Mind the truncation gap: challenges of learning on dynamic graphs with recurrent architectures

Hugo Ferreira; Jacopo Bono; Jo\~ao Bravo; Pedro Bizarro; Pedro Saleiro

REVIEW 1 major objections 5 minor 23 references

Mind the truncation gap: challenges of learning on dynamic graphs with recurrent architectures

T0 review · 1 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Full backprop beats truncated training on dynamic graphs by up to 22%.

desk verdict The synthetic task makes the core point convincingly; the real-world gap is real but the attribution to truncation alone is shakier than the paper claims. read the letter →

arxiv 2412.21046 v1 pith:2XB52WWO submitted 2024-12-30 cs.LG

João Bravo , Jacopo Bono , Pedro Saleiro , Hugo Ferreira , Pedro Bizarro This is my paper · ORCID

classification cs.LG

keywords continuous-timedynamicgraphsgraphrecurrentneuralnetworksbackpropagationthroughtimetruncationgaptemporaldependenciesreal-timelearningbenchmarksarchitectures

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 graph recurrent neural networks (GRNNs), the standard recurrent approach to continuous-time dynamic graphs, are trained with a truncated form of backpropagation-through-time that limits what they can learn about the past. On a new synthetic edge-regression task with a tunable memory parameter $M$, models trained with full BPTT (F-BPTT) reach near-zero error for every $M$, while truncated BPTT (T-BPTT) fails as soon as the task requires memory beyond a single interaction hop. On real-world benchmarks, switching from T-BPTT to F-BPTT improves Mean Reciprocal Rank by 18.1% on Reddit and 22.2% on MOOC, the gap the authors call the 'truncation gap.' Because full BPTT is too memory-hungry for large graphs, the finding implies that current training pipelines leave GRNN capacity on the table and motivates non-backpropagation training schemes.

What carries the argument

The central object is the GRNN edge update (Equation 1), where each event updates the hidden states of both endpoints with a recurrent cell. The argument runs through the difference between the forward computational graph and the backward graph: T-BPTT computes gradients only within a time-windowed batch, whereas F-BPTT propagates through the entire history of the epoch. In the synthetic task, each node keeps a FIFO buffer of length $M$, and the target for an edge depends on the buffer's last element from both endpoints, so learning requires backpropagating through at least $M$ interaction events; truncating to a single hop makes the gradient signal vanish once a dependency spans more than one interaction.

What would settle it

Train T-BPTT on the synthetic task with a truncation horizon equal to $M$ (for example by grouping batches around each node so that $M+1$ of that node's events are in the same batch). If T-BPTT then solves the task for $M>1$, the gap is a matter of insufficient horizon rather than a fundamental gradient-estimation failure; if it does not, the gap involves more than truncation. On the real benchmarks, a comparable check is to vary batch size while holding the forward pass fixed; if MRR does not rise with longer backward paths, the within-batch forward approximation, not the truncation, is the dominant error.

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Extended reading notes

Core claim

The central discovery is that the truncation horizon of the backward pass, not the recurrent architecture itself, is the binding constraint on learning temporal dependencies in dynamic graphs. With identical forward computation, batching, optimizer, and number of gradient steps, F-BPTT solves the synthetic task at every tested memory value $M\in\{1,\dots,5\}$ while T-BPTT collapses for $M>1$; on Reddit and MOOC, F-BPTT outperforms T-BPTT by 18.1% and 22.2% in MRR respectively. The authors attribute this 'truncation gap' to the fact that dynamic-graph batching defines batches over global time windows, so gradients cannot cross batch boundaries and each node effectively receives credit only for dependencies within a single event update.

Load-bearing premise

The load-bearing premise is that the measured gap is caused solely by the truncated backward pass, because forward computation, batching, optimizer, and gradient-step counts are identical across conditions; if the parallel within-batch approximation of inconsistent histories or the simplified GRU-only architecture interacts with backward-path length, part of the gap would not be attributable to truncation.

Editorial extensions

If this is right

Published GRNN benchmark results on dynamic graphs likely understate the achievable performance of recurrent architectures when trained with full-history gradients.
Training schemes that approximate real-time recurrent learning, or otherwise lengthen the backward horizon without storing the full history, are a direct route to closing the truncation gap on memory-constrained hardware.
Batch-size choices in GRNN training involve a trade-off between parallelism and truncation depth; the results imply that larger batches do not recover the lost cross-batch gradient signal.
The synthetic task (released as a benchmark) gives future methods a concrete pass/fail: a method that closes the gap must learn the task for $M>1$ without full BPTT.

Reading between the lines

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

The truncation problem should generalize to any recurrent model trained on one global time-ordered sequence that cannot be segmented into independent examples, including continuous-time models for medical records, sensor streams, and financial transaction networks.
A directly testable extension on the real datasets is to vary the backward-pass horizon by changing batch size while holding the forward pass identical; if MRR does not improve monotonically with horizon, then the parallel within-batch approximation, not truncation, causes the gap.
Because the paper strips out time encoding and attention-based embeddings, the results leave open whether those components can mask part of the truncation gap; ablating them on the same benchmarks would clarify how much of the gap is architectural versus purely due to training signal.

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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

First thing to know: the paper's core claim is true, and the synthetic task is the reason. With a one-hop truncation horizon, a GRU cannot learn dependencies that span more than one edge; full BPTT solves the same task cleanly across all memory sizes tested. That is a controlled, reproducible demonstration, and the synthetic task code is public. The real-world experiments on Reddit, Wikipedia, and MOOC are a reasonable adjunct, but they do not isolate truncation as cleanly as the paper sometimes implies.

What is new: the synthetic buffer task is a useful benchmark, and the paper is right that none of the earlier GRNN works (Dai et al., Trivedi et al., Kumar et al., Rossi et al.) discussed the effect of BPTT truncation on learning. The comparison design is careful: same forward pass, batching, optimizer, and number of parameter updates in both conditions, so the difference in the synthetic setting is attributable to the backward pass. Credit also for reporting the Wikipedia MRR null result instead of hiding it.

Soft spots, in proportion. The word 'solely' in the definition of the truncation gap (Section 1) is overreach. In the real-world comparison, both conditions use the TGN-style parallel batching from Rossi et al. (Section 2.2). F-BPTT is exact backpropagation for that approximate parallel-batched forward graph, not for the true sequential GRNN. The measured 18-22% MRR improvements on Reddit and MOOC could therefore partly reflect better training of the approximate aggregation rather than recovery of long temporal dependencies. The synthetic task controls for this; the real-world experiments do not. The single seed on Reddit and the non-significant negative MRR on Wikipedia further weaken the real-world leg, though the authors report these limitations honestly. Missing real-world code is a minor reproducibility gap; only the synthetic code is public.

Who this is for: anyone training GRNNs for temporal link prediction, and people building dynamic-graph benchmarks. The synthetic task is reusable as a stress test for new training methods. The discussion of RTRL-style alternatives is speculative but clearly labeled as such.

Recommendation: this deserves a serious referee. The central argument survives because of the synthetic task. A referee would want the 'solely' attribution toned down and ideally a real-world condition that also controls for the batching interaction, but that is revision material, not a rejection. Engage with it.

Referee Report

1 major / 5 minor

Summary. The paper studies the impact of truncated backpropagation-through-time (T-BPTT) on graph recurrent neural networks (GRNNs) trained on continuous-time dynamic graphs. It introduces a synthetic edge-regression task with a memory parameter M, and shows that while full BPTT (F-BPTT) solves the task for all tested M, T-BPTT (with a one-edge truncation horizon) degrades sharply for M > 1. The paper then compares T-BPTT and F-BPTT on the Reddit, Wikipedia, and MOOC benchmarks using the TGN-style parallel batching strategy, reporting a performance gap on Reddit and MOOC. The authors call this gap the 'truncation gap', argue that current training approaches underuse GRNN capacity, and discuss alternatives such as low-rank approximations to real-time recurrent learning.

Significance. The paper addresses a genuinely under-examined issue in training recurrent models on dynamic graphs, and the synthetic task is a valuable controlled benchmark: the forward pass, batching, optimizer, and number of parameter updates are identical across conditions, so the failure of T-BPTT for M > 1 is cleanly attributable to the backward-pass truncation. The real-world results are practically relevant, with F-BPTT improving MRR by 18.1% on Reddit and 22.2% on MOOC over T-BPTT. The manuscript also ships code for the synthetic benchmark, which is a reusable resource. The main weakness is that the real-world comparison uses TGN-style parallel batching, so the measured real-world gap may partly reflect an interaction between truncation and the batching approximation; this limits the strength of the 'solely caused by truncated backpropagation' claim in the real-world setting, although the synthetic experiment stands on its own.

major comments (1)

[Section 4 ('We train the GRNN model with both truncated and full BPTT...') and Section 1] The real-world experiments hold the forward pass fixed between conditions, but that forward pass is itself an approximation because it uses TGN-style parallel batching (Section 2.2), which ignores within-batch event order and aggregates simultaneous updates. Consequently, F-BPTT is exact backpropagation only for the approximate parallel-batched forward graph, not for the true sequential GRNN. The observed improvements on Reddit and MOOC could therefore reflect, at least in part, F-BPTT better optimizing the memory-aggregation parameters under the parallel-batching approximation, rather than recovering true multi-hop temporal dependencies. Because only the synthetic task controls for the interaction between truncation and batching, the real-world evidence does not by itself establish that the gap is solely truncation-driven in the sense of temporal dependency length. Please either qualify the 'solely caused' claim in Section 1, or add a sequential-batching comparison on at least one smaller dataset to show that the gap persists when the forward pass is exact.

minor comments (5)

[Section 4, Table 2] Reddit results are reported for a single seed and without error bars; the paper should either provide a measure of variance or explicitly state that the Reddit numbers are a single-run observation, so that the 18.1% improvement is not overinterpreted.
[Section 3.1] It is not fully explicit whether the model's prediction for an edge is computed from the pre-update or post-update hidden states; Figure 3 suggests the former, but Equation (1) is written as an update. Please clarify this detail for reproducibility.
[Section 2.2] The text refers to 'Figure 2.2' twice; these references should be to Figure 2.
[Section 3, first sentence] The word 'backpropragation' is a typo for 'backpropagation'.
[Table 2 caption] The caption begins with 'T runcated'; this should read 'Truncated'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the truncation gap is an empirically controlled comparison, not a derivation that reduces to its own inputs.

full rationale

The paper is an empirical comparison of two training algorithms (F-BPTT and T-BPTT) holding the forward computation fixed. The only place where a result is 'built in' is the synthetic task: the target y_k depends on the M-th buffer element, so a model whose gradient is truncated after one edge update cannot learn the required multi-hop dependency for M>1. But this is the experimental manipulation that defines the independent variable (truncation horizon), not a circular derivation: the claim is precisely that T-BPTT fails at tasks needing dependencies beyond its horizon, and F-BPTT succeeds, which the experiment tests. On real benchmarks, both conditions share the same TGN-style parallel batching, optimizer, epochs, hyperparameter search, and negative sampling; the only difference is whether gradients cross batch boundaries. Thus the measured gap is attributable to the truncation of the backward pass by construction of the comparison, and no fitted parameter is relabeled as a prediction. The paper does not invoke any uniqueness theorem, and the only self-references are to the authors' public GitHub repository for the synthetic task, which is not load-bearing evidence. No circular step can be quoted; score 0.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim is empirical; no new quantities are fitted to reach a prediction. The listed free parameters are training hyperparameters and design choices that bound the strength of the observed gap. The main ad hoc element is the synthetic buffer task, which is designed specifically to require multi-hop memory.

free parameters (7)

learning_rate = tuned in [10^-3, 10^-2] via 25-trial random search (Table 1)
Standard optimizer hyperparameter tuned per dataset and method; affects the magnitude of the observed gap but is not the object of study.
weight_decay = tuned in [10^-5, 1] via random search (Table 1)
Tuned to give both methods comparable optimization conditions.
mlp_dropout = tuned in [0, 0.3] via random search (Table 1)
Dropout on the classifier head; could interact with training dynamics of either method.
state_dropout = tuned in [0, 0.3] via random search (Table 1)
Dropout on node states; tuned per trial and method.
state_dropout_type = Regular or Recurrent, chosen uniformly (Table 1)
Choice of dropout scheme; tuned per trial.
hidden_size = 64
Set to 64 due to memory constraints for full BPTT (Section 4); the gap may depend on model capacity.
batch_size = 200
Chosen following Rossi et al. (2020); the truncation horizon is inversely related to this value.

assumptions (6)

domain assumption GRU cell dynamics (Equation 1) are a valid model of event-driven state updates in continuous-time dynamic graphs.
The paper builds on the GRNN framework from Dai et al. (2017), Trivedi et al. (2019), Kumar et al. (2019), and Rossi et al. (2020).
ad hoc to paper The synthetic buffer task is a valid proxy for multi-hop temporal dependencies in dynamic graphs.
The task is constructed so that the target at event k depends on node buffer entries M updates in the past; its external validity as a benchmark is asserted, not derived.
domain assumption TGN-style parallel batching (Section 2.2) is an acceptable approximation of sequential event processing, and F-BPTT over this graph is the appropriate reference point.
Both conditions share the same forward pass, so the approximation error is controlled but assumed not to interact with truncation.
domain assumption The Reddit, Wikipedia, and MOOC datasets, as preprocessed by Kumar et al. (2019), and the uniform negative-sampling evaluation are valid temporal link prediction benchmarks.
These are standard benchmarks in the temporal graph literature.
ad hoc to paper A single GRU cell of hidden size 64, without time encoding, is representative of the broader GRNN class for measuring the truncation gap.
The authors explicitly simplify the setup to fit full BPTT in memory; the representativeness is an assumption.
domain assumption Gradient accumulation over the epoch with a single parameter update makes T-BPTT and F-BPTT comparable.
The paper argues this is a fair common setup with the same number of epochs and updates.

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Cite this review

Pith. "Pith review of Mind the truncation gap: challenges of learning on dynamic graphs with recurrent architectures." pith.science (2026). https://pith.science/paper/2XB52WWO

@misc{pith2026241221046,
  author       = {Pith},
  title        = {Pith review of: Mind the truncation gap: challenges of learning on dynamic graphs with recurrent architectures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2XB52WWO}},
  note         = {Machine review of arXiv:2412.21046}
}

read the original abstract

Systems characterized by evolving interactions, prevalent in social, financial, and biological domains, are effectively modeled as continuous-time dynamic graphs (CTDGs). To manage the scale and complexity of these graph datasets, machine learning (ML) approaches have become essential. However, CTDGs pose challenges for ML because traditional static graph methods do not naturally account for event timings. Newer approaches, such as graph recurrent neural networks (GRNNs), are inherently time-aware and offer advantages over static methods for CTDGs. However, GRNNs face another issue: the short truncation of backpropagation-through-time (BPTT), whose impact has not been properly examined until now. In this work, we demonstrate that this truncation can limit the learning of dependencies beyond a single hop, resulting in reduced performance. Through experiments on a novel synthetic task and real-world datasets, we reveal a performance gap between full backpropagation-through-time (F-BPTT) and the truncated backpropagation-through-time (T-BPTT) commonly used to train GRNN models. We term this gap the "truncation gap" and argue that understanding and addressing it is essential as the importance of CTDGs grows, discussing potential future directions for research in this area.

Figures

Figures reproduced from arXiv: 2412.21046 by the authors.

**Figure 1.** Truncation of temporal history becomes severe in dynamic graphs. (left) Sequence based data can be grouped by sequence when defining batches. In this specific example of sequences with two events, with a batch capacity of 4 entity updates, we can include two sequences per batch. Temporal dependencies between the events (horizontal dotted lines) are not broken by batching. (right) Due to the interactions between stat… view at source ↗

**Figure 2.** Three different batching strategies illustrated. Four nodes with respective states [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Visual depiction of synthetic task dynamics. A fixed size FIFO buffer with length M (4 in the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Mean squared error (MSE) obtained for different sized GRU models trained with both F-BPTT [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: The dynamical system over the hidden states can in general contain two components: a function [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: The two different possibilities for merging the autonomous evolution and event update into a single [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 10, 2026 · model on record in the stance chip above.

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