempME, GNNExplainer, PGExplainer) and internal ablations (w/o memory, w/o topology, w/o selection) on nine held-out datasets; no free parameter is tuned to those fidelity numbers. Self-citations are limited to ordinary related-work references and do not supply uniqueness theorems or load-bearing premises. The only soft spot is the choice of redistribution heuristics (signal-take-all for GRU gates, AttnLRP half-split for attention bilinears), which is an assumption about attribution fidelity, not a circular reduction of the claimed ranking to the paper's own inputs. Score 0 is therefore the correct outcome.

Assumptions & free parameters 3 free parameters · 3 assumptions · 2 invented entities

The central claim rests on standard LRP conservation, a domain modeling choice for gate redistribution, and two invented tree structures whose correctness is verified only by the conservation algebra and downstream fidelity experiments. Free parameters are the usual algorithmic knobs (depth, neighbor count, sparsity budget) rather than fitted physical constants.

free parameters (3)
  • memory backtracking depth TL = 5 (default)
    Set to 5 in main experiments; sensitivity plots (Figs. 15–16) show that optimal depth varies by dataset and affects both fidelity and runtime.
  • neighbor sample size n = dataset-dependent / 20
    Number of most recent interactions retained for the embedding module; default and sensitivity at n=20 are reported.
  • sparsity budget |E*| / |E(t)| = 0.02–0.10
    Controls the cardinality constraint in the combinatorial selector; curves are shown for 0.02–0.10.
assumptions (3)
  • standard math Layer-wise Relevance Propagation redistributes a neuron’s relevance proportionally to its weighted activations while preserving the sum of relevance (Lemma 4.1).
    Invoked throughout Sections 4.2–4.3 and proved for the linear case in Appendix A.2.
  • domain assumption For multiplicative gates in GRU, the signal-take-all rule assigns all relevance to the signal neuron and none to the gate (Wu et al., 2022).
    Adopted without derivation in Proposition 4.3 / Appendix A.5; alternative redistribution rules would change the event scores.
  • domain assumption AttnLRP half-and-half split for bilinear attention products is a valid relevance decomposition.
    Used for the graph-attention embedding case (Appendix A.4); taken from Achtibat et al. 2024.
invented entities (2)
  • topology attribution tree
    purpose: Hierarchical structure that attributes a node embedding to neighboring events and leaf memory vectors via successive LRP steps.
    Defined in Section 4.2 and Algorithm 2; no independent existence outside the method.
  • memory backtracking tree
    purpose: Chronological tree that further attributes each leaf memory contribution to the historical events that updated it.
    Defined in Section 4.3 and Algorithm 5; correctness rests on the LRP rules for the memory updater.

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Cite this review

Pith. "Pith review of Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution." pith.science (2026). https://pith.science/paper/PL3OZGZB

@misc{pith2026260707716,
  author       = {Pith},
  title        = {Pith review of: Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PL3OZGZB}},
  note         = {Machine review of arXiv:2607.07716}
}
read the original abstract

Temporal graphs are ubiquitous in real-world applications and Temporal Graph Networks (TGNs) have achieved superior predictive accuracy. Understanding which historical events drive model predictions can enhance trustworthiness of TGNs. Existing explanation methods overlook the memory module, the core component that records and updates node histories, leaving the influence of past events unexplored. To address this, we attribute TGNs predictions through the topology attribution tree and memory backtracking tree. The topology attribution tree captures the influence of neighbors and their memory vectors, then the memory backtracking tree quantifies how historical events shape node memory vectors. We apply the LRP in TGNs, ensuring that the total contribution of events equals the logits of model. Finally, top-k selection may be unfaithful due to the nonlinear mapping from logits to probabilities, we design optimization objectives to identify the important events. Experiments on nine temporal graph datasets, spanning node property prediction, link prediction tasks and graph classification tasks, show that our method provides faithful explanations and outperforms state-of-the-art baselines. The code is available at https://github.com/yazhengliu/MemExplainer

Figures

Figures reproduced from arXiv: 2607.07716 by the authors.

Figure 1
Figure 1. Overview of TGNs and our explainability framework. (a) Temporal graph: each node has a memory vector and each event has features. (b) The memory module in TGNs: events are processed in batches. In the batch 1, the node 3 and 2 update their memory, because they receive the message from event e1 and e2. For event e1 = (1, 3, t1), the message is constructed from the memories of source node 1, destination node 3 and the… view at source ↗
Figure 2
Figure 2. The detailed process of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. We obtain these proportional matrices according to the Proposition 4.2. Summing their elements column-wise results in a vector of ones. Based on this property, the total contribution of R [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: The example of building a memory backtracking tree. process of selecting important events for link prediction task. The node property prediction is in Appendix A.12 and Algorithm 3, while the graph classification task is in Appendix A.13 and Algorithm 4. Algorithm 1 Th…
Figure 5
Figure 5. Figure 5: The performance of Fidelitykl. Each figure corresponds to a different dataset. Lower value indicates better performance. 0.02 0.04 0.06 0.08 0.10 Sparsity 0.08 0.10 0.12 0.14 F i d e l i t y p r o b Wikipedia 0.02 0.04 0.06 0.08 0.10 Sparsity 0.20 0.30 0.40 0.50 Reddit…
Figure 6
Figure 6. Figure 6: The performance of Fidelityprob. Each figure corresponds to a different dataset. Lower value indicates better performance. for the temporal evolution of node memories. To address this, we construct a topology attribution tree to quantify the spatial contribution of nei…
Figure 7
Figure 7. Figure 7: The overview of the LRP decomposition when the fupdate is GRU function Ur = Ug = Uh =  0.1 0 0 0.1  , br = bg = bh = [0, 0], R(s t u ) =  1 2 3 4 . Forward propagation: r t u = [0.526, 0.531], g t u = [0.537, 0.549], ˜s t u = [0.075, 0.080], s t u = [0.086, 0.179].…
Figure 8
Figure 8. Figure 8: Running time decomposition: each figure represents a dataset. The x-axis represents the depth of the memory backtracking tree, and the y-axis represents the running time. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: The performance of FidelityKL. Each figure corresponds to a different dataset. First and second rows represent link prediction and node property prediction, respectively. Lower value indicates better performance. The femb is graph attention model. 24 [PITH_FULL_IMAGE:…
Figure 10
Figure 10. Figure 10: The performance of Fidelityprob. Each figure corresponds to a different dataset. First and second rows represent link prediction and node property prediction, respectively. Lower value indicates better performance. The femb is graph attention model. 0.02 0.04 0.06 0.0…
Figure 11
Figure 11. Figure 11: The performance of FidelityKL. Each figure corresponds to a different dataset. First and second rows represent link prediction and node property prediction, respectively. Lower value indicates better performance. The fupdate is RNN model. 25 [PITH_FULL_IMAGE:figures/…
Figure 12
Figure 12. Figure 12: The performance of Fidelityprob. Each figure corresponds to a different dataset. First and second rows represent link prediction and node property prediction, respectively. Lower value indicates better performance. The fupdate is RNN model. initially decreases and the…
Figure 13
Figure 13. Figure 13: The performance of FidelityKL. Each figure corresponds to a different dataset. First and second rows represent link prediction and node property prediction, respectively. Lower value indicates better performance. The number of events from neighboring samples n is 20. …
Figure 14
Figure 14. Figure 14: The performance of Fidelityprob. Each figure corresponds to a different dataset. First and second rows represent link prediction and node property prediction, respectively. Lower value indicates better performance. The number of events from neighboring samples n is 20…
Figure 15
Figure 15. Figure 15: Performance of FidelityKL at different maximum depths of the memory backtracking tree, with each figure representing a different dataset. A.20. Case study We show the explanation results on pose-based action classification task [PITH_FULL_IMAGE:figures/full_fig_p027_…
Figure 16
Figure 16. Figure 16 [PITH_FULL_IMAGE:figures/full_fig_p028_16.png]

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Reference graph

Works this paper leans on

40 extracted references · 5 linked inside Pith

  1. [1]

    Companion Proceedings of the Web Conference 2021 , pages=

    What happens behind the scene? Towards fraud community detection in e-commerce from online to offline , author=. Companion Proceedings of the Web Conference 2021 , pages=

    2021

  2. [2]

    Proceedings of the Royal Society B , volume=

    From temporal network data to the dynamics of social relationships , author=. Proceedings of the Royal Society B , volume=. 2021 , publisher=

    2021

  3. [3]

    Proceedings of the 30th ACM international conference on information & knowledge management , pages=

    Continuous-time sequential recommendation with temporal graph collaborative transformer , author=. Proceedings of the 30th ACM international conference on information & knowledge management , pages=

  4. [4]

    Computer , volume=

    Explainable machine learning for fraud detection , author=. Computer , volume=. 2021 , publisher=

    2021

  5. [5]

    2021 , publisher=

    Explainable credit card fraud detection with image conversion , author=. 2021 , publisher=

    2021

  6. [6]

    NPJ digital medicine , volume=

    Machine intelligence in healthcare—perspectives on trustworthiness, explainability, usability, and transparency , author=. NPJ digital medicine , volume=. 2020 , publisher=

    2020

  7. [7]

    BMC medical informatics and decision making , volume=

    Explainability for artificial intelligence in healthcare: a multidisciplinary perspective , author=. BMC medical informatics and decision making , volume=. 2020 , publisher=

    2020

  8. [8]

    arXiv preprint arXiv:2006.10637 , year=

    Temporal graph networks for deep learning on dynamic graphs , author=. arXiv preprint arXiv:2006.10637 , year=

    arXiv 2006

Show all 40 references
  1. [9]

    Rex Ying and Dylan Bourgeois and Jiaxuan You and Marinka Zitnik and Jure Leskovec , booktitle=

  2. [10]

    Advances in neural information processing systems , volume=

    Parameterized explainer for graph neural network , author=. Advances in neural information processing systems , volume=

  3. [11]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , year=

    Flowx: Towards explainable graph neural networks via message flows , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , year=

  4. [12]

    The Eleventh International Conference on Learning Representations , year=

    Explaining temporal graph models through an explorer-navigator framework , author=. The Eleventh International Conference on Learning Representations , year=

  5. [13]

    Advances in Neural Information Processing Systems , volume=

    Tempme: Towards the explainability of temporal graph neural networks via motif discovery , author=. Advances in Neural Information Processing Systems , volume=

  6. [14]

    CVPR , year=

    Explainability methods for graph convolutional neural networks , author=. CVPR , year=

  7. [15]

    Sch¨utt and Klaus-Robert M¨uller and Gr´egoire Montavon , journal=

    Thomas Schnake and Oliver Eberle and Jonas Lederer and Shinichi Nakajima Kristof T. Sch¨utt and Klaus-Robert M¨uller and Gr´egoire Montavon , journal=. Higher-order explanations of graph neural networks via relevant walks , year=

  8. [16]

    PloS one , volume=

    On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation , author=. PloS one , volume=. 2015 , publisher=

    2015

  9. [17]

    arXiv preprint arXiv:2001.06216 , year=

    GraphLIME: Local interpretable model explanations for graph neural networks , author=. arXiv preprint arXiv:2001.06216 , year=

    2001 arXiv

  10. [18]

    GLOBECOM 2022-2022 IEEE Global Communications Conference , pages=

    An explainer for temporal graph neural networks , author=. GLOBECOM 2022-2022 IEEE Global Communications Conference , pages=. 2022 , organization=

    2022

  11. [19]

    The International Journal of Advanced Manufacturing Technology , volume=

    Layer-wise relevance propagation for interpreting LSTM-RNN decisions in predictive maintenance , author=. The International Journal of Advanced Manufacturing Technology , volume=. 2022 , publisher=

    2022

  12. [20]

    IEEE Transactions on Network Science and Engineering , year=

    COMEDY: Continuous-Time Anomalous Edge Detection in Dynamic Networks , author=. IEEE Transactions on Network Science and Engineering , year=

  13. [21]

    ACM Transactions on Information Systems , volume=

    TCGC: Temporal collaboration-aware graph co-evolution learning for dynamic recommendation , author=. ACM Transactions on Information Systems , volume=. 2025 , publisher=

    2025

  14. [22]

    IEEE Transactions on Knowledge and Data Engineering , year=

    Temporal insights for group-based fraud detection on e-commerce platforms , author=. IEEE Transactions on Knowledge and Data Engineering , year=

  15. [23]

    Advances in neural information processing systems , volume=

    Inductive representation learning on large graphs , author=. Advances in neural information processing systems , volume=

  16. [24]

    Retrieved December 2021 from http://snap

    Snap datasets: Stanford large network dataset collection , author=. Retrieved December 2021 from http://snap. stanford. edu/data , year=

    2021

  17. [25]

    Advances in Neural Information Processing Systems , volume=

    Towards better evaluation for dynamic link prediction , author=. Advances in Neural Information Processing Systems , volume=

  18. [26]

    Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining , pages=

    Predicting dynamic embedding trajectory in temporal interaction networks , author=. Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining , pages=

  19. [27]

    Information sciences institute technical report, University of Southern California , volume=

    The Enron email dataset database schema and brief statistical report , author=. Information sciences institute technical report, University of Southern California , volume=

  20. [28]

    Journal of the American Society for Information Science and Technology , volume=

    Patterns and dynamics of users' behavior and interaction: Network analysis of an online community , author=. Journal of the American Society for Information Science and Technology , volume=. 2009 , publisher=

    2009

  21. [29]

    Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining , pages=

    Laplacian change point detection for dynamic graphs , author=. Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining , pages=

  22. [30]

    Advances in Neural Information Processing Systems , volume=

    Temporal graph benchmark for machine learning on temporal graphs , author=. Advances in Neural Information Processing Systems , volume=

  23. [31]

    arXiv preprint arXiv:2403.06425 , year=

    A differential geometric view and explainability of gnn on evolving graphs , author=. arXiv preprint arXiv:2403.06425 , year=

    arXiv

  24. [32]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Explainability in graph neural networks: A taxonomic survey , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2022 , publisher=

    2022

  25. [33]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Yolo-pose: Enhancing yolo for multi person pose estimation using object keypoint similarity loss , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

  26. [34]

    2011 International conference on computer vision , pages=

    HMDB: a large video database for human motion recognition , author=. 2011 International conference on computer vision , pages=. 2011 , organization=

    2011

  27. [35]

    arXiv preprint arXiv:2402.05602 , year=

    Attnlrp: attention-aware layer-wise relevance propagation for transformers , author=. arXiv preprint arXiv:2402.05602 , year=

    arXiv

  28. [36]

    arXiv preprint arXiv:2404.00060 , year=

    Temporal graph networks for graph anomaly detection in financial networks , author=. arXiv preprint arXiv:2404.00060 , year=

    arXiv

  29. [37]

    2024 International Conference on Machine Learning and Applications (ICMLA) , pages=

    Developing the temporal graph convolutional neural network model to predict hip replacement using electronic health records , author=. 2024 International Conference on Machine Learning and Applications (ICMLA) , pages=. 2024 , organization=

    2024

  30. [38]

    arXiv preprint arXiv:2511.01249 , year=

    KAT-GNN: A knowledge-augmented temporal graph neural network for risk prediction in electronic health records , author=. arXiv preprint arXiv:2511.01249 , year=

  31. [39]

    SIGKDD , year=

    XGNN: Towards Model-Level Explanations of Graph Neural Networks , author=. SIGKDD , year=

  32. [40]

    Proceedings of the IEEE international conference on computer vision , pages=

    From actemes to action: A strongly-supervised representation for detailed action understanding , author=. Proceedings of the IEEE international conference on computer vision , pages=

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