Temporal-Aware Evaluation and Learning for Temporal Graph Neural Networks

Junwei Su; Shan Wu

REVIEW 4 major objections 6 minor 43 references

Temporal-Aware Evaluation and Learning for Temporal Graph Neural Networks

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A proof that AP and AU-ROC can't see temporal error patterns, plus the metric that fixes it.

desk verdict A useful empirical observation buried under an incorrect theorem and an unexplained training signal. read the letter →

arxiv 2412.07273 v2 pith:YR5AJHJD submitted 2024-12-10 cs.LG cs.AI

Junwei Su , Shan Wu This is my paper · ORCID

classification cs.LGcs.AI

keywords temporalgraphneuralnetworksevaluationmetricsvolatilityclusteringerrorpatternsHopkinsstatisticlinkpredictionregularizationinstance-based

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

This paper argues that the standard metrics used to evaluate Temporal Graph Neural Networks (TGNNs) cannot distinguish between predictions that make the same number of errors but arrange those errors in different temporal patterns, such as bursts of failures. It proves this insensitivity in Theorem 3.1 and introduces a new statistic, Volatility-Cluster Statistics (VCS), adapted from Hopkins statistics, that measures how clustered prediction errors are in time. The paper also converts VCS into a differentiable training objective, Volatility-Cluster-Aware (VCA) learning, which reduces error clustering in TGNNs. A sympathetic reader should care because if the claim is right, current TGNN benchmarks systematically miss a failure mode that matters for fault-tolerant and financial systems.

What carries the argument

The central object is the Volatility-Cluster Statistics (VCS), built from a Hopkins-style ratio $T(E_{disg}, E_r) = D_r / (D_r + D_{disg})$ that compares the summed nearest-neighbour distances from randomly sampled times to the disagreement events against the same sum computed within the disagreement set. VCS is the absolute deviation $|1/2 - T|$ averaged over repeated random samples; a value near 0.5 indicates random timing of errors, near 1 indicates clustering, and near 0 indicates regular spacing. The training variant VCA replaces the non-differentiable nearest-neighbour distance with $d_{soft}(e, E) = -\log(\sum_{e' \neq e} \exp(-\beta |t_e - t_{e'}|))/\beta$, making the cluster penalty a differentiable regularizer that can be added to the prediction loss.

What would settle it

Take a fixed sequence of correct/incorrect test labels with a fixed number of errors and shift the confidence scores among the errors (for instance, give the clustered errors higher scores); if AP or AU-ROC changes while the disagreement pattern stays the same, the theorem's reduction to a mere disagreement count fails.

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Extended reading notes

Core claim

The central claim is that any instance-based evaluation metric, defined per-sample and then aggregated, collapses all information about a model's predictions into a count of disagreements with ground truth. Two predictors that make the same number of mistakes but concentrate those mistakes at different times, randomly scattered versus grouped in a short window, receive identical AP and AU-ROC scores under this characterization. The paper formalizes this as Theorem 3.1 and demonstrates empirically that memory-based and RNN-based TGNNs produce distinctly clustered error patterns while attention-based models are more uniform, a difference standard metrics do not surface. It then establishes that the proposed VCS metric detects such clustering and that the VCA learning objective mitigates it, with reported experiments showing VCA reduces VCS by about 0.09 to 0.10 on average across datasets.

Load-bearing premise

The theorem that instance-based metrics see only disagreement counts assumes such a metric never looks at the model's numeric scores, only at whether each prediction is right or wrong.

Editorial extensions

If this is right

If VCS is adopted, model selection among TGNNs can incorporate error timing rather than only error count, which matters for real-time systems that prefer uniformly distributed failures.
The paper's experiments show memory-based TGNNs (TGN, Tiger) cluster errors at the end of the test period while RNN-based models (JODIE, DyRep) cluster at the beginning, implying that the temporal mechanism of a TGNN shapes its error dynamics.
The reported results indicate that VCA regularization reduces VCS with little or no AP loss at a modest regularization strength, so mitigating error bursts does not necessarily sacrifice predictive accuracy.
Attention-based models already exhibit near-uniform error distributions in the paper's experiments, so VCA offers comparatively small improvements for that class of model.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the same insensitivity that VCS addresses applies to any evaluation that only counts hard errors, so a VCS-style correction could serve other temporal predictors such as traffic or anomaly detection, not just TGNNs.
Editorial inference: because AP and AU-ROC read score rankings, a metric that blends ranking with temporal clustering may capture more nuance than VCS's hard-error formulation; the paper does not explore this direction.
Editorial inference: VCS measures clustering in absolute clock time; an alternative worth testing is measuring in event-index or log-time space, which would make the statistic invariant to uneven event arrival rates.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper has a genuinely useful empirical core, but the central theorem is wrong and the VCA training objective, as written, cannot train. It attacks a real gap: instance-based metrics like AP and AU-ROC throw away the temporal structure of errors, and volatility clustering is genuinely important for fault-tolerant and financial applications. VCS, a Hopkins statistic on the time axis, is a sensible complement to AP. The empirical observation that memory-based TGNNs cluster errors late in the test period while RNN-based models cluster them early is fresh and could be useful for model selection. The theory, however, is not sound. Theorem 3.1 claims any instance-based metric with the same Hamming distance to the ground truth must give the same value. The proof in Appendix A only gets that by assuming f(y_i, y_hat_i) = c * 1[y_hat_i != y_i]. That is not what AP or AU-ROC do. They are functions of the score or rank; you can have two predictions with the same number of thresholded errors and different AP. The theorem as stated is simply false, and it carries the paper's framing. That is not a side issue. I also have a serious problem with VCA. The regularizer in Eq. 4.4 is built on Tsoft, which uses the set Edisg of hard-thresholded disagreements. Even with the soft-min distance, the selection of Edisg is not differentiable with respect to the model parameters. As written, the regularizer supplies no gradient at all. The paper reports consistent VCS reductions, so either I am missing an approximation, or the experiments are not implementing what the text describes. The text does not tell us which, and beta is never reported. That makes the central empirical claim hard to trust. The experimental section is also missing a sanity check for VCS itself. There is no synthetic dataset with known ground-truth error patterns showing that VCS separates random, clustered, and regular patterns. Without that, the differences across model families could be an artifact of the metric. On the plus side, the authors clearly understand TGNNs and the applications, and the idea of a volatility-aware regularizer has potential. The paper is not nonsense, and the empirical observations, if they survive a proper check, would be a modest contribution to evaluation practice. But this version is not publishable. The false theorem needs to be removed or corrected, and the VCA gradient issue needs to be resolved or made explicit. If the empirical part holds up, a rewritten paper could be worth a real review. For this version, I would not accept it, and I would not cite it.

Referee Report

4 major / 6 minor

Summary. The paper studies evaluation metrics for temporal graph neural networks (TGNNs), arguing that instance-based metrics such as AP and AU-ROC reduce a model's predictions to a mere disagreement count and therefore cannot capture temporal structures such as volatility clusters. It introduces a new metric, volatility-cluster statistics (VCS), inspired by Hopkins statistics, and a differentiable training objective, volatility-cluster-aware (VCA) learning, that regularizes against clustered errors. Experiments on five datasets and six TGNN models show that different TGNN families exhibit different temporal error patterns and that training with VCA reduces VCS values.

Significance. If the formal claim were correct, the paper would address a genuine gap: TGNN evaluation currently relies on AP and AU-ROC, which ignore temporal order, and the observed error-clustering patterns (memory-based models clustering at the end, RNN-based at the beginning, attention-based uniform) are interesting and potentially useful for model selection and system design. The VCS metric is intuitive and the empirical study is reasonably broad, covering five datasets and six models. However, the main theoretical result is invalid as stated, and the empirical contribution is weakened by the fact that VCA directly optimizes a smooth surrogate of VCS. The paper's core conclusion that AP and AU-ROC are merely counting processes is unsupported and in fact false for score-based metrics.

major comments (4)

[Section 3, Theorem 3.1 and Appendix A] The proof of Theorem 3.1 assumes that f(y_i, ŷ_i) can be written as c·1[ŷ_i ≠ y_i], i.e., that an instance-based metric sees only binary correctness per sample. This is false for AP and AU-ROC, which are functions of predicted scores and their rankings. For example, with ground truth Y = [1, 0, 1, 0], the prediction score vectors (0.2, 0.1, 0.9, 0.3) and (0.9, 0.1, 0.4, 0.2) both have Hamming distance 1 from Y, but their AP values are 0.833 and 1, respectively. Thus Theorem 3.1 is false for the metrics it names, and the claimed 'counting process' characterization is not established.
[Section 3, Definition 2] Definition 2 allows f to be any function of (y_i, ŷ_i), including one that returns the predicted score. The proof in Appendix A unilaterally restricts f to be c·1[ŷ_i ≠ y_i]. This restriction is not implied by link prediction being reducible to binary classification, since classification outputs are typically continuous scores. Without this restriction, the conclusion that all instance-based metrics depend only on the disagreement count does not follow.
[Section 4, Eq. (4.4) and Table 1] The VCA loss is a smooth and differentiable version of VCS itself. Consequently, the consistent decrease in VCS reported in Table 1 is a direct effect of optimizing an objective that includes that quantity. This demonstrates that the optimizer can trade off AP against VCS, but it does not by itself show that VCA captures a generalizable property beyond minimizing the metric it is defined from. The paper would need a comparison against alternative regularizers or an evaluation on metrics not included in the training objective to support the broader claim.
[Section 3 and Appendix A] The main text defers technical proofs and experimental details to the extended arXiv version (Su and Wu 2024), which is a self-citation. The proof of Theorem 3.1 is actually contained in Appendix A of this submission, so the pointer is unnecessary and obscures the fact that the proof is present. Please reference the appendix within the submission rather than an external self-citation.

minor comments (6)

[Section 3, Visualization Example] In the text, 'Fig. 2(b) is the pattern for regular error' appears to be a typo; the caption labels (b) as 'Cluster Error' and (c) as 'Regular Error'.
[References] References Xu et al. 2020a and 2020b are identical (both arXiv:2002.07962); one should be removed.
[Throughout] The model name 'JOIDE' appears to be a typo for 'JODIE'.
[Section 4 and Algorithm 3] Equation (4.4) uses a squared absolute difference of the VCS term, while Algorithm 3 uses an absolute value; please harmonize the notation.
[Table 1] The table reports means and standard deviations but no significance tests; several VCS reductions are within one standard deviation (e.g., TGAT on Reddit: 0.13±0.02 vs 0.10±0.02).
[Figure 4] Figure 4 shows variance for τ but the curves for γ have no error bars; please clarify whether these are single runs or averaged results.

Circularity Check

1 steps flagged · score 6.0 of 10

Theorem 3.1's proof assumes the conclusion by restricting f to an error-counting indicator, making AP/AU-ROC 'failure' follow by construction rather than from the stated formalism.

self definitional [Appendix A, proof of Theorem 3.1 (with Definition 2 in Section 3)]
"Proof. Let bY1 and bY2 be two distinct predictions for the set E with ground-truth Y with µ( bY1, Y, E) = µ( bY2, Y, E), ... As link-prediction problem can be reduced to a binary classification problem, this means that f (.) can be written as, f (yi, byi) = c · 1[byi ̸= yi], where c is some constant that weight the wrong prediction."

The proof starts by assuming the equality it is supposed to prove, and then restricts f(y_i, ŷ_i) to c·1[ŷ_i ≠ y_i]. That restriction is exactly the theorem's conclusion that instance-based metrics 'reduce all diverse information of predictions to a mere disagreement count.' Definition 2 allows f to be any function of y_i and ŷ_i; for AP and AU-ROC, ŷ_i is a score whose relative ranking matters, so two score vectors with identical Hamming distance can have different AP/AU-ROC values. The theorem therefore does not follow from the formal definition; it is imposed by the proof's choice of f.

full rationale

The central theoretical result, Theorem 3.1, is partially circular. The proof assumes µ(Y_hat1, Y, E) = µ(Y_hat2, Y, E) at the outset, then further assumes f(y_i, ŷ_i) = c·1[ŷ_i ≠ y_i]. This second assumption is precisely the 'mere disagreement count' characterization the theorem claims to establish for instance-based metrics such as AP and AU-ROC. Since Definition 2 permits f to depend on the full predicted score, and AP/AU-ROC are functions of score rankings rather than binary correctness, the theorem's applicability to the metrics it names is not derived but stipulated. The proposed VCS metric itself is adapted from an external Hopkins-statistic construction, with τ and γ tuned on validation, so the VCS/VCA empirical contributions are largely independent of the flawed theorem. The references to the extended arXiv version for technical details are self-citations, but the appendixes here contain the proof and algorithms, so those citations are not load-bearing. The overall circularity is concentrated in the proof of the motivating theorem, while the empirical evaluation of VCS and VCA retains independent content; hence a moderate score of 6 is appropriate.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central new artifacts are the VCS metric and VCA loss; they introduce no new physical or mathematical entities. The main free parameters are tau, gamma, and beta, two of which are tuned empirically. The core theoretical derivation rests on a questionable characterization of instance-based metrics and a false theorem.

free parameters (3)

tau = 5
Number of repeated samples in VCS; chosen for stable estimate (Section 5, Fig. 4a).
gamma = 0.1
Regularization weight in VCA; chosen as a trade-off between VCS reduction and AP loss (Section 5, Fig. 4b,c).
beta = not specified
Sharpness parameter for the soft-min approximation in VCA; no value or ablation is given.

assumptions (3)

ad hoc to paper Instance-based metrics are expressible as g of a set of per-sample functions f(y_i, y_hat_i) depending only on binary disagreement
Definition 2 and the proof in Appendix A; this assumption excludes score-based ranking in AP/AU-ROC and is false.
domain assumption The test period can be represented as a continuous time interval, and random sampling from it provides a valid null model for error distribution
Section 4, VCS construction; assumes the pattern of error timestamps can be meaningfully compared to uniform random points.
ad hoc to paper The link prediction problem can be reduced to binary classification with hard thresholding for the purpose of defining errors
Appendix A, proof of Theorem 3.1; ignores that AP and AU-ROC are rank-based metrics on soft scores.

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Cite this review

Pith. "Pith review of Temporal-Aware Evaluation and Learning for Temporal Graph Neural Networks." pith.science (2026). https://pith.science/paper/YR5AJHJD

@misc{pith2026241207273,
  author       = {Pith},
  title        = {Pith review of: Temporal-Aware Evaluation and Learning for Temporal Graph Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YR5AJHJD}},
  note         = {Machine review of arXiv:2412.07273}
}

read the original abstract

Temporal Graph Neural Networks (TGNNs) are a family of graph neural networks designed to model and learn dynamic information from temporal graphs. Given their substantial empirical success, there is an escalating interest in TGNNs within the research community. However, the majority of these efforts have been channelled towards algorithm and system design, with the evaluation metrics receiving comparatively less attention. Effective evaluation metrics are crucial for providing detailed performance insights, particularly in the temporal domain. This paper investigates the commonly used evaluation metrics for TGNNs and illustrates the failure mechanisms of these metrics in capturing essential temporal structures in the predictive behaviour of TGNNs. We provide a mathematical formulation of existing performance metrics and utilize an instance-based study to underscore their inadequacies in identifying volatility clustering (the occurrence of emerging errors within a brief interval). This phenomenon has profound implications for both algorithm and system design in the temporal domain. To address this deficiency, we introduce a new volatility-aware evaluation metric (termed volatility cluster statistics), designed for a more refined analysis of model temporal performance. Additionally, we demonstrate how this metric can serve as a temporal-volatility-aware training objective to alleviate the clustering of temporal errors. Through comprehensive experiments on various TGNN models, we validate our analysis and the proposed approach. The empirical results offer revealing insights: 1) existing TGNNs are prone to making errors with volatility clustering, and 2) TGNNs with different mechanisms to capture temporal information exhibit distinct volatility clustering patterns. Our empirical findings demonstrate that our proposed training objective effectively reduces volatility clusters in error.

Figures

Figures reproduced from arXiv: 2412.07273 by the authors.

**Figure 2.** An illustration of different error patterns. Fig. 2(a) is the pattern for random error pattern where wrong predictions [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** An illustration of the error patterns across different types of TGNNs. The x-axis represents the time during the test [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: An illustration of the effects of the hyper-parameters [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Illustration of TGNN Training Procedure. The figure depicts the training flow of TGNN for two epochs. The incoming [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Banerjee, A.; and Dave, R. N. 2004. Validating clusters using the Hopkins statistic. In 2004 IEEE International conference on fuzzy systems (IEEE Cat. No. 04CH37542), volume 1, 149--153. IEEE

work page 2004

[2] [2]

P.; Joshi, C

Dwivedi, V. P.; Joshi, C. K.; Luu, A. T.; Laurent, T.; Bengio, Y.; and Bresson, X. 2023. Benchmarking graph neural networks. Journal of Machine Learning Research, 24(43): 1--48

2023

[3] [3]

Errica, F.; Podda, M.; Bacciu, D.; and Micheli, A. 2019. A fair comparison of graph neural networks for graph classification. arXiv preprint arXiv:1912.09893

arXiv 2019

[4] [4]

Guo, S.; Lin, Y.; Feng, N.; Song, C.; and Wan, H. 2019. Attention based spatial-temporal graph convolutional networks for traffic flow forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 33, 922--929

2019

[5] [5]

Haghani, S.; and Keyvanpour, M. R. 2019. A systemic analysis of link prediction in social network. Artificial Intelligence Review, 52: 1961--1995

work page 2019

[6] [6]

Hopkins, B.; and Skellam, J. G. 1954. A new method for determining the type of distribution of plant individuals. Annals of Botany, 18(2): 213--227

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