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REVIEW 5 major objections 6 minor 38 references

A Comparative Study on Dynamic Graph Embedding based on Mamba and Transformers

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Mamba-based models match or beat transformers on dynamic graph link prediction.

desk verdict Useful empirical comparison, but the headline Mamba-vs-Transformer claim hinges on an ambiguous classifier split and a missing GraphSSM baseline. read the letter →

arxiv 2412.11293 v2 pith:6IKXNK2D submitted 2024-12-15 cs.LG cs.AI

Ashish Parmanand Pandey , Alan John Varghese , Sarang Patil , Mengjia Xu This is my paper · ORCID
classification cs.LGcs.AI
keywords dynamicgraphembeddingstate-spacemodelsMambatransformerslinkpredictiontemporalgraphsneuralnetworks
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 tries to establish that selective state-space models (Mamba) can substitute for attention-based transformers in dynamic graph embedding, yielding comparable or better temporal link prediction on volatile real-world benchmarks while cutting the computational cost of long histories from quadratic to linear. The authors introduce three models, ST-TransformerG2G, DG-Mamba, and GDG-Mamba, and evaluate them on five datasets, reporting that Mamba variants outperform transformer-based models on datasets with high temporal variability. If correct, the finding matters because attention's quadratic cost is the main barrier to modeling long graph histories, so linear-complexity SSMs would let temporal graph models scale to longer and larger sequences.

What carries the argument

The carrying object is the Mamba selective state-space layer, a linear-time sequence model whose state update uses input-dependent matrices B, C, and time step delta to selectively compress history. In DG-Mamba and GDG-Mamba, this layer processes the per-node sequence of graph-snapshot features, optionally preprocessed by GINE convolutions that fold node and edge attributes into node features, followed by mean pooling, a linear-tanh projection, and two heads emitting Gaussian embedding means and variances. The Mamba layer replaces the transformer's pairwise attention so that temporal mixing cost is linear in lookback length, and the hidden-attention identity is used to interpret the learned state matrix as cumulative attention-like weights between timestamps.

What would settle it

If the classifier were trained on node pairs sampled from test-snapshot edges, the reported numbers would not measure temporal generalization. A direct check would be to re-run the link prediction evaluation with a strict temporal split where the classifier sees no edges from the test interval, then compare MAP and MRR; if the performance drops substantially, the paper's central claim would be weakened.

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Extended reading notes

Core claim

The central claim is that Mamba-based models achieve comparable or superior performance to transformer-based approaches in link prediction tasks while offering significant computational efficiency gains on longer sequences. On the paper's own terms, DG-Mamba and GDG-Mamba beat TransformerG2G and ST-TransformerG2G in MAP and MRR on UCI, Bitcoin-OTC, and Reality Mining, match them on the stable SBM benchmark, and fall short only on Slashdot, which has just 12 timestamps. The paper also claims that analysis of the learned state transition matrix A reveals an attention-like mechanism, so Mamba is not merely an efficient approximation but captures focused long-range temporal dependencies, and that measured FLOPs and MACs scale linearly with lookback while the transformer baselines grow quadratically.

Load-bearing premise

The load-bearing premise is that the logistic regression link prediction classifier is trained only on edges from training timestamps, so that the reported MAP and MRR measure prediction of future graph snapshots rather than reconstruction of already-seen edges.

Editorial extensions

If this is right

  • Dynamic graph embedding can use longer lookback windows without the quadratic blowup of attention, so models can attend to entire histories rather than a few recent snapshots.
  • Adding edge features through GINE convolutions helps most on transient datasets, suggesting that spatial edge information is key where links churn quickly.
  • On datasets with very few timestamps, the extra complexity of SSMs and GINE can hurt, so transformer with GCN remains the better choice for short histories.
  • The attention-like interpretation of the Mamba state matrix gives a way to inspect what temporal dependencies a trained model has learned, similar to attention weights.
  • Linear complexity makes these models candidates for streaming or online link prediction on long-running dynamic graphs.

Reading between the lines

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

  • If the hidden-attention view of Mamba is faithful, one could distill trained Mamba graph models into sparse or structured attention transformers that run fast on existing hardware, or vice versa.
  • The same architecture could be extended to continuous-time temporal graphs by replacing fixed snapshots with event-driven state updates, where the linear scan maps naturally to event sequences.
  • The reported efficiency suggests a testable extension: stress-test lookback length on large graphs to see where transformer memory fails and Mamba plateaus in accuracy.
  • The probabilistic Gaussian output already gives per-node uncertainty; a natural next step is to calibrate those uncertainties on future-edge prediction and use them for anomaly detection, not just ranking.
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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

5 major / 6 minor

Summary. This paper presents a comparative empirical study of dynamic graph embedding methods based on transformer and Mamba (state-space) architectures. The authors propose three models: ST-TransformerG2G, which augments a prior TransformerG2G model with graph convolutional layers; DG-Mamba, which replaces attention with a selective state-space model; and GDG-Mamba, which adds GINE edge convolutions before the Mamba layer. The models embed each node as a multivariate Gaussian and are trained with a triplet-based contrastive loss. The experiments evaluate temporal link prediction on five datasets (Reality Mining, UCI, SBM, Bitcoin-OTC, Slashdot) using MAP and MRR, with results reported across lookback values and against several baselines. The central claim is that Mamba-based models achieve comparable or superior link prediction performance to transformers while being computationally more efficient, especially on datasets with high temporal variability.

Significance. If the empirical claims hold, the paper would provide a useful data point for the dynamic-graph-embedding community: it shows that selective state-space models can replace attention in a probabilistic temporal graph encoder without losing accuracy, and it analyzes the learned state matrices to motivate this finding. The paper's strengths include the breadth of datasets, per-lookback reporting, multiple random initializations with standard deviations, and a direct FLOPs/MACs comparison. The main contribution is comparative rather than theoretical; its value depends on the correctness of the evaluation protocol, which is currently not fully specified. The absence of code, the ambiguous classifier split, and the omission of a cited SSM baseline (GraphSSM) are the main factors limiting the paper's current conclusiveness.

major comments (5)
  1. [Section 4.3] The temporal split for the logistic regression link-prediction classifier is unspecified. Section 4.2 states that after training, the model is used to 'predict and save the embeddings of the nodes for all timestamps,' and Section 4.3 describes the classifier as trained on positive and negative pairs 'sampled ... from each graph snapshot.' This wording does not restrict classifier training to the 70% training timestamps or to the validation timestamps. If test-snapshot edges enter classifier fitting, the MAP/MRR values in Tables 5-10 reflect memorization rather than temporal link prediction on held-out snapshots, which would invalidate the paper's central performance claim. The authors should state explicitly that classifier training pairs come only from training/validation timestamps, or, if they do not, revise the protocol and all reported numbers accordingly.
  2. [Tables 2-4 and Table 10] The hyperparameter and lookback selection procedure is not clearly separated from the test set. Tables 2-4 report per-dataset optimal lookbacks and Optuna-tuned hyperparameters, and Table 10 selects the best-performing lookback for each model. If these values were chosen by maximizing MAP on the test split, the reported results are optimistically biased and the comparison is not a fair evaluation of model selection. The paper should state whether the Optuna objective and lookback choices used the validation split only, and should provide validation-selected results or a nested selection procedure.
  3. [Section 2.2 and Section 4.3] GraphSSM [27] is cited as an existing state-space model for temporal graphs, yet it is not included as a baseline in Table 10 or anywhere in the experiments. For a paper whose title and abstract promise a comparative study of Mamba-based and transformer-based dynamic graph embedding, omitting the most relevant SSM baseline weakens the comparison. The authors should either add GraphSSM to the experiments or justify its exclusion, for example by explaining that it targets continuous-time event data or a different link prediction protocol.
  4. [Table 10 and Section 4.3] The baseline comparison is incomplete and inconsistently reported. The prose in Section 4.3 lists ROLAND as one of the six baselines, but Table 10 contains results for only DynGEM, dyngraph2vecAE, dyngraph2vecAERNN, EvolveGCN, DynG2G, and the proposed/prior transformer models; ROLAND results are absent. Additionally, several baseline rows report no standard deviations, making it unclear whether those numbers were obtained under the same five-seed protocol and the same evaluation split as the proposed models. The authors should provide complete baseline results under a shared protocol or explicitly state which numbers were taken from prior publications.
  5. [Table 9] The DG-Mamba results on Slashdot contain a striking anomaly: for lookback l=5 the MAP is 0.0006 +/- 0.0003, while at l=3 it is 0.0676 +/- 0.0009. This sudden collapse is not explained in the text and may indicate a training failure, a degenerate embedding, or a numerical issue in that configuration. Because Table 10 uses the best lookback for DG-Mamba on Slashdot, this anomaly does not directly affect the headline comparison, but it should be investigated and either explained or removed, and the reported best value should be verified.
minor comments (6)
  1. [Section 4.1] The Slashdot dataset description is inconsistent: Table 1 lists 50,825 nodes while the prose says 50,824 nodes; the two should be reconciled.
  2. [Abstract and Table 1] The abstract refers to 'Bitcoin' while the experiments use the Bitcoin-OTC dataset; use the full name consistently throughout the paper.
  3. [Section 4.3] The classifier is said to use 'Mean Average Precision (MAP) loss,' which is not a standard loss for logistic regression; the authors should define the exact objective or clarify that they mean a ranking-style loss.
  4. [Tables 3 and 4] Several hyperparameter values, such as dmodel = 1899 for UCI in Table 3 and dmodel = 1000 for SBM in Table 4, appear to equal the number of nodes in the dataset; this is surprising for a model dimension and should be explained in the text.
  5. [Section 4.5] The computational efficiency comparison reports FLOPs and MACs as a function of lookback, but it does not report wall-clock training or inference times; a brief runtime comparison would strengthen the efficiency claim.
  6. [Section 4.4] The visual analysis of state and attention matrices is qualitative and uses only two datasets; the authors should state whether the figures are representative or provide a quantitative summary of the claimed difference in temporal focus.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the empirical comparison is self-contained, includes independent baselines, and does not reduce its performance claims to fitted inputs or self-citations.

full rationale

This paper is an empirical comparative study rather than a formal derivation, so most circularity patterns do not apply. The proposed models (ST-TransformerG2G, DG-Mamba, and GDG-Mamba) are new architectures built on the authors' earlier TransformerG2G and DynG2G work, and the headline claim is supported by running these models and external baselines (EvolveGCN, DynGEM, dyngraph2vec) on five public benchmarks. The self-citations to [16] and [12] provide architectural provenance and baseline comparisons, but they are not load-bearing in the sense of substituting for evidence: the paper reports MAP/MRR values from executed experiments, and independent baselines are included in Table 10. The Mamba 'hidden attention' discussion in Section 4.4 is attributed to external reference [38], so it is not presented as an internally derived uniqueness result. No equation in the paper is defined in terms of the quantity it is said to predict, and no fitted parameter is renamed as a prediction. A separate methodological ambiguity exists in Section 4.3, where the logistic-regression classifier is described as trained on node pairs sampled 'from each graph snapshot' without explicitly excluding validation/test snapshots; if test-snapshot edges entered classifier fitting, the reported MAP/MRR would not measure held-out temporal link prediction. This is an evaluation-protocol concern and a correctness risk, not a circularity by construction, and is therefore not counted in the circularity score.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central empirical claims rest on several untested modeling choices: the triplet loss with KL divergence as the training signal, zero-padding of adjacency matrices, validation-based hyperparameter selection, and the specific link prediction classifier protocol. None of these are derived from first principles, and the paper does not ablate them. These are standard practice in the subfield, but they are assumptions nonetheless.

free parameters (3)
  • Per-dataset optimal lookback = Varies by dataset and model; see Tables 2-4
    Selected from {1,..,5} by validation MAP; headline results use these chosen values.
  • Optuna-tuned hyperparameters (dmodel, dstate, dconv, lr, weight decay, intermediate space, dropout) = Per dataset in Tables 3-4
    Tuned on validation to maximize MAP; reported performance depends on these values.
  • Embedding dimension dout = 64 or 256 per dataset
    Set to match prior TransformerG2G; affects capacity and comparability.
assumptions (4)
  • domain assumption Triplet-based contrastive loss with KL divergence produces embeddings that are useful for temporal link prediction.
    Invoked in Section 3.4 as the training objective for all models; no evidence is given that this loss is optimal or standard for link prediction.
  • domain assumption Zero-padding adjacency matrices to the maximum node count n preserves the information needed for embedding.
    Stated in Data Preprocessing; padding introduces artificial structure and assumes absent nodes carry no signal.
  • domain assumption Optuna validation-based hyperparameter search and early stopping on validation loss generalize to test timestamps.
    The models are tuned per dataset on validation; the paper assumes this does not overfit to the test period.
  • domain assumption MAP and MRR on the 1:10 positive-negative sampling are meaningful link prediction metrics.
    Evaluated in Section 4.3; class imbalance and sampling strategy affect the scores materially.

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Cite this review

Pith. "Pith review of A Comparative Study on Dynamic Graph Embedding based on Mamba and Transformers." pith.science (2026). https://pith.science/paper/6IKXNK2D

@misc{pith2026241211293,
  author       = {Pith},
  title        = {Pith review of: A Comparative Study on Dynamic Graph Embedding based on Mamba and Transformers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6IKXNK2D}},
  note         = {Machine review of arXiv:2412.11293}
}
read the original abstract

Dynamic graph embedding has emerged as an important technique for modeling complex time-evolving networks across diverse domains. While transformer-based models have shown promise in capturing long-range dependencies in temporal graph data, they face scalability challenges due to quadratic computational complexity. This study presents a comparative analysis of dynamic graph embedding approaches using transformers and the recently proposed Mamba architecture, a state-space model with linear complexity. We introduce three novel models: TransformerG2G augment with graph convolutional networks, \mathcal{DG}-Mamba, and \mathcal{GDG}-Mamba with graph isomorphism network edge convolutions. Our experiments on multiple benchmark datasets demonstrate that Mamba-based models achieve comparable or superior performance to transformer-based approaches in link prediction tasks while offering significant computational efficiency gains on longer sequences. Notably, \mathcal{DG}-Mamba variants consistently outperform transformer-based models on datasets with high temporal variability, such as UCI, Bitcoin, and Reality Mining, while maintaining competitive performance on more stable graphs like SBM. We provide insights into the learned temporal dependencies through analysis of attention weights and state matrices, revealing the models' ability to capture complex temporal patterns. By effectively combining state-space models with graph neural networks, our work addresses key limitations of previous approaches and contributes to the growing body of research on efficient temporal graph representation learning. These findings offer promising directions for scaling dynamic graph embedding to larger, more complex real-world networks, potentially enabling new applications in areas such as social network analysis, financial modeling, and biological system dynamics.

Figures

Figures reproduced from arXiv: 2412.11293 by the authors.

Figure 1
Figure 1. The proposed ST-TransformerG2G model architecture enhanced the previous [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. The main architecture of the proposed DG-Mamba model. It processes a sequence of discrete-time graph snapshots {Gt} T t=1, where a look-back parameter l = {1, 2, 3, 4, 5} allows for historical context integration. Each graph snapshot first goes through projection and convolution to capture localized node features while maintaining spatial relationships. The SSM layer is followed to efficiently capture long-range tem… view at source ↗
Figure 3
Figure 3. The main architecture of the GDG-Mamba model. It first processes a series of discrete-time graph snapshots {Gt} T t=1 using the GINE convolution to enhance the spatial representation of the graph by considering both node and edge-level features at each timestamp. The generated graph sequence representations are then processed through the Mamba block to capture temporal dynamics, followed by mean pooling and a linear… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Comparison of MAP (1st column) and MRR (2nd colum) for temporal link [PITH_FULL_IMAGE:figures/full_fig_p022_4.png]
Figure 5
Figure 5. Figure 5: Comparison of DG-Mamba state transition matrices (Columns 1, 3, 5) and TransformerG2G attention matrices (Columns 2, 4, 6) across 24 randomly selected time steps for Reality Mining. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_5.png]
Figure 6
Figure 6. Figure 6: Comparison of DG-Mamba state transition matrix and TransformerG2G atten￾tion matrix for SBM for odd timestamps from 5 to 33. 4.5. Computational Efficiency Comparisons and Analysis We compare the computational cost of GDG -Mamba, DG -Mamba, Trans￾formerG2G, and ST -Tran…
Figure 7
Figure 7. Figure 7: Computational cost comparison of GDG-Mamba, DG-Mamba, TransformerG2G, and ST -TransformerG2G as a function of the lookback window size. Left and Right display the measured FLOPs and MACs values over lookbacks. 5. Conclusion This study provides a comparative analysis of…

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