From Link Prediction to Forecasting: Addressing Challenges in Batch-based Temporal Graph Learning
Authors: Moritz Lampert
Christopher Blöcker
Ingo Scholtes
Venue: Accepted by TMLR ()

Abstract: Dynamic link prediction is an important problem considered in many recent works that propose approaches for learning temporal edge patterns. To assess their efficacy, models are evaluated on continuous-time and discrete-time temporal graph datasets, typically using a traditional batch-oriented evaluation setup. However, as we show in this work, a batch-oriented evaluation is often unsuitable and can cause several issues. Grouping edges into fixed-sized batches regardless of their occurrence time leads to information loss or leakage, depending on the temporal granularity of the data. Furthermore, fixed-size batches create time windows with different durations, resulting in an inconsistent dynamic link prediction task. In this work, we empirically show how traditional batch-based evaluation leads to skewed model performance and hinders the fair comparison of methods. We mitigate this problem by reformulating dynamic link prediction as a link forecasting task that better accounts for temporal information present in the data.

Published in Transactions on Machine Learning Research (02/2026)
From Link Prediction to Forecasting: Addressing Challenges in Batch-based Temporal Graph Learning
Moritz Lampert
Chair of Machine Learning for Complex Networks Center for Artificial Intelligence and Data Science (CAIDAS)
Julius- Miris-Mazimilianss Universität Würzburg, DE
Christopher Blöcker
christopher wheerp/ereeeeeeeeeeeeeeeverrrrre
Chair of Machine Learning for Complez Networks Center for Artificial Intelligence and Dala Science (CAIDAS)
Julius-Ma Mariss-Maiiiliaasse... Universität Würzburg, DE
Ingo Scholtes
ing.schhotes@ruiiuuuerbbyyy
Chair of Machine Learning for Complex Networks Center for Artificial Intelligence and Dula Science (CAIDAS) Mazimilaz Universiläl Würzburg, DE
Reviewed on OpenReview: https: openreview. net/ forum? id= 62PAybLE31
Abstract
Dynamic link prediction is an important problem considered in many recent works that propose approaches for learning temporal edge patterns. To assess their efficacy, models are evaluated on continuous- time and discrete-time temporal graph datasets, typically using traditional batch-oriented evaluation setup. However, as we show in this work, a batch- oriented evaluation is often unsuitable and can cause several issues. Grouping edges into fixed-sized batches regardless of their occurrence time leads to information loss or leakage, depending on the temporal granularity of the data. Furthermore, fixed-size batches create time windows with different durations, resulting in inconsistent dynamic link prediction task. In this work, we empirically show how traditional batch-based evaluation leads to skewed model performance and hinders the fair comparison of methods. We mitigate this problem by reformulating dynamic link prediction as a link forecasting task that better accounts for temporal information present in the data.
1 Introduction
Many scientific fields study data that can be modelled as graphs, where nodes represent entities connected by edges, such as social (Lazer et al. 2009), financial (Bardoscia et al. 2021), or molecular networks (David et al. 2020). Apart from the mere topology of interactions, that is, who is connected to whom, network data increasingly include information
when interactions occureed. The resolution of such temporal graphs varies from snapshots with, for example, yearly political collaboration networks (Fowler) 2006) called discrete-
time temporal graphs (Kazemi et al. 2020 to high-resolution online interactions (Kunar et al. 2019 or
contacts between individuals via proximity Vanhemss et al. 2013), named continuous-ling temporal graphs.
Building on the growing importance of temporal data and the success of graph neural networks (GNNs) for static graphs (Corso 2024), deep graph learning has recently been extended temporal (or dynamic) graphs (Feng al. 2024 To this end, several temporal graph neural network (TGNN) architectures have

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Published in Transactions on Machine Learning Research (02/2020)
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(a) Information loss: Three edges with different time- stamps are grouped into the same batch with batch size The batched (blue) edges are processed in paral- lel and can only utilise information from previous batches (grey dashed edges). This implies that edge (b, a, fa) cannot be used for the prediction of edges (a, b, 12) (high- lighted with red bolt) or (c, b, t2).
(b) Information leakage: Edges (a, f2) and (c, b f2) with the same timestamp are grouped into different batches with batch size b cessed consecutively due to their batch assigmment. Thus, information about edge (a, t2) (grey dashed edge in B2 because it was previously processed in B1) is leaked dur- ing the prediction edge (c, b, t2) in batch B2 (green).
The two edges are pro-
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(c) Varying batch durations: The durations batches Bi and Bg differ for batch size b 2. This changes the
(d) Tunable batch size: Treating the batch size as
hyperparameter aggravates the problem shown in (c). Since batch duration depends on batch size, using differ- ent batch sizes results in different batch durations, such as for b == 2 vs. = 4. This effectively makes it possible to tune the task difficulty the model.
difficulty of the link prediction task for each batch because
this difficulty can strongly depend on the prediction hori- zon. For example, it is often easier to predict interactions in the near than in the distant future.
Figure 1: Illustration of the issues in batch- based evaluation of dynamic link prediction.
been proposed that simultaneously learn temporal and topological patterns. These architectures are often evaluated in dynamic link prediction sctting, where the task is to predict the existence of edges during some future time window, for example, to provide recommendations to users (Kumar et al. 2019
TGNNs utilise temporal batches to speed up training for dynamic link prediction. To construct these batches, the temporally ordered edges are divided into a sequence of chunks, all containing the same number of edges, which causes several problems illustrated in Figure [ (a) Some TGNNs process edges within a batch as if they occurred simultancously, essentially discarding the temporal information between edges of the same batch, which is problematic in high-resolution data. (b) In low-resolution data, snapshots typically contain many edges with identical timestamps; such edges often assigned to different batches. This introduces artificial temporal order amongst those edges that is not present in the data, leaking information that should not be available to the model. (c) Fixed-size batches often result in varying batch durations, effectively leading to an incoherent lask with varying diffieulty for each batch. For example, it is easier to predict the weather 24 times tomorrow (at each hour) than to predict for the next 24 days at midday, (d) Related to the previous issuc, treating the batch size as a tunable parameter affects the resulting batch durations and changes the task difficulty, thus making model performance between different models incomparable when they choose different batch sizes.
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The issues (a)-(d) arise mainly from applying standard procedures from static link prediction to temporal graphs, and can be problematic for real-world applications where the timing of edge occurrences is crucial. For example, consider routing in opportunistic networks, where the goal is to find the fastest routes between nodes in a temporal network, such as for cellular traffic offloading (Trifunovic et al., 2017). Using temporal link prediction to find edges that will occur in the future can improve routing efficiency (Fang el al. 2021 Gou
& Wu, 2022 Huang et al. 2015 Shu et al., 2022). However, incorrect predictions harm routing efficiency, especially during periods of low activity, when the routing problem is harder due to the graph's sparsity [Garg et al., 2020). Therefore, an accurate performance estimate of the prediction model for each time window is crucial. Yet, current batch-based evaluation approaches group edges into equally-sized batches, regardless of their occurrence time. Because this approach weighs each edge equally, it essentially ignores the detrimental effect of incorrect predictions on routing efficiency during periods of low activity.
To address these issues in the evaluation of link prediction in temporal graphs, we propose link foreensting a task definition based on equally long and, therefore, oqually weighted time windows instead of batches of varying duration. Our link forecasting definition mitigates the aforementioned issues (a)- of link prediction by adequately considering the available temporal information. Link forecasting provides more realistic performance estimates for applications such as routing in opportunistic networks. In addition to introducing link forecasting, we make the following contributions:
We quantify information loss and leakage resulting from the aggregation of edges into batches on 14 empirical temporal graphs.
We experimentally evaluate state-of-the-arl TGNNs for link forecasling. Our results identify scenar- ios where batch-based evaluation leads to skewed model performance, for example, in datasets with inhomogeneously distributed temporal activity for evaluation. Further, we show that the batch- based approach overestimates the performance of memory-based models in discrete-time datasets.
We provide implementations of the link forccasting task for commonly used graph learning frame- works such as DyGLib Yu et al. 2023) and PyTorch Geometric (Fey & Lenssen 2019
Although parallel processing of edges is a technical necessity for efficient model training, we demonstrate how ignoring the occurrence time of edges when splitting them into batches leads to various problems. With dynamic link forecasting, we propose a simple yet effective solution. While having a similar runtime to dynamic link prediction, our time-window- based evaluation facilitates a fairer and more realistic evaluation that better reflects real-world scenarios.
2 Preliminaries and Related Work
Temporal Graphs. A temporal (or dynamic) graph G = (V, E) is a tuple where V is the set of n | nodes and E (1, (Mms Umn fm)) with f < ... < f. is chronologically ordered sequence of m [ time-stamped edges (Wang et al. 2021c Yu et al. 2023 Each node can have static node features h; E Hy and each temporal edge (2,, uj, t) can have edge features eij, E HE. We assume that interactions occur instantaneously with timestamps t E R. This type of temporal graph is often categorised as contimuous-time (Kazemi et al.) 2020 (kkarding et al. 2021). In contrast, discreto-time temporal graphs coarse-grain time-stamped edges into a sequence of static snapshots (Gr,,t), where Grat, = (V, Brst,) with Er,,, ((u,v) 3(u, v(,,v,t) e E: t
(uue et al. 2022).
Dynamic Link Prediction. Given time-stamped edges up to time t, the goal of dynamic link prediction is to predict whether an edge (v, u, r) exists at future time t (Kazemi et al. 2020 Wang et al. 2021e Poursafaci et al.] 2022] Yu et al. 2023). In practico, it is often computationally infcasible to train and evaluate models on all possible edges, one edge al a time. Thus, the chronologically ordered sequence of edges E is usually divided into temporal batches B,,, where each batch has a fixed size, containing 6 edges. Edges within the same batch are typically processod in parallel (Rossi et al., 2020 Su et al. 2024).. In addition to the existing (positive) edges (u, v. E B non-existing (negative) edges (u "u,""" .7 E B, are sampled and used for training and evaluation (see Appendix A for brief overview of negative sampling
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approaches). This is done since real-world graphs are typically sparse, and using all possible negative edges between all possible node pairs at all points in time would lead to large class imbalance and prohibitively long runtime. Formally, the dynamic link prediction task is defined as follows:
Let G = E) be temporal graph with node features Hv and edge features HE. Let b be the batch size and B := {[u,, ug ty)tt) B(u,, tyytt) E E b. < j S b- (i + 1)} the i-th batch containing edges. We further use B to denote a set of negative edges drawn using negative sampling as described in Appendix A For a given batch i we use E. = {[un, uk, vk,42) (2) 3ux, Uk, lx) E E k S b. to denote the past edges up to batch i. The goal of dynamic link prediction is to find a model fo(u,U, E,, Hv, Hz,)) with parameters 0 that, for all future edges (u, U, B U Bi in each batch i, predicts whether (u, E B or (u, U.) E B, using the past edges É,.
Definition 2.1.
State-of-the-Ar Art TGNNs. Current state-of-the-ar dynamic link prediction methods, such as JODIE
(Kumar et al. 2019) DyRep (Trivedi et al. 2019), TGN (Rossi et al., 2020) keep an up-to-date memory of temporal information in the graph by utilising recurrent neural networks. TGAT (Xu et al., 2020)) extends
graph attention to the temporal domain and replaces positional encodings in GAT (Velickovic et al., 2018) with a vector representation of time. TCL (Wang et al.) 2021a) uses capture the nodes' timo-evolving properties. CAWN learns temporal motifs based on causal anonymous walks (Wang et al. c021ch. GraphMixer takes an attention-free and transformer-free approach, using an MLP- based link encoder, a mean soeannpooling-aeee based node encoder, and an MLP-based link classifier for predictions (Cong et al. 2023 DyGFormer combines nodes' historical co-occurrences as interaction targets of the same source node with a temporal patching approach to capture long-term histories (Yu al. 2023). Further approaches for temporal graph learning exist, including ROLAND Youu et al., 2022), DyGEM (Taheri al. 2019), DySAT (Sankar et al. 2020 EvolveGCN (Pareja et al. 2020), and DBGNN (Qarkahhiaa et al. 2022 For recent survey of
caausformr-basset architecture to
based dynamic link prediction, we refer to Feng et al. (2024).
Open Challenges in Dynamic Link Prediction
Training. Recent works (Zhou et al. 2022 2023 Feldman & Baskin 2024 Su et al. 2024) identified issues in the training of memory-based TGNNs with large batch sizes: Processing edges belonging to the same batch in parallel ignores their temporal dependencies, resulting in varying performance depending on the chosen batch size. This issue, called lemporal discontinuily, is caused by Problem (a) from above, that is, treating edges within the same batch as if they occurred simultaneously (see Appendix D). To mitigate this issue, Zhou et al.] )023) introduced a distributed training framework using smaller batch sizes. Another approach, PRES (Su et al. 2024). accounts for intra- temporal dependencies using a prediction-correction scheme. Feldman & Baskin (2024) proposed a model with a decoupling strategy to mitigate this problem. However, these works focus on training instead of evaluation, which is our work's focus.
Parallel to our work, Huang et al. 2024) formulate the unified temporal graph (UTG) representation, which facilitates learning on continuous-time graphs with discrete-time TGNNs by proposing conversion methods between discrete- and contimuous-tine temporal graphs. They also train continuous-time TGNNs on discrete-time graphs and briefly touch upon information leakage as we described in Problem (b). However, their work does not consider all Problems (a)- nor include an empirical evaluation of how Problem (b) affects model performance, which we address here. Related to the above, Rossi et al. (2023) investigated how different conversion approaches from continuous- to discrete-time temporal graphs affect the graphs' structural properties.
Evaluation. Recent progress in terms of TGNN evaluation includes the temporal graph benchmark (TGB)
(Huang al. 2023), similar to the static open graph benchmark (OGB) (Hu et al., 2020). Poursafaei et al. 2202)) identified problems with random negative sampling for dynamic link prediction and proposed novel Lime-dependent. negalive sampling techniques to improve the evaluation of TGNNs. [asttinger el al. (2023) pointed out issues in the evaluation of temporal knowledge graph forecasting. Although none of the models used for temporal knowledge graph forecasting overlap with regular TGNNs for dynamic link prediction, some of the problems are related, for example, differences in forecasting horizons leading to incomparable results.
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3 From Link Prediction to Link Forecasting
Learning temporal patterns in batch-oriented fashion leads to issues in cont and discrete-time graphs. We demonstrate these issues in eight continuous-tin and six discrete-time temporal graphs, whose characteristics are summarised in Table ! and Appendix C To address these issues, we formulate the link forecasting task based on time windows with a fixed duration.
3.1 Problems in Batch- based Dynamic Link Prediction
Below, we show empirically that batching causes information loss or leakage because ignores the existing temporal order of links induces an artificial order between them. When link densities vary over time, temporal batches lead to incoherent tasks because they produce varying prediction durations. Consequently, the results from different models become incomparable if they use different batch sizes. In practice, this happens the batch size is treated like a hyperparameter and different models choose different batch sizes.
(a) Information Loss. For effi- ciency, edges from different timestamps are grouped into batches and processed in parallel. This parallel processing im- plies that earlier edges cannot inform the prediction of later edges if they are in the same batch, for example, recent neighbours or as part of the memory in memory-basee models (see Figure la Therefore, assigning tem- poral edges with different timestamps to a single batch discards the tempo- ral ordering those edges, resulting in information loss. In Figure 2 we use normalised mutual information (NMT) (Vinh al. 2010) to measure this in- formation loss. NMI quantifies how much information observing one ran- dom variable conveys about another random variable (see Appendix B for details and an example). NMT yields values between 0, meaning "no infor- mation", and 1, i.c. "full information". By treating the index i of each batch B, assigned to each edge (u, v) E B, one random variable and the associated edge's timestamp & as the other, we measure the temporal information that is retained after dividing edges into batches. An NMI value of means that we can reconstruet the timestamps of edges correctly from their batch number, and value of 0 means that batch numbers do not carry any information about timestamps, that is, total loss of information.
Table Characteristics of continuous- (top) and discrete-time (bot- tom) temporal graphs. For each dataset, we list the number of nodes n and edges m, the resolution of timestamps, the dataset's 's total duration T, the average number of edges [Eg] with the same timestamp t, and the temporal density 7/m. The US L. datasct is measured in congresses (c). The other datasets are measured in conventional units of time, i.e., seconds (s), minutes (min), days (d) years (a). See Appendix C for more information each dataset.
Dataset
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Enron
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UCI
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LastFM
1980
1 293 103
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Myket
17 988
694 121
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Social
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Reddit
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60 396
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Can. P.
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74 478
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Flights
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1 927 145
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300.9 + 342.4
1.0
Figure shows that larger batches result in higher information loss (lower NMT) for contimuous-time tempo- ral graphs where timestamps have high resolution. This is because assigning edges that occur at different times to the same batch discards their temporal ordering the larger the batch size, the stronger the coarse- graining effect and the more information is lost. A batch size of b = 1 preserves most temporal information and maximises NMI because we obtain bijective mapping between almost all timestamps and batch num- bers, except. when multiple edges occur simultaneously.
Figure 2b shows the batch-size dependent NMI for discrete-time temporal graphs. The "optimal" batch size that retains most temporal information depends on the average number of links per snapshot and, thus, on the characteristics of the data. Too small batch sizes impose an ordering on the edges within the snapshots
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that is not present in the data. Too large batches stretch across snapshots and discard the temporal ordering of edges from different batches.
(b) Information Leakage. In discrete-time graphs, the number of edges with a given timestamp often exceeds the batch size (see Appendix C.4). This means that edges with the same timestamp need to be assigned to different subsoquent batches, which are processed soquentially (sec Figure The same problem can arise in continuous-time graphs in moments of high activity, where the number of edges with a specific timestamp surpasses the batch size. Memory-based models utilise information from previous batches make predictions for later batches by updating their internal node representations. But because of the issues above, this can include edges with the same timestamp and lead to an unfair advantage for memory- memory-based models, as the already processed edges leak information about the remaining edges that have the same timestamp.
(c) Varying Time Window Durations. In Fig- ure 3 we show the temporal activity for a selection of temporal graphs as the number of time-stamped edges within given time interval (see Appendix C.2 for the remaining datascts). The results show that many real-world temporal graphs have highly in- homogeneous activities. For batch-oriented eval- uation, this introduces the issuc that each fixed- size batch B leads to generally different durations 1b-((+1) la (see Figure Tcb, that is, batch dura- tions shorter during periods with higher activity and longer during periods with lower activity (more details in Appendix C.3
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(d) Tunable Batch Size. The varying amount of temporal information (see Figure 2 and the chang- ing durations (see Figures 3 and 10) for different batch sizes highlight that changing the batch size influences the dynamic link prediction task (see Fig- ure id Effectively, the batch size is a hidden hyper- parameter that directly impacts the task's 's difficulty. This possibility of tuning the task by changing the batch size makes the results incomparable between models with different batch sizes.
Figure 3: Real-world datasets exhibit diverse edge oc- currence patterns. For selected graphs, we visualise the edge density over time by counting the edges per time interval as indicated in the axis captions (his- tograms for all datasets in Appendix C.2). Dashed lines divide the datasots into 70% train, 15% valida- tion, and 15% test sets as used in Section
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(a) Continuous time: Larger batch sizes assign more edges with different timestamps to the same batch, re- sulting in increased information loss.
(b) Discrete time: Edges with the same timestamp are processed in different batches sequentially, discard- ing the information that edges co-oceur in snapshots.
Figure 2: NMT (y-axis) measures the temporal information loss as function of different batch sizes (x-axis), where smaller NMI values indicate more information loss.

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Consider the Myket dataset (Loghmani & Fazli 2023) as example: It contains users and Android applications u, connected at time 1 when user V installs application u. The timestamps are provided in seconds, and edges occur roughly every 30 seconds on average (see Table D making the expected time range for a batch with size b= = approximatcly 30 seconds. Thus, the task is to predict who installs which applications during the next 30 seconds. Choosing b = 120 or b = 2880 turns the task into a prediction problem for approximately the next hour or day, respectively. For empirical validation, we compare the performance of state-of-the-art TGNNs using two different batch sizes during evaluation in Appendix D and show that the performance can vary substantially between different batch sizes.
3.2 Our Solution: Dynamic Link Forecasting
In real-world applications, the prediction time window is inherently connected to the problem at hand, necessitating task formulation that is chosen carcfully - and fixed - for each dataset. To address the afore- mentioned issues, we propose link forecasting, which replaces link prediction with a task definition utilising a fized-duration time window, generally resulting in a variable number of edges per window. Compared to dynamic link prodiction with a fixed batch size, this task (i) controls the window durations in which the tem- poral ordering of edges is lost; (ii) does not introduce an artificial temporal ordering that leaks information: (ifi) has fixed time window duration regardless of edge occurrence frequency; and (iv) does not depend on pepraaaraeterr that is tuned for each model.
Motivation, The study of temporal information is at the centre of time series forecasting (Benidis et al., 2023), where the goal is to forecast. the values of time series for given time window in the future. We define our task accordingly and interpret the temporal edges E as n² Boolean time series, each of which takes the value 1 when an edge occurs. Standard multivariate models output a value for each timestamp over forecasting horizon h. In large-scale temporal graphs, it is computationally infeasible to forecast the existence of all n² possible links, thus, only a sample of negative edges is considered instead. In continuous- time dynamic graphs, observations are available at high resolution, such as seconds, however, for many practical applications, predicting at lower granularity suffices. For example, it is typically enough to predict whether a customer will purchase a certain product within the next day or week. Therefore, we consider forecasting for all timestamps (t,t+h) h] during time window at once instcad of for cach of them individually. We define the link forecasting task as follows:
Definition 3.1. Let G EV. be a temporal graph with node features Hy and edge features Hg. Let h be the time horizon and W {(u, v, r, Hu,,,, T) E i h < (1+ 1))h) the set of edges in the i-th time window. We use W, to denote sample of [Wi+| negative edges that are sampled using one of the negative sampling approaches described in Appendix A and do not occur as positive edges in time window (i h, (i+ 1)- h). We further use É, = {(O, 0, [(, 0,t) E E ::E. f
< i- h} to denote the set of past edges up
to time i h. The goal of dynamic link forecasting is to find a model (u, v, E,, Hv, HR,) with paramoters f that, for all edges (u, (,) W U.; at future time i- h in each time window i, forecasts whether (u, v, E W.+ or (u, EW; W.
Crucially, link forecasting makes the evaluation independent of a batch size b and, instead, introduces a time horizon h that defines the forecasting time window for coarse-graining the temporal information. This requires deliberately choosing the temporal resolution based on the dataset and application (see Appendix E for examples). Similar to batch-based dynamic link prediction, adopting a windwwindow- based perspective enables parallel processing of edges by aggregating temporal information.
To summarise, link prediction depends on the batch size, which can become a hyperparameter, tuned for each model to get the best performance. In contrast, link forecasting is based on a dataset- or task specifc time horizon that controls the amount of temporal information and ensures that the information is consistent for different models, facilitating fair performance comparisons.
Computational Cost. We can assign all links to their corresponding time window in ((m) by checking each link's interaction time. After each link is assigned, the time complexity during model evaluation is the same for the batch-based approach. Since the number of links per time window varies, windows
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NMI
Wiki.
Roddit
MOOC
LastFM
Myket.
Enron
Social
UCI
Flights
Can. P.
US L.
UN Tr.
UN V.
Cont.
Harch
0.9982
0.9933
0.9908
0.99966
0.9985
0.9030
0.9449
0.9988
0.9023
0.8316
0,9864
0.8918
0.8945
0.9240
Window
1.0000
1,0000
1,0000
1,0000
1.0000
1.0000
1,0000
1.0000
1.0000
1.0000
1,0000
1,0000
1.0000
1,0000
Table 2: Maximum NMI as measure for the maximum amount of information that is preserved using the optimal batch size (top row) and horizon (bottom row) for each continuous- (left) and discrete-ting (right) datasct. The results show that our window-based approach preserves full temporal information.
can become large during periods when many temporal edges occur. For those periods, time windows be subdivided into smaller chunks for GPU-based computations. To prevent information leakage between chunks of the same time window, steps such as memory updates need to be accumulated and done based on the whole time window. We provide a more detailed explanation of possible memory overflow mitigation strategies and report the empirical runtime of both approaches in Appendix
Implementation. We provide implementations for our evaluation procedure in commonly used PyTorch libraries. Specifically, we implement a new DataLoader called SnapshotLoader that replaces the widely used TemporalDataLozder in PyTorrh Geometric (Fey & Lenssen 2019p. We extend DyGLib (Yu et al. 2023) by an argument horizon in the evaluation pipeline"] The latter was used for the experiments in this work and can be used to reproduce our results.
4 Link Prediction vs. Forecasting
First, we verify empirically that our proposed window-based evaluation can mitigate the information loss issue inherent to batch-based based evaluation. We compare the maximum amount of information preserved (that is, the maximum achievable NMT) of both approaches for each dataset in Table 2 The top row of the table shows that no batch size cxists that leads to no information loss for all datasets. In contrast, our window-based approach (bottom row) does not leak any information by definition, as demonstrated by NMI values of one.
Next, we experimentally evaluate the performance
of nine state-of-the-art, models (Kumar et al.
2019:
Table 3: Average links per window [W; and stan- dard deviation for horizon h used in the evaluation. We chose b = 200, that is, |B,1| = 200, and appro- priate horizons for each dataset get |W;+| Rs 200. Detailed window size histograms are presented in Fig- ure 13 NMI uses time window and batch IDs of the test set (see Appendix B to quantify how much the chosen chunks differ wetween approaches.
Trivedi et al.]
2019 Xu et al. 2020 Rossi et al.
2020
Wang et al.]
2021a Poursafaei et al., 2022
Cong
et al. 2023 Yu et al. 2023), both for the (conven-
tional) dynamic link prediction task as well as our proposed dynamic link forecasting task. We use im- plementation and model configurations provided by DyGLib (Yu et al. 2023) (see Appendix F) and re- peat each experiment five times with different seeds to obtain averages. We use historical negalive sam- pling (Poursafaci et al., 2022) (see Appendix A and train cach model using batch-based training and val- idation with batch size = 200, which was found "to be a good trade-off between speed and update gran- ularity" (Rossi et al.] 2020) and adopted in later works (Poursafaci et al.) 2022 Yu et al. 2023). Afterwards, we evaluate each trained model with weights obtained by batch-based training using both our proposed hine-window-based evaluation method and the common batch- based evaluation approach.
Dataset
h
NMI
Enron
172 800s (48h)
214.1 + 274.1
0.8017
UCI
57 600s (16h)
208.5 :: 335.5
0.8252
MOOC
1200s (7/sh)
199.3 167.2
0.8803
Wiki.
3600s (1h)
211.7 56.3
0.8903
LastFM
21 600s (6h)
204.4 120.2
0.9089
Myket
5400s (3/2h)
220.1 + 133.6
0.9139
Social
1800s (1/2h)
186. + 165.3
0.9131
Reddit
900s (2/sh)
226.0 + 54.5
0.9152
The setup is visualised in Figure
https://github cwm/M http:///ww..aaaaeellooo////eet/e
https://github... com/M Lanpert/DyLLib
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Batch-based
Training Set
Test Set
Batch-based Training
Evaluation
Results
Initialised TGNN
Trained TGNN
Window- based Evaluation
Figure 4: Experimental setup: All TGNNs are trained using batch-based training and evaluated using batch- and window-based evaluation ensure as much comparability possible.
Continuous-Time Temporal Graphs. Following previous work (Rossi al., 2020 Poursafaei et al, 2022 Yu et al. 2023). set the batch size to b 200 and choose the forecasting horizon h such that the resulting time windows contain 200 edges on average to facilitate comparability with the batch-oriented approach (see Table for the exact values). We quantify the amount of information shared between the
two approaches in Table 3 as the NMI score between time window ID and batch ID (see Appendix B for a detailed explanation).
Figure 0 shows the change of AUC-ROC scores for bino-window-based link forecasting relative the batch-based evaluation of dynamic link prediction (detailed scores are provided in Appendix H.. and H.2 The performance changes are presented in detail a heatmap in Figure 6a and ag- gregated for each dataset across all models in Figure 6b Both figures show that the change in performance between our window-based and the batch-based approach largely depends on the dataset: The lower datasets in both figures with a similar window duration for all fixed-sized batches (quantified by NMI scores close to one in Table 3 and a narrow window size distribu- tion in Figure [3). such as Wikipodia, Reddit, or Myket, only exhibit small performance differences.
This is expected since chose the horizon h to produce time windows close to the same average size the fixed-sized batches. Nevertheless, we ob-
Enron: JODIE
Enron: GraphMixer
AUC-ROC
serve tanggt distributions in Figure 13 and lower
NMT values in Table 3 for datasets with in inhomoge- neously distributed temporal activity, such as Enron
or UCI-that is, the time windows do not fit the fixed-sized batches well. These datasets (placed the top in Figure G) with lower NMIs show substan-
1100
1200
1300
1100
1200
1300
MOOC: TGN
MOOC: DyGFormer
AUC-ROC
tial performance changes across models. This high-
lights that the performance scores of batch-based
evaluation are skewed and may not reflect the mod-
Basch Window
cls' performance in a real-world sctting on temporal
datasets with inhomogeneous activities.
28
29
Time (1d)
Time (1d)
To explain the causes of the performance differences of both evaluation approaches, we analyse the AUC- ROC scores for each batch and time window indi- vidually in Figure 5 (and Appendix H.3 for other datasets and models). We observe that the perfor- mance between the two approaches diverges most during phases of irregular temporal activity. Specif- ieally, the batch-based evaluation is affected by an anomaly in the Enron dataset at day 1181, where the performance of all models drops substantially. At this time, 1705 temporal edges with identical times- tamps are evaluated in 9 consecutive batches. In contrast, our approach uses single time window for all 1705 edges with identical timestamps. During the second half of the observation period for the Enron dataset (117 days), the batch-based approach yields only 5 batches, with durations up to 73 days. contrast, the average batch duration of the whole datasct is two days, which consistent with the durations of the time windows of our window-basse based approach. Most models perform better during this period using our window-based evaluation compared to the batch-based approach. This performance increase suggests
Figure 5: Model performance of selected continuous- time datasets varies over time (cf. Appendix H.3 for all datasets and models), which is visualised by AUC-ROC scores (y-axis) for each batch (blue) and time window (orange). For both datasets, the best- performing memory- and non-memory- based model is shown. The time (x-axis) is limited to the test set.
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Enron
8.6
9.2
-0.2
17.5
13.9
3.6
9.0
10.6
15.0%
Earos
UCI
4.2
17.1
-1.5
-7.4
-3.0
4.9
-6.2
-0.5
-0.6
UCI
MOOC
-2.1
-2.1
-1.2
-2.9
-2.2
-3.4
-5.8
-5.5
-1.5
10.0%
Dataset
Wiki,
-0.4
-0.1
-0.6
-0.7
-0.4
0.1
-0.6
-0.6
-0.3
MODC
5.0%
LastPM
-2.2
-3.7
-1.9
-4.7
-2.6
-0.2
-2.7
-9.2
-1.0
Myket
0.6
-0.1
0.1
0.4
3.1
1.3
-0.3
0.5
0.0%
Last
Social
0.8
-0.5
0.5
-0.1
-1.4
-1.1
-0.6
0.6
-5.0%
Mykes
Reddit
0.00
0.0
-0.0
-0.1
-0.0
-0.1
-0.1
-0.1
0.0
Sucial
JODIE
DyRep
TGN
TGAT
CAWN
EdgeBank
TCL
Graphâfizer
DyGioormer
Reddi
0.00
0.05
Model
AUC Change
(a) Healmap showing the change in performance in percentage. Datasels with lower NMI exhibit larger performance changes (Lop rows with warm cold coloured cells), whereas datasets with NMT values close to perform equally well (bottom with mostly white cells) for both evaluation approaches.
(b) Average absolute perfor-
mance change. Dalasets with lower NMT values (top) show
larger performance changes.
Figure 6: Performance change of our window-based approach relative to the batch-based approach (a) for each continuous-time dataset and model combination and (b) averaged for each continuous-ting dataset. The datasets are ordered by NMI reported in Table 3
that the loss of information that happens because edges across such a long period of time are grouped into one batch has a large impact on the performance. Additionally, when using the batch-based evaluation, the performance of the second half only has small impact on the overall performance because it is outweighed by the other half with more batches. In contrast, our window-based approach weighs the performance of each time period equally. A similar (daily) pattern can be observed for MOOC, where each period of low activity follows a high-activity period. Our time-window-baser evaluation reveals that most models are particularly unreliable during the low-activity periods, which is again outweighed by periods with high activity in the batch-bases approach.
Discrete-Tine Temporal Graphs. We set h = 1 to obtain one time window per snapshot with prediction time intervals ranging from five minutes to year, depending on the dataset (see Table D Similar to Figure Figure 7 shows the AUC-ROC score change and highlights the performance discrepancy between the two evaluation approaches link prediction and link forecasting for discrete-time temporal graphs. For link forecasting, the performance of memory-based models (JODIE, DyRep, TGN) decreases substantially on half of the datasets. This is expected since these models incorporate leaked information about the present snapshot by updating their memory based on prior batches, which means using part of the snapshot's edges to predict its remaining edges. This leakage happens when the batch size is smaller than the snapshot, thus splitting the snapshot into a sequence of batches that are processed sequentially. With link forecasting, we prevent this information leakage, explaining the substantial drop in performance.
We validate the effectiveness of our ovaluation protocol in preventing information leakage in Appendix H.4. By shuflling the edges inside each snapshot, we destroy the implicit edge ordering within snapshots that may help memory-based models in their prediction. We compare the model performance on snapshots with and without shuffled edges and find that shufiling leads to substantial drop in performance for link prediction but not for link forecasting. These results confirm that information leakage occurs for link prediction and that our evaluation prolocol solves this issue
Realistic Choice of Time Horizons. In the evaluation above, we chose the time horizon h to match the achieve as much comparability as possible between the link forecasting and
batch size b approximately prediction tasks. Thereby, we emphasise performance differences between both approaches since we use the same trained models and "only" group edges differently. In real-world applications, however, the models'
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UN V.
-26.7
-28.2
-27.1
3.0
7.1
0.0
0.6
1.1
3.3
5.0%
0.0%
0.20
-22.6
-31.2
0.2
0.2
-0.3
0.2
5.0%
Datazot
UN Tr.
-12.8
-20.4
-14.0
3.6
4.5
-1.0
4.5
3.4
3.4
AUC Chonge
0.15
10.0%
Can.
-0.5
1.2
-0.2
1.5
2.9
0.4
2.0
-0.6
-12.5
15.0%
20.00 20.0%
Flighte
-3.1
-43
-1.0
0.0
0.1
0.0
-0.0
-0.0
0.1
25.0%
Cont.
0.1
-0.6
0.5
0.6
4.1
0.9
1.3
1.1
0.6
-30.0%
JODIE
DyRep
TON
TGAT
CAWN
EdgeBank
TCL
Graph
DyGPormet
0.00
Jonn
Dyftep
Toi
TeAY
CAWN
Edd bank
Tea
Model
(a) Heatmnap showing the change in performance in percentage. Memory-based models exhibit large drop in performance when using our window-based evalua- tion, when compared to the batch-based evaluation three discrete-time datasets.
(b) Avg. abs. perf. change. Performance for memory-based models changes substantially.
Figure 7: Performance change of our window-based approach relative to the batch-based approach (a) for each discrete-time dataset and model combination and (b) averaged for each model. Models are ordered by type. The three leftmost models are nemory-basody all others are non-memory-based.
performance should be evaluated using time horizons adjusted to specific use case or research question. We provide examples for such an evaluation using the above datasets in Appendix E When evaluated on
realistic time horizons, the performance differences (reported in Table S between link prediction and link lorecasting are even larger than in Figure G Furthermore, the best-perlorming model using link lorecasting
with realistic horizons (see Table 6 compared link prediction (see Table 15] changes for datasets such
as LastFM or Myket, emphasising the need to evaluate the models in realistic scenarios to get accurate performance estimates.
5 Conclusion
In this work, we considered issues in current evaluation practices for dynamic link prediction in temporal graphs. For computational reasons, odges are split into fixed-size batches, which lcads to multiple issucs, including (a) information loss for continuous-lime and (b) information leakage for discrele-time datasets. Additionally, (c) fixed-size batches have varying-length durations that depend on temporal activity patterns. (d) Treating the batch size as tunable paramcter further affects the duration of cach batch, resulting in incomparable results between models that use different batch sizes.
We address these issues by formulating the dynamic link forecasting task. Dynamic link forecasting acknowl- edges the resolution at which temporal interaction data is recorded and explicitly considers a forecasting horizon corresponding to a time window with fixed duration. Depending on the dataset and problem setting, the horizon may span minutes, hours, or longer, but crucially, time windows always span the same length. We compared the dynamic link prediction and forecasting performance of nine state-of-the-art temporal graph learning approaches 14 real-world datasets. We found substantial performance differences, especially for memory-based TGNNs on discrete-time datasets due to information leakage, which has been overlooked far. On datasets with periods of irregular activity, we also observed large performance differences, indicating that most TGNNs are unreliable in these periods. However, periods with irregular aclivity are common in many real-world settings, like opportunistic networks (Huang et al. 2015). By providing a novel evaluation method with implementations commonly used PyTorc librarics that better suited to capture the performance in such data, our work aids the development of better methods for these tasks, e.g. cellular traffic offloading (Trifunovic et al. 2017
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Limitations and Future Work Limitations of our work include that the used metrics treat dynamic link prediction and forecasting as binary classification problem, using one negative sample for each positive edge. Other approaches (You et al. 2022) consider the problem as a ranking task, e.g., using the mean reciprocal rank (MRR), and compute the ranking of cach positive edge inside a single batch with a large number of negalive samples. Such a ranking-based approach provides the following advantages: (T) A large number of negative samples provides a better estimate of the models' precision, (IT) using only one positive sample (with single timestamp) per batch alleviates the problems of varying and tunable batch sizes, and (III) there is information loss since no positive edges (with potentially different timestamps) are grouped. While this mitigates three out of the four problems in Figure L the problem of information leakage could become more severe because multiple edges with the same timestamps are assigned to their own batch. Most importantly, ranking- based evaluation results in a substantially longer runtime, as it introduces a large number of additional negative samples. In contrast, our window-based approach enables the parallel processing of many positive samples in cach time window, leading to a considerably faster evaluation. Moreover, we argue that window-based forecast is closer to real-world applications, which commonly consider forecasts for fixed time horizon that has lower temporal resolution than the data. For example, it may not be required to predict whether customer will purchase certain product within the next second; making such a prediction for the next day or week may be sufficient. A promising direction for future work is combining the ad adnatages of both approaches. In particular, ranking-based metries that include multiple positive samples, such as the Hits@K metric (Hu et al. 2020 could be extended to the link forecasting task.
Furthermore, our reformulation of the dynamic link prediction task suggests a time-window-based model training approach, which was not considered in our experiments. We hypothosisc that window-based training approach changes model performance in two ways: First, memory-based models may perform better since they can learn from the actual temporal patterns in the data rather than from leaked information (see Appendix H.4 showing that memory-based models learn leaked information). Second, we expect the models to become more robust against bursty patterns. With a window-based training algorithum, the gradients for updating the model weights will be accumulated for each time window instead for each equally sized batch. This means each time window will have an equally large influence on the model weights, which we expect to result in more consistent model performance across time. We leave the investigation of the expected changes to model performance introduced by wandow-based training to future work and note that a misalignment between the training objective and the downstream task is common practice in model evaluation, for example, in dynamic link prediction with ranking-bace based metrics (You et al. 2022).
Broader Impact Statement
We believe that more practice-oriented, window-based evaluation of dynamic link forecasting methods, as proposed in this work, is crucial for the adoption of proposed models in real-world applications and for investigating the potential ethical implications of existing models.
Acknowledgments
Moritz Lampert acknowledges funding from the Federal Ministry of Research, Technology and Space in Germany, Grant No. 100582863 (TissueNet). Ingo Scholtes and Christopher Blöcker acknowledge funding from the Federal Ministry of Research, Technology and Space in Germany, via the project "Software Campus 3.0" (FKZ: 011S24030). Ingo Scholtes and Christopher Blöcker acknowledge funding through the Swiss National Science Foundation, Grant No. 176938.
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A Negative Sampling Approaches
A.1 Definitions
Dynamic link prediction is typically framed as a binary classification problem to predict class for existing links during a certain time window and 0 otherwise. Due to the sparsity of most real-world graphs, it usually suffices to train and evaluate using all existing (positive) edges and a sample of non-existing (negative) edges out of all possible odges V2. In static link prediction, negative edges are typically sampled randomly from V² without replacement, but Poursafaei et al. (2022) showed that this technique is ill-suited for dynamic link prediction. One reason is rooted in the characteristics of temporal graphs, where already-seen interactions tend to repeat several times during the observation period. To address this issue, Poursafaci et al. (0022) introduced negative sampling, which we cover in the following.
Let test be the time that splits the temporal edges E into training and test sets. We define Etrain = {(y U2) 13 (uy Uj, (j) E E: i2 < (eest} and Evst = {(u,, vj) [3 (uj, Ug,4;) ) E E :y 2 [eest) that contain the edges occurring before and after the split time trest. respectively. We define the following commonly used sampling strategies for drawing negative samples B, corresponding to set of positive samples B
{[ Ugs ()) 3(u, u,,t,) E b: j s b. (i+ 1)} with |B |,,|| (Poursafaei et al. 2022 Yu et al. 2023
Random: Sample Bi from 2 without replacement and assign the timestamps according to the positive samples B, The subgraph corresponding to B is assumed to be sparse, making it unlikely to sample a positive edge e e B, as negative.
Historic: Sample the set of negative samples B from set of historical edges Enist without replacement with timestamp assignment according to the positive samples B The historical edges Epist consist of all training edges except the ones appearing at the same time as the edges in BT:
Enist = Etrain \ (() uj, (,) E E: ta < S (.((4)))
(1)
If Enisal < [B draw the remaining edges randomly as described above.
Inductive: Sample BJ without replacement from set of inductive edges Eind with timestamp assignment according to the positive samples B," Inductive edges Ein are all test set edges that have not occurred in the training set and do not occur at the same time as edges in Bt:
Find Frest \ (Eerain {(u,),)) ( Ug Ug,dy) E the <t S ((+1))
(2)
If [inaa < [B7,, draw the remaining edges randomly as described above.
Note that we leave out the validation set Eval for simplicity. Nogative edges for Eval can be sampled as for Erest-
A.2 Influence of Link Forecasting on Negative Sampling
The above definitions historic and inductive negative sampling exclude edges from the same time as positive edges from each batch or window from the edge sets to sample from. The sampled negative edges may be different for both approaches since the edges in the batches and windows differ. Different negative samples could explain the performance differences we observed in the experiments in Section 4 We investigate how much the negative samples differ between the two approaches in the following.
Figure M counts the number of edges that could be sampled for each batch and time window. For most datasets, the plots show straight lines for historic and inductive negative sampling. By definition (see Equations
[1] and (2), the negative samples are essentially generated from the set of train and test edges, respectively, but excluding the edges in the current batch or window. Consoquently, the sets of available negative edges for sampling are nearly identical across all batches or windows, resulting in the observed straight-line patterns in the plots. Moreover, the number of possible negative samples is nearly identical
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for the window-based based and the batch-based approaches in all continuous-time datasets. For discrete-time datasets, the number of possible negative edges is identical in all points where both approaches share the same a-coordinate. The batch-based approach has additional points which are a small distance below the linear interpolation between the points the window-based method. This behaviour is caused by batches that contain edges from two different snapshols, resulting in more edges that need to be excluded from the set of possible negative samples. In particular, all edges occurring at the same time as any edge the batch have be excluded as per the definition of historic and inductive negative sampling. Thus, our window- rindow-based approach excludes only edges within the given window, whereas the batch- approach must exclude edges from one or two snapshots.
Overall, Figure S shows that the number of possible negative samples is very similar for all batches and win- dows across datasets, and we expect the generated negative samples to be very similar for both approaches.
Type
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Approach
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(a) Number of edges that can be sampled as negative samples for continuous- time datasets. The T-axis counts the time in days starting with the first edge occurrence in the training set. Note that for some datasets, the lines for the different approaches overlay each other.
Type
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butch
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(b) Number of edges that can be sampled negative samples for all discrete-time datasets. Since the snapshots capture different time ranges for each dataset (see Table D. each dataset has its own temporal resolution counted from the beginning of the training set.
Figure 8: Number of edges that can be sampled negative samples for each batch and each time window, The r-axis shows the arithmetic mean of all timestamps inside each batch/ window from the test set.
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B Normalised Mutual Information
Normalised mutual information an informationn-heoorliee measure based on mutual information. It is based mutual information, which for two random variables X and Y captures the bits of information we gain about the outcome of Y if we know the outcome of X and vice versa. A formal definition is given in the following:
Definition B.1 (Mutual Information). Consider two random variables, X and Y with joint probability mass function (z, y) and marginal probability mass functions p (a:) and (yy- Mutual information is the reduction in the uncertainty of X due to the knowledge of Y defined as (Cover & Thomas, 2006
p (2r, v) log (x, (v)
((X,))= = EE FEX VEY
Note that mutual information can be defined using different logarithms. The intuitive understanding de- scribed above using bits of information is defined using log2- This work utilises the implementation of the Python library scikit-learn (Pedregosa et al. 2011), which uses the natural logarithm log.-
The specific value of mutual information depends on the entropy
H(X)= = ppx))oogp(a
- ØEX
of the underlying random variables, and is thus difficult to compare across different settings. To address this issue, normalised mutual information provides measure between zero and one that is normalised based on the entropies of the underlying random variables (Vinh et al. 2010). We use the following normalisation as implemented in scikit-learn's function germalized_mutaan inlii_nnorrreeeee score:
1(X,Y) NMT(X,Y) 3 (H(()++((Y)
In the context of our work, the NMI mcasure how much information about the edges' timestamps is lost by grouping the edges into use the number of each batch B UB, of the definition of dynamic link prediction in Section g assigned to each edge in the corresponding batch as one random variable and the timestamps of the edges as the other. With this setup, we can measure how much information about the timestamps of edges we gain or keep based on the batch number only.
the NMI to capture the loss of temporal information. In Figure 2 we use
batches. Specifically,
Additionally, we use the NMT in Table 3 to quantify the difference between the assignments of edges time windows and batches, respectively. Similar to above, we assign each edge in the test of each dataset its batch number and also time window number corresponding to the time window the edge belongs to and then compute the NMI between those two variables.
In the following, we present an educational example that illustrates the usage of NMI in the context of our work to facilitate comprehension among readers who may not be familiar with the measure:
Example B.1. Let G be temporal graph with nodes V = (a,
b, c) and temporal edges
E = ((a, 6, 1), (b, c, 2), (c, a, 2), (a, c, 4), (a, b, 5), (6, (6,a,)))
We define the timestamps 4 of the edges e; E E, the batch number for b - 2 and the window number with h = 1 as random variables X, Y and Z, respectively. We obtain the following realizations of X, Y and Z:
x (1,2,2,455,5)
y 2,3,,,
(1, 3,4)
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In the next step, we compute the marginal probability mass functions p(X z),p({ y) and p(Z 2):
1
p(x = 5) 2
p(x = 1)
p(X = 2)
p(X = 4)
6'
6
6
2
2
p\Y 1)
p(Y 2)
p(Y 3)
6
1
1
2
p(Z 1) 6'
p(Z= = 2) 6"
p(Z 3)
1(Z=
6"
6
Afterward, compute the joint probability mass functions p(X p(Y y, -,,=aa ===] 2):
x, = y). p(X = x, 2 2), and
p(X 1,Y 1)
p(x = 2, =) 6
6'
x(x 1) 1
p(X = 2,2 2
6'
6
P(Y - 1, = 6
p(Y = -,7 = 2)
Using these marginal and joint probabilities, compute the mutual information I(X,Y,, I(X, and T(Y, B) using the formula from above:
I(XY))
log
log 0.868
I(X, 2)
loge
loge
1.330
1
I(Y, 2)
log.
loge 0.868
6
Finally, we obtain the normalised mutual information (NMI) by normalising based on the entropies of both random variables:
0.868
NMI(X,Y)
~ 0.715
2 (1.330 1.099)
1.330
NMI(X, 2)
~ 1.0
1 (1.330 1.330)
0.868
NMI(Y, 2 (1.099 1.330)
~ 0.715
Note that the NMT calculations in the main part of the paper are done accordingly. Table 3 reports NMT values that follow the example calculation of NMI(Y, Z).
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C
Datasets
In this work, use eight continuous-time and six discrete-time datasets, listed in Table LI In the following, we describe what systems were observed to create the datasets and analyse the data in more detail.
C.1 Descriptions
We list details about each dataset in the following
Enron Shettyy & Adibi 2004) is a bipartite contimuous- time graph where nodes are users and the temporal edges represent emails sent between users. Emails with multiple recipients are recorded as scparate and simultancously occurring odges, one per recipient. The temporal edges are resolved the second level, and the dataset spans approximately 3.6 years.
UCI (Panzarasa et al. 2009) is a unipartite continuous- time social network dataset from an online platform at the University of California at Irvine. The nodes represent students, and the time- stamped edges represent communication between the students. The dataset spans approximately six and half months.
MOOC (massive open online course) (Kunar et al. 2019 is a bipartite contimuous graph where nodes represent users and units an online course, such as problems or vidcos. Temporal edges are resolved at the second level and encode when a user interacts with a unit of the online course. The dataset spans approximately one month.
Wikipedia (Wiki.) (Kunar et al. 2019) is a bipartite continuous- time graph where nodes represent oditors and Wikipedia articles. The time-stamped edges are resolved at the sccond level and represent when editor has edited an article. The dataset spans approxinately one month.
LastFM a bipartite continuous-tinn time graph where nodes represent users and songs. Temporal odges are resolved at the second level and model the users' listening behaviour and represent when a user has listened to song. The dataset was originally published by Celma (2010) and later filtered by Kumar et al. (019 for in a temporal graph learning context.
Myket" Looghmani & Fazli 2023) is a bipartite continuous- time graph where nodes represent users and Android applications. The time-stamped edges represent when user installed an application. The dataset spans approximately six and half months.
Social Evolution (Social) (Madan et al. 2012) is a unipartite continuous-time graph of the prox- imity between the students in a dormitory, collected between October 2008 and May 2009 using mobile phones. Temporal edges connect students when they are in proximity and are resolved in seconds.
Reddit (Kumar et al. 2019 is a bipartite continuous-time graph where nodes represent Reddit users and their posts. The time-stamped edges are resolved in seconds and represent when a user has made post on Reddit. The dataset spans approximately one month.
UN Vote (UN V.). et al. 2009 Poursafaei et al. 2022) a weighted unipartite discrete-time graph of votes in the United Nations General Assembly between 1946 and 2020. Nodes represent countrics and edges connect countries if they both vote "yes". The datasct resolved at the year level, and edge weights represent how many times the two connected countries have both voted "yes" in the same vote.
US Legislators (US L.) (Huang et al., 2020 Fowler 2006 Poursafaei et al. 2022 a weighted unipartite discrete-time graph of interactions between legislators in the US Senate. Nodes represent legislators and edges represent co-sponsorship, i.e., edges connect legislators who co-sponsor the same bill. The datasct is resolved at the congress level, and edge weights encode the number of co-sponsorships during congress.
&acc datasct is part of the Zenodo package provided by Poursafaci et al. 2022 under the Creative Commons Attribution 4.0 International (CC BY 4.0) license, other license information provided. 4 License: Attribution Attribution-NnnCommecc. NomCommrriall 4.0 International (CC BY-NC 4.0)
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UN Trade (UN Tr.) MMcDonnald al. 2015 Poursafaci et al. 2022 is directed and weighted unipartite discrete-time graph of food and agriculturay trade between countries, where nodes repre- sent countries. The dataset spans 30 years and is resolved at the year level. Weighted edges encode the sum of normalised agriculture imports or exports between two countries during a given year.
Canadian Parliament (Can. P.) [Huang et al. 2020 Poursafaei et al 2022 is a weighted uni- partite discrete-time political network where nodes represent Members of the Canadian Parliament (MPs) and an edge between two MPs means that they have both voted "yes" on bill. The dataset resolved at the year level, and the edges' weights represent how often the two connected MPs voted "yes" on the same bill during a year.
Flights (Schafer et al. 2014 Poursafaci et al. 2022 is directed and weighted unipartite discrete- time graph where nodes represent airports and edges represent flights during the COVID-19 pan- demic. The edges are resolved at the day level, and their weights are given by the number of flights between two airports during the respective day.
Contacts (Cont.) (Sapiezynski et al. 2019 Poursafaei et al. 2022 is unipartite discrete-time proximity network between university students. Nodes represent students who are connected by an edge if they were in close proximity during a time window. The dataset is resolved at the 5-minute level and spans one month.
C.2 Edge Activity patterns
Similar to Figure 3 show the link densities over time for all datasets in Figure 9 While some datasets, such as Enron, UCL, and LastFM, contain very inhomogeneously distributed activity, others exhibit recurring or scasonal patterns, c.g. MOOC, Wikipedia, and Reddit. In addition to scasonality, we also observe trends like growing number of edges in the Myket, UN Vole, and UN Trade datasets, which are also often found in standard time series data (Brockwell & Davis 2016
C.3 Time Window Durations for Different Batch Sizes
In Figure 10 evaluate the dependency between batch size and time window for empirical temporal graphs. The figure shows the distribution of batch durations (y-axis) for different batch sizes (x-axis). We observe that, both in innuus and discrete-time temporal graphs, a single batch size can create time windows with varying durations even within the same dataset. For continuous-time temporal graphs, we typically have much bigger batches than edges per timestamp, such that the time window defined by the batches becomes long (cf. Table D. The number of edges per snapshot in discrete-time temporal graphs is generally larger than the batch size b any period, regardless of the density (Table D This means that edges in a batch often belong the same snapshot, leading small window durations.
C.4 Number of Links per Timestamp
In Figure 11 we show how often each number of links with the same timestamp (x-axis) occurs in each dataset. We can observe that all contimuous-time datasets have a large number of edges that appear at a unique point time. Additionally, the number of edges that occur at once for many continuous- is less than ten (MOOC, Wiki., Myket, Reddit) and less than 50 for most datasets, except for Enron, which has outliers with more than 1000 links a certain timestamp. For discrete-time datasets, many edges occur in cach snapshot.
datasets
C.5 Window Sizes for Different Window Durations
Figure 12 shows the distribution of the number of links per lime window for continuous- and discrele-time data sets. We can see that the distribution of window sizes depends on the distribution of edges across time as visualised in Figure g Datascts with a more uniform activity pattern, such as Wikipedia and Reddit, show similar number of edges across windows of the same duration. Datasets with inhomogeneously distributed activities, e.g. Enron UCI, exhibit wide range of window sizes. For large values of h, i.e. horizons that
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1500
Euron
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(a) Continuous-time temporal graphs resolved in seconds. For visualisation purposes, edges are binned into 6-hour time periods and then represented bar in the histogram.
UN V.
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UN Tr.
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(b) Discrete-tims temporal graphs where each bar histogram corresponds to one snapshot. Since snapshots capture different time ranges for each dataset (see Table 1. each dataset has its own temporal resolution.
Real-world datasets exhibit diverse edge occurrence patterns that are visualised using the edge density across time, i.e., histograms counting the number of edges per timestamp. Dashed lines divide the datasets into 70% train, 15% validation, and 15% test sets as used in Section
Figure 9:
include more than half the observed time, the window sizes diverge because the window of the last time window that still includes observed links gets smaller.
Figure 13 shows the histograms of window sizes for the horizons used in the experiments of Section (scc
Table 3 We observe that continuous-time datasets with only small performance differences (in particular, Wikipedia and Reddit) between our window-based and batch-based evaluations exhibit a narrow distribution of window sizes. Datasets with larger changes in performance (MOOC, LastFM, UCI, and Enron) have an increasingly longer tail. This supports our hypothesis that a batch- based evaluation results in skewed model performance estimates for temporal datasets with inhomogeneous temporal activity, that is, datasets with long-tailed window-size distributions.
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15000
Euron
UCI
MOOC
Wiki.
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Myket
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Social
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(a) Continuous-time temporal graphs: Batch size determines the average time window length. However, single batch size creates time windows with various lengths within and across datasets.
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(b) Discrete-time temporal graphs: Fixed-size batches fall mostly within snapshots when the batches are much smaller than the snapshots. Depending on the dataset, larger batches can also span across many snapshots.
Figure 10: Using low opacity value for individual points, the distribution of time window durations is shown for different batch sizes. Le. points appear less see-through with an increasing number of points with the same duration and batch size stacked on top each other.
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10a
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(a) In the contimous-tine time temporal graphs, it is most common that at most edge occurs per timestamp.
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(b) The snapshots in discrete-time temporal graphs contain large numbers of edges, typically much larger than commonly utilised batch sizes. The Contacts dataset has fewer links per snapshot due much higher resolution than the remaining discrete-time datasets.
Figure 11: The link count histograms show how many edges occur per timestamp in oatinmous-time temporal graphs and per snapshot in discrete-time temporal graphs, respectively.
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10a
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horizon & (h)
horizon h (h)
horizon à (h)
(a) The number of links window in continuous-time temporal graphs for horizons ranging from second to one year. The r-axis labelled hours.
UN V.
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horizon h
horizon h
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(b) Window sizes for discrete-time temporal graphs where h represents the number of snapshots.
Figure 12: Window sizes, i.c number of links per time window, for different horizons.
MOOC 10a
Enron
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Figure 13: Histogram of window sizes, i.e. number of links per time window, for contimuous-time temporal graphs.
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D Link Prediction using Different Batch Sizes
The results in Table
1 and 5 show the differences in AUC-ROC and average precision scores using two different batch sizes. While the same models with the same trained weights are used for both evaluations, the results show substantial differences in performance. This is in line with our expectations as described in Problem (d).
As expected due to Problem (a); the performance differences are especially large for memory-based models, and the performance drops almost consistently for all datasets when using a larger batch size. Other models show no clear preference for whether larger or smaller batch sizes lead to better performance. This drop in performance for memory-based models specifically can be explained because they update their internal node representations after processing each batch, thus, larger batches lead to less frequent updates and more "out-of-date" internal representations {Su et al.) 2024 Feldman & Baskin, 2024). In other words, larger batches lead to a larger information loss because more edges at the beginning of each batch are missing in the internal representation for the prediction of edges at the end of each batch.
Table 4: Mean AUC-ROC performance for dynamic link prediction (b = 800) over five runs for the continuous- (top) and discrete-time (bottom) datasots. Values in parentheses show the relative change compared to an evaluation using batch size 200.
Dataset
JODIE
DyRep
TGN
TGAT
CAWN
EdgeBank
TCL
GraphMiser
DyGFormer
Euron
67.9(17.7%) 74.8(33.15)
68.1(10.5%)
59.4(11.25)
67.1(t1.1%)
78.5(11.7%) 7%))
12.2(11.1%) 68.4(+1.15%)
(7.3(11.193)
2.1%=2 2%
UCI
47.7(17.99) 79.9(14.195)
61.0(19.3%)
67.6[10.99% 59.2(10.75)
64.6(16.69%
79.9(10.9%) 58.6(10.69)
76.0(
2.7% 7%
MOOC
82.0(13.45)
17.9(13.5%)
87.5(11.19)
70.5(10.1%)
57.2(17.69 6%)
72.6(10.0%)
74.5(10.1%)
81.3(10.15))
1.8% 6%
Wiki
47.4((3.49)
83.7(10.5%)
13.3
72.0(10.5%)
76.5(10.88)
85.2(10.15))
88.0(10.290)
80.4(10.5%)
1.4%=2.11 1%
LastFM FM
76.5(12.05)
70.4[11.8 8%)
80.1(10.88)
68.4(70.05)
67.9( 10..2%
77-1(11 0%%
64.3(70.19)
65.9(10.19)
78.9(
0.7% 8%
Myket
61.4(10.7%)
63.6(11.0%) 0%
(7.4() 60.7(10.79)
32.6( (0.3%)
52.0K10.199
58.4(10.055)
59.1(10.2%)
33.0 (3.56)
0.1%=0.80 3%
Social
87.31 (44.48)
88.2([4.8%)
92.0(10.3%)
92.7(10.158 19%)
87.8(10.2%)
86 06.00)).298)
95.3(10.193)
(4.1(10.1%)
97.4(10.195
1.19:=200 0%
Reddit
79.0((1.9%)
76.4(13.9%%
10.3(10.19)
10.3(10.1%) 18.7(10.19)
78.5(10.2%)
76.2(10.0%)
77.2(10.1%)
80.2
0.7%% 1 1.3%
V.
66.9(17.8%) 71.3(18.15)
50.2(10.2%) 52.8(10.0%) (7.2()4)4%)
80.6(10.19)
53.0(10.155)
56.5(10.4%)
63.3(10.456
1.8% 2.7%
US T..
58.6(10.658)
73.5[17.9%)
76.7(18.7%)
78.6(10.195 195)
62.6(10.9%%
67. 67.2(10.4%)
90.3()0.1%) 1..9()
2.49%-3.4%% 00.2()
UN It.
63.2()).11) 65.7()0.655)
61.4(10.3%) 61.5(12.69)
64.6(10.2%)
86.5(10.19))
60.9(10.155)
66.2(10.1%)
(1.25)
0.5% 0 8%
Can. P.
(2.75)
64.6(13.0%)
72.9()07%%)
71.1()0.7%
62.1(1145% 67.9()).2%)
68.2(10.0%)
61.0(10.2%)
90.3( (4.55))
1.5% 1 1.6%
Flights
68.4(10.9%) 68.9(10.99)
68.5 68.5(1
72.7(10.155)
66.0(10.0%)
74.6(10.09)
68.7( 70.7[10.0%) 70.6(10.0%)
0.3%
Cont.
83.4((2..25)
93.3(12.2%)
95.5(10
13.3(10.1%) 15.5(10.19)
((.069))
04.6(10.1%)
04.2(10.1%)
97.2(10.195
0.7% 0.9%
2.5%%
4.1%%.2.8%
1.8%%
0.3%610.4%
0.4%%10.4%
2.44%
0.3%....6%
0.3%.103%%
1.6%
Table 5: Mean AP performance for dynamic link prediction (b = 800) over five runs for the continuous- (top) and discrete-time (bottom) datasets. Values in parentheses show the relative change compared to an evaluation using batch size 200.
Dataset
JODIE
DyRep
TCN
TGAT
CAWN
EdgeBank
TCL.
GraphMixer
DyCPormer
Enron
68.2(15.4%)
62.4[]30.455
65. (5.2()))2%)
63.2(10.1%)
66.8(11.2%)
75.8()1.5%)
70.7(10.6%)
(3.1(10.9%)
77.2(11.0%)
2.4%
UCI
77.5(11.5%)
16.5()
68.3(10.1%) 50.1(11.5%)
(5.2(10.15)
61.9()6.2%))
85.5(10.15) 68.9(10.2%)
81.1(10.6%)
2.2% 5%
MOOC
80.5(13.15)
74.7 74.7((3.11))
85.6(11.69%
73.5(10.08) 84.6(10.1%)
56.1(0)))5%
78.3(10.2%)
77.8(10.1%)
62.4(10.0%)
1.7% 5%
Wild.
29.7(15-35%)
77.3(44.3%)
98.591
67.9(10.1%)
75.4(10.6%)
72.6()
19.6(10.1%)
91.3(10.2%)
83.6(10.7%)
1.4%++2.00
Last/M
75.9(19.095)
68.6[ 13..99
80.1(10.395)
69.8(10.08) 75.2(10.3%)
72.5( (1.05)
T1.9[10.395
74.2(10.2%)
81.2(10.2%))
1.0% 4%
Myket
61.0(12.4%) 63.7(10.44%)
61. ((0.88))
56.6(10.9%)
(0.39))
51.2( 10. 15%)
57.9(10.7%)
58.8(10.6%)
44.6(10.3%)
0.7%.++0.7%
Social
66.7() 13.2(15.88%)
93.5(10.99)
80..( 91.9
80.8( (1..35)
96.9(10.19))
(5.5(10.0%)
97.5(10.2%)
1.5%
Reddie
78.9(12.095)
75.7([4.4%)
80.3(10.39%)
(5)5)
81.1(10.0%)
(3.5( (0.25)
76.5(10.15)
77.4(10.1%)
82.7[
0.8% 55%
v.
62.2(18.39%) 65.1(14.09))
63.1(14.55)
51.8(10.8% 5%
(0.7)
84.9(10 1%))
52.9(10.7%)
53.7(10.5%)
2.2% 60.0(10.0%)
US L.
48.2(10.0%%
67.8(17 2%%)
74.4(19.398
(0.6(10.6%)
11.361
63. 1 (10.3%
78.8(11.8%)
86.2(10.2%)
86.7(11.1%)
2.2% 3
UN Tr.
67.9(11.79))
68.6(11.255 (
57. 2212.89)
67.2()1 2%%
67.4(10.8%)
81.1(10. 155)
56.7(10.995 9%)
63.7(10.0%)
64.6(10.4%)
1.0% .%%
Can. P.
(0.4( 51.4(12.6%)
69.1(10.8%)
(1..6))))%)
64.5(10.9%)
65.0 33.39)))
78.9(12.2%)
(14.11%))%
- 2.2%
Flights
66.8(11.495)
65.7(1 6%%)
68 2,.0..28
13.0(10. )
(4.86)))3%)
70.4(10. 1%5
10.8.10.0%)
71.4(10.3%)
68. (8.4[10. ((..2.9)
0.5% 6%%
Cont.
53.3(12.3%) 91.4(13.0%)
95.6 05.6()0)65)
(6..110.1%)
88 88.4(3055%) (1.5()))))))
95.1(10.1%)
94.4(10.1%)
97.5 (7.8(10.1%)
0.8%
o
3.0%
4.8%
1.6%
0. 4.4%+0.4%% 4.%%
1.6%
0.3% 5%
0. 0.6%%t1..15 0.4%%+0.6%
27

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Published in Transactions on Machine Learning Research (02/2026)
E Evaluation based on Realistic Time Horizons
In our main experiments, we determined the time horizon based on the average number of links per time window to enable a fair comparison to the batch-based approach. In Section 3.1 we discussed that the time horizon for a realistic evaluation should instead be chosen carefully for each individual dataset. Tn the following, we provide guidelines for selecting the time horizon in practice and, as an example of such a realistic evaluation, assign a reasonable horizon for each dataset used in this work.
E.1 Guidelines for Selecting a Good Time Horizon
Three factors restrict the choice of possible time horizons for an application domain: (Q1) Which time horizons are reasonable in the context of the task? (Q2) Which time horizons fit the characteristics of the dataset, and (Q3) Which time horizons are possible given the available computational resources?
The first question (Q1) should be the primary focus for the selection. We list typical ranges for common application domains of link forecasting models in the following:
Recommender systems: Recommender systems are employed in a multitude of diffcrent areas, and depending on the area and the type of recommendation to give, the time horizons can change drastically (Wang et al. 2021b). Session-based recommendattons are made on timescales from seconds to hours, e.g., for single browser session. Recommendations for short-term preferences use a time horizon of days to weeks and usually model evolving preferences, in which a user, for example, researches specific product calegory before purchasing product from that category. Lastly, recommendations for long-tern per-term or static preferences use time horizon of months or years and capture user behaviour, such as a preference for buying products from a certain brand.
Traffic forecasting: Similar time ranges as for recommender systems also exist for traffic fore- casting, depending on the goal of the forecast. It can range from seconds to minutes for real-time management or incident detection, from minutes to hours for traffic control systems, from days to months for infrastructure planning (Mystakidis et al. 2025
Opportunistic networks: The time gramularity for forecasts in opportunistic networks is usnally in the range of minutes (Shu et al. 2022 to hours (Gou & Wu 2022 Huang el al., 2015).
Note that even within the same application domain, e.g., traffic forecasting, the time range is highly task- dependent, making it difficult to provide general recommendations. Therefore, we select appropriate time horizons for all datascts used in this paper's experiments and explain the rationale for our choices, providing examples to guide time horizon selection in other scenarios in Appendix E.2
Given a reasonable time horizon for an application, the second question (Q2) must additionally be considered. In particular, the results in Section[sshov that especially bursty or highly irregular temporal edgo-occurrence patterns lead to skewed model performance when using batch-based evaluation. We further observe that the model's performance for individual time windows can vary substantially with the window size, that is, the number of edges per window. Therefore, an evaluation can highlight the model's ability to handle irregular edge-occurrence patterns by choosing a time horizon that reflects the dataset's 's non-uniform patterns in its window-size distribution. On the other hand, if we are not interested the model's robustness to irregular odge-occurrence patterns the datasct, we can choose a time horizon that "destroys" these patterns. For example, the window size distribution would be uniform for dataset with a seasonal pattern if we choose the period of the seasonal pattern as the time horizon. Additionally, the task context might have already been a deciding factor in the datasot's 's temporal resolution during its creation, making the datasct's 's temporal resolution a natural choice for the time horizon.
Given the time horizons possible under (Q1) and (Q2), we must additionally consider (Q3) to determine the final time horizon. Depending on the datasct's temporal edge density, the time horizon should usually be a multiple of the dataset's timestamp resolution to enable parallel processing for many edges. Datasets with high temporal resolution (contimuous-time) are often sparse where many timestamps have only
28

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single reee-requiiing large time horizon in terms of multiples of the resolution to enable high GPU utilisation. Ideally, the time horizon required by the task enables high parallelisation for contimous-timme temporal graphs. If this is not the case, one needs to compromise between computational requirements and how well the horizon fits the task. The temporal resolution for discrete-time datascts (low resolution) often represents a natural choice for the time horizon because each snapshot already contains enough edges for high parallclisation. Note that we suggest mitigation strategies Appendix G if the chosen time horizon contains too many edges and causes memory overflows.
E.2 Selecting Exemplary Time Horizons
We use 14 real-world datasets to evaluate our approach in Section For each dataset, we assign an appropriate horizon. Note that this enables a fair model comparison since we use the same horizon for all models across each dataset. The temporal resolution of most discrete-time datasets is limited by the data collection process. The US Legislators dataset, for example, contains one snapshot for each Congress, which provides natural horizon of one snapshot. Thus, we will only consider continuous-time datasets and discrete-time datasets where the duration of snapshot is not yet a natural time horizon for evaluation, i.e. Contacts.
We list the considered datasets and the chosen horizon, with the reasoning behind it as follows:
Enron is a network of users with edges representing emails sent between them. We choose 24 hours as a reasonable horizon since 90% of all email replies are typically sent within a day (Kooti et al. 2015).
UCI is a social network based on student communications. We use 30 min the horizon since users receiving lext message lypically feel pressured to reply between the next 20 minutes and the end of the day (Aranda & Baig 2018).
MOOC connects students to units of an online course based on their interactions. We set h = min since Guo et al. (0144) recommend keeping the learning video of unit shorter than this time frame.
Wikipedia represents the editing behaviour of users in a graph. Since editing Wikipedia articles is unpaid, we do not expect frequent interactions from each user. We assume that users come from different time zones and consider that the total duration the dataset is only one month. Therefore, we see the typical working time of 8 hours as an appropriate time horizon take into account that interactions won't appear very frequently, but there are still enough time windows for evaluation.
LastFM connects users to the songs they listen to. We select 24 hours as the horizon to evaluate this dataset on a task where the goal is to predict the songs that users will listen to lomorrow based on their listening behaviour during the last days.
Myket represents users and Android applications that connected when application is in- stalled. Considering that, similar to the Wikipedia dataset, no frequent interactions are expected, we choose 24 hours as the time horizon since the total duration of the dataset is longer than the total duration of the Wikipedia dataset.
Social Evolution is proximily network gathered from students in dormitory. Thus, we select 2 hours typical duration of lecture including breaks as the time horizon.
Reddit contains the posting behaviour of Reddit users. Since dynamics in a social network are typically fast, we select a time horizon of 15 minutes.
Contacts: Similar to Social Evolution, select 2 hours as the time horizon since the network also captures the proximity of students.
We use the trained models from the experiments of the main part of our work and reevaluate the specified datasets with the selected time horizons. The results are presented in Table and 7 For completeness,

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Published in Transactions on Machine Learning Research (02/2026)
Table 6: Average AUC-ROC performance and standard deviation over five runs using the trained models from the above experiments and the window-based evaluation with the horizons specified above. The tables also include the datasets that have been reevaluated using performance scores obtained from the main experiments' time horizons. The best performance score for each dataset is highlighted in bold.
Datasets
JODIE
DyRep
TGN
TGAT
CAWN
EdgeBank
TCL
GraphMixer
DyGFormer
Enron
84.2 + 4.8
80.4 + 2.5
70.0 + 4.5
68.3 + 1.8
75.5 + 0.4
83.1 + 0.0
74.2 + 4.8
87.9 + 0.6
83.9 + 0.6
UCI
89.4 + 0.7
2.
64.0 + 1.3
52.2 = 1.1
56.0
0.2
75.3
0.0
55.3 + 1.3
82.7 = 0.9
75.1 = 0.4
MOOC
84.0 - 4.1
81.3 3.3
87.6 + 1.3
80.7 0.9
69.3
1.5 1.5
62.9 = 0.0
08.1
70.4 1.6
79.9 = 10.0
Wiki.
75.5 75.5::00 0.8
73.2
81.5 + 0.6
83.5 0.2
71.9 0.8
76.1 0.0
85.2
0.6 0.6
87.9 + 0.3
80.6 = 1.6
LastFM
2.1
67.5
78.6 2.9
66.0 0.9
67.2
0.3
77.5 0.0
63.2 6.7
60.6 = 1.3
78.9 + 0.6
Myket
64.5 1.8
62.7 3.1
60.4 233
57.8 + U.4
32.2 + 0.4
51.4
0.0
58.3 + 2.0
58.9 + 0.3
32.8 + 0.9
Social
87.0
4.7
92.3
92.6
86.7
85.1
94.7 + 0.5
94.7
0.2
97.4 = 0.1
Reddit
80.6 0.1
79.5 + 0.8
80.4 + 0.4
78.6 = 0.7
80.2 + 0.3
78.6 =
76.2 + 0.4
77.1 + 0.4
80.2 = 1.1
Avg. Rank
3.0
5.2
3.8
6.1
6.9
6.0
6.1
4.2
3.6
UN V.
34.0 1.8
52.2 + 2.0
51.3
7.1
54.4
+ 3.6
53.7
+ 2.1
89.6
1: 0.0
53.4
+ 1.0
56.9
1.6
65.2 = 1.1
US L.
52.5
61.8 118+400 3.5
57.7
+ 1.8
78.6
+ 7.9
82.0
+ 4.0
68.4
0.0
75.4
+ 5.3
90.4
+ 1.5
89.4 = 0.9
UN Tr.
57.7 + 3.3
50.3 + 1.4
34.3
+ 1.5
64.0
+ 1.3
67.6
+ 1.2
85.6 + 0.0
63.7
+ 1.6
68.6
+ 2.6
70.7 + 2.6
Can. P.
63.6 10
67.5 2 8.5
73.2 + 1.1
72.7
+ 2.2
70.0
+ 1.4
63.2 0.0
69.5 3.1
80.7
+ 0.9
85.5 + 3.5
Flights
67.4 2.0
66.0
+ 1.9
68.1
+ 1.7
72.6
+ 0.2
66.0
+ 1.7
74.6 + 0.0
70.6
+ 0.1
70.7
+ 0.3
08.8 = 1.0
Cont.
85.4 d: 0.5
74.5
4 3.1
94.6
+ 0.6
96.0
+ 0.2
86.6
+: 0.1
85.8 + 0.0
95.7 1 0.4
95.2
1 0.2
97.8 1 0.0
Avg. Rank
7.3
8.0
6.5
3.5
5.5
4.2
5.2
2.7
2.2
both tables also include the performance scores of the discrete-tine datasets that have not been reevaluated because we determined the horizon used above as realistic.
The results using both the AUC-ROC as well as the average precision score mostly agree on a best-performing model, yet for different datasets, there is no clear winner among the models. For contimuous-time datasets, JODIE, GraphMixer, and Dy DyFrrrrrr are among the best-performing models, while EdgeBank, GraphMixer, and DyGFormer performed best for discrete-time data.
DyGFormer performs best for both Contacts and Social Evolution, suggesting that DyGFormer is best suited for proximity networks among all models. For UN Voie, UN Trade, and Flights, EdgeBank simple baseline model that predicts an edge if it has occurred before is among the best. These datasets are highly repetitive because they are, c.g. based on a schodule or relations among countrics that rarcly change. Thus, since they are all outperformed by simple baselines, none the proposed TGNN models adequately address the task of these datasets, i.e. finding edges that do not follow the schedule or some other recurring pattern. For other types of datasets like communication (e.g. Enron or UCI) or user-interaction networks (e.g. Wikipedia or MOOC), no clear patterns visible.
Table 7: Mean average precision scores and standard deviation following Table 6
Datasets
JODIE
DyRep
TGN
TGAT
CAWN
EdgeRank
TCL.
Graph
DyGForner
Enron
82.2 4.8
80.0 + 3.4
71.2
+ 4.2
72.6 + 1.3
77.1
+ 0.3
81.6 0.0
77.9 + 2.6
89.2 + 0.4
85.0 + 0.6
UCI
03.0 + 0.5
81.5 +
78.0
+ 0.9
71.6 0.7
73.3
+
0.2
75.6 0.0
73.2 4 0.7
89.6 + 0.5
85.2 4 0.3
MOOC
84.1 + 5.4
79.4 438
87.4
+ 1.6
81.9
0.8
73.8
+ 1.1
62.1
+ 0.0
75.8 + 0.5
75.6 + 0.9
82.6 + 8.9
Wiki.
78.3 + 1.2
16.4011 0.7
88.3
+ 0.4
58.0 0.2
75.7
1.1
72.4 = 0.0
89.7 4 0.4
91.3 + 0.2
$4.0 1.2
LastFM
73.6 + 2.0
61.8 + 1.8
78.6
3.7
73.0 0.5
69.2
+ 0.5
72.9 0.0
71.2 4 6.7
71.0 + 1.1
81.3 + 0.9
Myket
62.9 + 1.5
60.2 + 1.9
61.1
1.7
56.8
0.4
44.9 +: 0.2
51.1
+ 0.0
57.8 + 2.2
59.0 + 0.2
44.4
Social
82.5 + 4.0
81.6
+ 5.7
94.0 + 1.8
95.0 0.3
85.8 + 0.1
79.9
+ 0.0
96.2 + 0.8
95.8
0.2
97.8 + 0.1
Reddit
80.1 0.3
79.2 + 0.9
80.6 + 0.6
1.0 78.6
81.3 + 0.4
73.5
0.0
76.5
77.5 -
82.8 = 0.8
Avg. Rank
3.4
5.8
3.8
5.5
6.8
7.2
5.4
4.0
3,2
UN V.
52.6 - 1.8
49.6 + 1.9
49.7 3.9
52.7 0077222 2.6
52.4 +: 2.0
84.2
0.0
52.4 + 0.9
54.0 + 1.4
62.4 4 1.7
US L.
46.0 + 0.9
62.5 3.6
58.6
2.4
71.0 8.9
80.7
4 3.7
63.2
0.0
77.5
4 4.3
86.5 + 1.9
86.1 1.1110 1.0
UN Tr.
52.7 3.0
49.4 0.9
5322
1.5
58.9
59.2 + 1.7
79.0 + 0.0
57.5
1.9
65.8
67.1 + 2.7
P.
52.1
6L0 7.6
69.9
0.8
70.8 1.6
68.3 1 2.3
59.4 0.0
68.2
4 1.6
$0.9
83.2 - 2.9
Flights
65.2 2.7
63.9 + 2.8
68.3
2.2
73.5 - 0.3
65.5 1: 1.3
70.4 0.0
71.0 -
71.
69.1
Cont.
53.3 + 0.7
69.7 4 3.7
95.0
0.8
0.2
88.1 + 0.2
82.3
0.0
96.7
95.8
98.5 + 0.0
Avg. Rank
7.7
6.3
3.3
5.2
4.7
4.8
2.5
2.2
30

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Published in Transactions on Machine Learning Research (02/2026)
Table 8: Test AUC-ROC scores for link forecasting with realistic horizons and the relative performance change compared to link prediction using the trained models from the experiments Section 4 The table compares the AUC-ROC scores for all datasets that have been reevaluated on a different horizon. The last row now/column provides the mean μ and standard deviation of the absolute values (without sign) of the relative change per column/row.
Model
JODIE
DyRep
TGN
TGAT
CAWN
EdgeBonk
TCL
GraphMixer
DyGForeer
p
Earon
80.4(19.39 81.2()8.88%)
70.0(12.8%)
68.3(116.8) 4%)
75.5(113.79)
63.1(-4.13)
74.2(19.7%)
87.9("8.2%)
83.9(19.8%)
9.29 4.2%
UCI
88.4(17.3%)
70.4(136.9%)
64.0()
52.2(112.559
56.0(13.855
75.9(-8.93)
55.3(17.858)
82.7(-2.5%)
75.4(.10%%)
9.1% 11.
MOOC
84.0(10.2%)
81.3(
87.6011.0%)
80.71 199)
(0.58)
62.9()1.63)
68.1(16.398
70.4(_5.4%)
79.9(11.6%)
2.2% +-.1%
Wiki
78.5(17.8%))
73:21 (9.
83.5(10.88%)
83.5(10.190)
71.9(10/45))
16.1(11.3%)
85.2(10.19()
57.9("0.0%)
80.6(70.736
2 2.0%%tt3300
LastFM
71.((1099))
67.5115.7% 7%6)
(8.6()
08.0(13.5%)
(7.2(1
17.5(.0.9%)
63.2(11.6%)
8..6(_8.1%)
78.9(.0.19)
3.1 3.196:22.0 6%
Myket
64.5(10.8%)
62.7(12.45) 49%)
60.4(11.155
57.8(10.3%%
32.2(10.895)
58.3(10.2%) 51.4(110%%
50.9(*0.7%)
32.8(10.0%)
0.8%%-:0..77
Social
47.0014.758
84.4(1
92.3:10.7%)
02.6(
86.7(11.25
(5.1(,0.9%
94.7(10.55%)
94.7("0.6%%
97.4(70.115
2.0% +-.06
Reddit
80.6(10.096)
79.5(10.0%)
80.4 10.4000.055)
63.6((10 10.00000000000
80.2(10.09)
78.6 (.136)
76 76.2(10.190)
TT. 17.1(.0.19)
80:2( 80.2(10.096)
0. 0.0% 1%6
Cont.
85.4(.10.7%)
71.8(121.9%)
91.0011.55
96.0(10.0%)
86.6(11.08)
95.7(11.396 8..8(_
(6.2())22%)
97.8(10.73%)
5. 5.4%
4.9%.44000%
10.3%++11.9%
1.399+00.9%
3.9%
3.0%
2.99643.1%%
3.1%-43.8%
3.0%+:344%%
1.6%64:3.1%
Table 9: Test average precision scores for link forecasting with realistic horizons and the relative performance change compared to link prediction using the trained models from the experiments Scction 4 The table compares the average precision scores for all datasets that have been reevaluated on different horizon. The last row/colf cclumm provides the mean μ and standard deviation of the absolute values (without sign) of the relative change per column/row.
Model
JODIE
DyRep
TCN
TCAT
CAWN
EdgeBBonk
TCL
CraphMixerr
DyCFormer
Enron
12.2(114.0%)
14.7%)
71.2()
72.6(114.9%)
(7.1(116.8%)
81.6(16.15)
77.9(11
89.2(11.4%)
85.0(111.2%)
11.8%
UCI
93.0(114.%)
81.5(160.5%)
9..0%
71.6
(1.6(12.6%)
75.6(116.3%)
16.2()
89.6(1...3%
85.2(15.7%)
15.5% 19.6%
MOOC
84.1(%0.9%)
79.4(12.9%%)
83.9(J0.7%) 87.4()
73.8(10.4%)
62.1(12.3%)
75.8([3.4%) 4%5
75.6((3.0%)
82.6(10.2%)
1.8%%+:1.39
Wiki.
18.9%)
18.4(1
08.3%
88.0(10.198]
(5.7(10.9%)
72.4(10.9%))
89.7(10.2%)
91.3(10.15)
81.0(11.9%)
1.8%%112.5%
LastF'
73.6(15.1%)
64.8(1
78.0(22.2%)
73.0(22.79)
69.2(10.9%%)
72.9(10.4%)
71.2(10.6% (0.6))
71.0((4.19))
81.3(10.3%)
2.8% 9%
Myket
62.9(30.89)
60.2(19.68%)
61.1(116%%
58.8(00.6%)
41.9(10.5%)
51.1(10.3%)
57.8(10.9%)
59.0K.0.3%)
41.4(00.5%)
1.0%%.11.1
Social
82.5(.8.69)
81.6(110.99%)
94.0(*0.99%)
95.0(10.2%))
85.8(10.4%%
79.9(10.9%)
06.2(10.0%5
95.8(10.4%)
97.8(10.5%)
2.0% 8%
Reddit
80.1030.09)
79.2(10.09))
78.6(.0.19) $0.8(10.09%)
81.3(10.995
(8.5(1022%)
76.5(10.0%)
77.5(00.09)
82.8(10.19)
0.15:11.11 10.1%
Coul.
83.9(111.69)
69.7 69.7
1.39)
96.9(10.99)
88.1 (90)
82.3 (21.())))
96.7(11 8%))
95.8(11.79))
(1.3(10.8%)
6.3%
6.75%
25.6%
2.9%%%..7%%
2.7%
4.1%
3.9%%45..%%
2.7%%43.7%
2.5%
2.37%-1..8%
In Table S and 9 the differences in performance between link forecasting with a realistic horizon and link prediction are reported, similar to Table 13 in Section 4 The results show that for most datasets, the difference in performance between the current link prediction evaluation and our proposed link forecasting is even larger when choosing a realistic horizon based on the application scenario. This emphasises that the model performance is skewed if the models are evaluated with link prediction without taking the application scenario into account.
31

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Published in Transactions on Machine Learning Research (02/2026)
F Experimental Details
For reproducibility, we provide a Python package extending the dynamic graph learning library DyGLit (Yu et al. 2023) as a supplement, including a bash script to run the experiment:
We use the best hyperparameters reported by Yu et al. (023) and, for completeness, list these hyperparam eters for the 13 datascts used by Yu et al. (2023) below. However, the Myket datasct (Loghmani & Fazli,
2023) was not included in the study. Therefore, for Myket, we use each method's default parameters suggested by the respective authors.
We use 9 state-of-the-art dynamii graph learning models and baselines (JODIE (Kumar et al. 2019 DyRep (Trivedi et al. 2.19), TGAT (Xu et al. 2020). TGN (Rossi et al. 2020). CAWN Waag et al. 2021c), Edge- Bank (Poursafaci et al. 2022). TCL. (Wang et al. 2021a), Graph approaches (all except EdgeBank) are trained five times for 100 epochs using the Adamn optimiser with learning rate 0.0001. An early-stopping strategy with patience of is employed to avoid overfitting. For training and validation, a batch size of 200 used. The training, validation and test sets of cach dataset contain 70,, 15% and 15% of the edges, respectively. The sets are split based on lime, L.e,, the training set contains the edges that occurred first, while the test set comprises the most recent edges.
(Cong et al. 2023) and FoGmer
(Yu et (dl])22))))) The neural-networr--asse
The experiments were conducted on a varicty of machines with different CPUs and GPUs. list of machine specifications provided in Table T0
Table 10: Hardware details of the machines used for the experiments.
(a) CPUs
(b) GPUs
CPU
GPU
AMD Ryzen Threadripper PRO 5965WX 24 Cores
NVIDIA GeForce RTX 3090 Ti
AMD Ryzen 9 7900X 12 Cores
NVIDIA GeForce RTX 4080
11th Gen Intel(R) Core(TM) i9-11900K 8 Cores
NVIDIA GeForce RTX 3090
AMD Ryzen 9 7950X 16 Cores
NVIDIA GeForce RTX 4090
13th Gen Intel(R) Core(TM) 19-13900H 14 Cores
NVIDIA GeForce RTX 4060 (Laptop)
AMD Epyc 7543 (3rd Gen)
NVIDIA A100
AMD Epye 7763 (3rd Gen)
NVIDIA GeForce RTX 2080 Ti
AMD Epyc 7713 (3rd Gen)
NVIDIA TITAN Xp
Intel Xeon Platinum 8480+ (4th Gen)
NVIDIA TITAN X
NVIDIA Quadro RTX 8000
NVIDIA H100
NVIDIA T.40
NVIDIA L40s
For all model architectures, time-related representations use size of 100 dimensions, while all other non- time-related representations set to 172. An exception is DyGFormer, where the neighbour co-occurrence encoding and the aligned encoding each have 50 dimensions. We use eight attention heads for CAWN, and two attention heads for all other attention-based methods. The memory-based models either use a vanilla recurrent neural network (JODIE and DyRep), or a gated recurrent unit (GRU) to update their memory. Other model-specific parameters are provided Table [I]
bttpe://gghuubbcc///ulbBBBBuuuut (MIT License)
32

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Published in Transactions on Machine Learning Research (02/2026)
Table 11: Specific hyperparameters for different models and datasets.
(a) Hyperparameters for neighbourhood sampling- based models. WNeighhours the number of sampled neighbours using the specified neighbour sampling strategy. nu is the number of transformer layers (for TCL), the number of MLP-MMixer layers (for GraphMixer) or the number of GNN layers otherwise.
(b) Hyperparameters DyGFormer.
Dataset
Modal
Sequence Langth
Size
Dropout
Wikipedio
DyGomee
Reddit
DyGPormer
84
0.2
MOOC
DyGFormes
256
8
0.1
Last M
DyGRoree
512
16
0.1
Reron
DyGRormer
256
8
0.0
Social Rvo.
DyGRormer
32
0.1
UCI
DyGRoree
32
0.1
Model
Samplinx
"Netgh.
"[.
Flights
Myket
Gyormee
DyGRoree
256
32
0.1
Dyltep TGAT
recent
10
Dy GFForeer
2048
Wikipedin
TGN TCL
recent
20
Legis.
DyGoormer
GFormes
GraphMiver
recent
recent
30
20
2
0.1
0.5
Vote
DyGroreer
DyKep
TCAT
unilorm
receal
20
10
0.1
0.1
(c) Hyperparameters CAWN.
Reddit
TON
receat
10
0.1
GraphMizer
recent
Model
Walk
Time Scale
Dropout
Wakipedia
CAWN
0.000001
0.1
MOOC
TGN
Reddit
CAWN
3.003601
0.1
TCL
MO0n
CAWX
3.000001
GraphMixer
Last
CAWN
1.000001
0.1
DyRep
Enran
CAWN
0.000001
TGAT
20
LastFM
Eoron
GraphMiser
TOAT
TGN
TGN
TCL.
DyKep
recent
recept
recent
recent
20
20
10
10
10
0.6
0.1
0.2
0.0
0.3
0.0
Myles
Flighta
UN Vose
US Legtte.
UN Trade
CAWN
CAWN
CAWN
CAWN
CAWN
CAWN
0 000001
0.000000
0000011
0.1
0.1
GraphMiser
receat
Contacts
CAWN
0 000000
0.1
(d) Hyperparameters EdgeBank
Social
TGN
TCL
GraphMixer
Datases
Model
Neg. Nampliin
Memory Mode
Time Window
DyEep
10
TGAT
20
random
unlimittd
UCI
TCN
10
0.1
Wikipedia
Pilgeltakk
repest
TCL
recent
20
0.0
Myket
GraphMiser
TGAT
GraphMiser
TGN
LyKep
recept
necett
receat
recal
recent
recel
20
10
0.4
0-1
Reddit
MOOC
EdgeBeak
EdgeBeak
inductive
Indinttive
Listorieal
bistorical
random
random
repest threcheld
time window
time window
Fime window
threshold
threshold
fixed propection
Rsed propartion
interval
TGAT
LastF
EdgaBank
bistorical
time window
repeas Interva)
Flighta
TGN
inductive
repent Uhresheld
TCL.
random
Uime Window
Rixed propertion
GraphMiser
20
Earon
EdgeBank
historical
time window
repeat interva)
ByTlap
uniform
10
inductive
repent threshejd
TOAT
unfform
20
0.2
candom
repent Uhreboold
Can. Pael.
TGN
uniform
10
0.3
repest
TCL
uniform
20
0.2
threcheld
GraphMiser
uniform
20
0.2
candom
unlimtted
EyKep
receul
10
0.0
UCI
Edgellank
Indnctive
bletorical
time window
time window
fixed proportion Interval
Lagte
TGN
candom
unlimited
Myset
EdgeBeak
Listorical
repent Uhresoold
GraphMixer
inductive
repent Uhreshold
random
unlimited
TGAT TGN
Flighta
EdgeBank
bistorical
repent threrbeld
UN Trade
Indnctive
repest thresheld
TCL
uniform
20
random
Time Window
Bled proportion
GraphMiser
unifarm
20
Can. Park.
EdgeBank
kistorical
time window
Rsed propartion
DyHep
10
inductive
reponi Uhresheld
UN Vote
TGAT TGN TCL
uniform
recent
20
10
0.1
0.2
EdgeBank
candom
Lsue window
propertion
uniform.
20
0.0
GraphMiser
DyRep
uniform
receal
20
10
0.0
0.0
UN Trade
EdgeBannk
bistorical
inductive
time window
threchold
Interval
Contacts
candom
Giee window
repont intervol
UN Vote
EdgeBaak
bistorionl
time window
repeat interval
GraphMiser
Inductive
time window
repeat Interval
random.
time window
repent interval
Contucts
EdgeBoak
bistorical
time window
repeat interval
Inductive
repest thresheld
33

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Published in Transactions on Machine Learning Research (02/2026)
G Runtime and Memory Implications
In the following, we discuss how to avoid memory overflows in datasets with time windows with many edges. Additionally, we present the empirical runtime of the experiments in Section for dynamic link prediction and forecasting averaged across five runs.
G.1 Avoiding Memory Overflows
In highly bursty datasets, the window size can become very large during periods of extreme density. This can lead to memory overflows the evaluation is implemented on a GPU. The casiest mitigation strategy to avoid overflows, the runtime is not a deciding factor, is to move the evaluation to the CPU. This can mitigate the problem because CPU memory is usually larger than GPU memory, and if the CPU memory is also full, strategies such as paging or swapping can prevent overflows. While this mitigation strategy was sufficient for the experiments conducted in this work, stricter runtime requirements or larger datasets might require faster and more reliable solution.
We explain a faster and more reliable solution without memory overflow problems that can be implemented on the GPU in the following: To enable adaptation to any model and framework, we provide a conceptual implementation with pseudocode since the specific implementation may vary across TGNNs and frameworks. We first present pseudocode for a basic implementation of our window-based evaluation approach in Listing [ for reference. In this pscudocode, timestamps) that can be positive samples with label 1 negative samples with label 0. For each window, we first sample the neighbourhood of all nodes that are sources or destinations of the target edges based on the recent history of the temporal graph. Next, we can optionally include a memory for each node to enable the evaluation of memory- models and then do message passing as defined by the TGNN model on the sampled recent neighbourhood. Afterwards, the resulting node representations are combined obtain a forecast for cach target temporal edge, which can be used to compute arbitrary performance metries for each window. Lastly, the memory needs to be updated if the model uses memory.
iterate over time windows containing target temporal edges (with
We extend this pseudocode to avoid memory overflows by subdividing the time window into smaller chunks in Listing 2 This subdivision into smaller chunks is possible because the temporal information is coarse- grained into time windows, thereby deliberately discarding temporal information within each time window. Thus, we do not need to save any temporal information, but only need to ensure that our subdivision introduces no information leakage. We implement this subdivision with an additional loop compared to Listing I The outer loop encompasses all steps that could potentially leak information, including sampling the recent neighbourhood, calculating performance metrícs, and updating memory. The inner loop comprises resampling reduce the size of the recent neighbourhood graph and inferring whether an edge occurs using the TGNN model. Lastly, the results for each edge and the intermediate node representations are saved to enable the metric calculation and memory update of the whole window, combined in the outer loop.
G.2 Empirical Runtime
We compare the empirical runtime of window-based link forecasting against the batch-based link prediction in Figure 14 The runtime of both approaches is generally comparable, with both approaches being faster than the other on some datasets and models. For continuous-tim datasets, we can see that the runtime is often similar and large differences are caused by specific characteristics of the datasets. The model evaluation on UCI, for example, faster using the batch-based approach because consistently evaluates batches of size 200 while the time windows are mostly smaller, which leads to less parallelisation. This is because the duration of each window was chosen so that the average window size across the whole dataset is comparable to the chosen batch size of b = 200. For this specific dataset, there are large bursts of activity in the first third of the total dataset duration and low activity afterwards. This leads to small window sizes for the temporal edges of the test set (see Figure 9
For discreto-time datasets, each snapshot contains more than 200 edges for most datasets, leading to better parallelisation for link forecasting and, thus, smaller runtime. However, the basic implementation of our window-based approach leads to GPU memory overflows on datasets with many edges per time windows
34

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Published in Transactions on Machine Learning Research (02/2026)
def dealuate_tgnn(tnm t_graph):
# Initialise window loader that iterates over all windows Str_wiiddww_ooddee get_ window_loader' t t_graph, # temporal graph for evaluation horizon=3600, # specify time horizon as 1 hour
test_ test_ratiom0.155 15, # use the last 15% of the time as test set n_negatives-1 sample 1 negative edge for each positive sample
# Iterate over all time windows with positive and negative sample lesples for tonget__eddgee t_edge_ latelllblll__ in test_ pest_window___e _andowwloader:
11
# Sample recent neighbourhood that occurs before all "target_ t_ edgess' of the window neighbour_t_grape
t_graph seaaph-ge_rree get_recent, srrcent_eeighbuurs (target_ t _ddgees)
12
Get updated memory of all modes involved in the window's computation.
13
14
z sgan.get_memoryyee (weighbour_t_grg)
Use the TGMN to get temporal node features tgnn meighbour_t )
15
16
17
# Get forecast for each edge using the temporal node feature # of the edge's source and destination node out = perecast_linket Compute performance metrics using the forecast and the ground truth metrica- calculate @ (out, t_edge_label) Update memory wi th truth state tgnn arddatememoryCa (z, [edge_label]
18
19
harget_t_edgeat
20
21
22
28
Listing 1: Python-like pseudocode for a basic implementation of our window-based evaluation approach as 8 reference.
for some model implementations in particular TGAT, CAWN, GraphMixer and DyGFormer. For those models, the employed mitigation strategy (running the evaluation on CPU) resulted in larger runtime for the window-based evaluation. Table 12 shows the detailed runtime of the evaluation of all models and datasets for dynamic link prediction and forccasting.
Table 12: Mean and standard deviation in seconds of the evaluation runtime of all models for dynamic link prediction and forecasting averaged across five runs.
Datasee
Appeoach
JODIE
DyRap
TGN
TGAT
CAWN
EdgeBBnk
TCL
Grapabliuc
Faron
Pred
Roses
3.47 + 1.57
3.42 0.26
4.15 = 0.50
1.16 + 1.50
4.30 0.51
4.20
1.92
37.20
36.16 0.85
200
73.05 +: 1.38
07.06 =: 0.76
7:70 + 0.09
9.50 = 0.11
7:51 1.18
7.76 a: 0.25
12.05 1:21
12.46 0.85
47.79 +: 11.00
43.68 4: 0.43
D01
Posi.
Boce.
2.60 1.02
6.54 0.47
5:00 : 0.30
305- = 0.72
8.44 0.50
3.00
0.72
21.58
37.72 2: 0.44
0.85
97.97 :: 1.38
85.00 + 2.72
4.56 2: 0.17
1.15 + 0.02
12.35 :: 0,30
4.50 0.97
8.03 0.30
13:50 2: 2.031
23.85
15.29 + 0.78
: 00.00
3000
Prod.
Rove.
61.10
53.41 0.32
30.23 0:37
58.06 01.34
65.40 0.35
210.16 0.28
530
656.37
301.55 5.18
W64.73
95,00 1.19
W9.27 0..00
140.45
132 012-410 0.42
2.8.80
254.47
1.38
Rune:
Prod.
13.07
14,31
13:1
0.99
M9.25
1.72
0.43
15.99
1.44
19.01
49.27
1.50
LastFM
Prod.
Reve:
119.50
271.34
097
1.76
340.44 = 12:33
281.58
1.81
338.74 1: 1.73
400.6
4: 11.46
185.54
1150.90
31.00 M3
53.27
3472
3316-72
70.24
1413.11 18 US
1723.99 = 25.39
674.69 4: 12.96
578.05 08 6: 3.05
582.02
702.00
0.50
1.33
1037 0S
1193.25
3.40
Myket
Pred.
Rume:
167.24
00.36-44 6.72
3.9
12130
105.55 = 6.00
7.38
115.55
J11.12 4: 9.27
11.19
680.26
7111 21 2 8.51
15.71
876.41 :: 17.00
851
+ 21
445.51 1: 5.62
479. 179.92 6.45
5/7.77 + 7.10
475.26 2: 5.32
402.05
360
7.51
19:39
613.35 + 5.05
622.20 4: 7.03
Sucial
Pwel
Buse.
500.15
436.55
3.05
1.80
14
121.6
3,02
510.61
419.62
4: 2.44
311
1256.04
1511
2.50
12.50
0020.21 4.50
1000.46 1.38
1559-11
955
700.50
2:45
1.51
590.58
12/3.01
2.20
1.07
1923.54 2: 2.20
1201 80
Rodiix
Race.
121.79
124.5
0.07
210
$61.97
174.34
26 1.12
1.06
227.88
248.51
254.54
0.30
161 31
0.05
9.10
137.99
Prod.
101.49
174.20
0.09
500.17
6209.27 02.08
654.51
310.50
1220.42 5.09
406.54
T.
Pred.
Rume:
2.55 4: 1.82
1.01
2113 :: 1.77
0.51
2.4 4 1.77
0:31
15.40 0.82
13.25 0.30
42.72 1.06
33.43
0.35
0.05 0.01
0.71 :: 0.02
3.19 0.25
5.75 0.98
0.87 :: 1.25
3,03
25.85 1: 1.21
15.07
UN Tr.
Prod.
Reree
34.63
1,50 8 0.26
0,42
37.36 4: 1.44
1.13 = 0.24
3.7
36.17
8 0.12
0.44
271.15 15 3.10
44 4:33 2.36
2502 364.16
05 = 2488
161.55 3: 0.63
1.55 0.05
00.81 2: 0.41
19 02 0.20
SUT 83 14.74
719.00 70007
81.71 8: 0.32
213.38 4: 1.02
Con. P.
Rune:
Pred.
0.50
0.22
2.00 = 0.21
346.74 0.54
1.5 0.24
1.36
0.31 60.15
1661 22 1.00
1242
0.11 0.02
0.0
0.63
0.21
20.65 + 0.50
350.33 2.02
661.15 +: 25.61
Flights
Ruse.
9.66
6.58
10860.33 2098..15
68.14 0.77
1923.
31.16
Bicoe:
2.85 938.18
673.36
2.15
1906
10.54
3878
11:00
2548555
1129.57 :: 4.24
1378
4.22
1318.44 12:00
Prvd.
0.81
940.65
953.46 :: 8.02
2628.33 01 54.70
21.10
3554-40 02
1523.29 :: 36.65
1848.28
40.53
1573.09
11.28
35

---

Published in Transactions on Machine Learning Research (02/2026)
def @aaluate_tgnn(tee t_graph):
Weet_wwndoww_osse wowder_odrrree get moaddw (
t_graph,
horizon=3600,
test_ratio=O.I5
n_negatives=1
for target_t_ t_dge,, t_edge_labbel _abeellalll__e in test rest_window _oader::
Initialise lists to save the individual forecasts and # intermediate node respresentations
window_oud out, window_z neighbour _____apt_pphh___ neighbour_t_graph Divide the time window into chunks of size 10 for chunk_t_edget
0, []
t_graph. le.ggraphet__.... get_ pet_recent__o neighbours (target t__dges)
12
18
14
(abdivide(targeen) tedde,
edges, chunk chunk_size=100 size=
# Resample neighourhood to remove unnecessary nodes from neighbourhood # Sample from the "neighour_t__ t_graph" to make sure information is leaked, # e.e. edges from the same batch are sampled chunk chunk_t_gree t__raph
15
srighbour_t_graphe get_rrecet_neiieeeeeee (chunk, t eddges) 2 tgnn.get..n.. (epemory(chuukt.aoo
19
20
z tgnn (z, tounkk)_ggrah) out forecast_linket (2, chunk chunk_t_edgent t_edees)
21
22
Save the edge forecasts of this chunk window_oud _utt__ot___g wttploowout.pppeeeee apppdd
# Save the intermediate node representations window_ z. (p)end
26
metrics calculate metrics es (window_ouu out, t_edge s_edge_label) tgnn update wwwputteeeearyaaeeeeeee (window_a, __edge_label
27
Listing 2: Python-like pscudocode explaining how to subdivide windows to prevent GPU memory overflows.
We only add comments to the code sections that differ from the basic implementation in Listing I
36

---

Published in Transactions on Machine Learning Research (02/2026)
Enron
Approach
Approach Forec.
Forec. Pred.
UCI
Pred.
MOOC
Wiki.
LastFM
10a
Myket
Average Time
Dataset
Social
Reddit
UN V.
US L.
UN Tr.
102
Can. P.
Flights
Cont.
10
10a
103
JODIE
DyRep
TGN
TGAT
CAWN
EageBank
GraphMiser Dy Former
TCL
A Average Time (s)
(a) Average runtime dataset.
Model
(b) Average runtime per model.
Figure 14: Runtimes of the experiments in Section 4 averaged across datasets or models.
37

---

Published in Transactions on Machine Learning Research (02/2026)
H Detailed AUC-ROC and Average Precision Results
Here, we provide detailed tabulated results for all models' AUC-ROC and average precision performance across five runs, including standard deviations. We further include visualisations investigating the causes of the large performance differences between dynamic link prediction and forecasting.
H.1 AUC-ROC
The following reports the complete results (including standard deviations) of the experiments conducted in Section ! For casier comparison between the performance of the batch-basod and our window-basod approach, we visualise the results in two different table formats. Table 13 and Table 14 show AUC-ROC scores for time-winddo-baased link forecasting and the relative change compared to the batch-based evaluation of dynamic link prediction. Table 15 and Table 16 show the full results, including standard deviations for both approaches separately.
Table 13: Test AUC-ROC scores for link forecasting and the relative performance change compared to link prediction for continuous-timo graphs using the same trained models (standard deviations in Appendix H.] The last row/coll /colummmn provides the mcan μ and standard deviation of the absolute values (without sign) of the relative change per column/row.
Doraset
JODIE
DyRep
TCN
TGAT
CAWN
Edge-Bank
TCL.
Grxph
DyCFor
Earon
81.0(18.6))
80.3("9.2%)
67.9 07.9(10.29)
69.0 (9..5))))58)
75.7(113.9%)
82.7(r3.6%)
75.1(111.1%)
88.6(19.0%)
9.3%f=0.18% 81..("10.6%)
UC1
60.2( 86.8(14.2%%
35.2()7.49) ((.15))))5)
56.3()3.0%)
72.5("4.9%)
56.3(16.2%)
80.2[10.5%)
75.7(.0.6%)
5.
MOOC
83.1((2.15)
79.0(_2.1%)
87.4(1122%)
79.90 (2.9%)
68.8(12.2%)
59.8(.3.4%)
68.4(15.8%)
70.3([5.5%)
80.0(_1.5%)
3.0% 1.7%
81.6(10.43)
78.3(_0.1%)
43.7(10.6%)
82.90 (0.79)
71.3( (0.46)
77:2(+0.1%)
84.6(10.6%)
87.3(10.6%)
79.8(_0.3%)
0.4%
LastFM
76.3(12.28)
69.0(.3.7%)
79.2(11.9%)
65.2( (6.2(
66.3112.6%
78.0(.0.2%)
62.5(12.7%)
59.9(19.2%)
78.2(_1.0%)
3.1% 6%
Myket
64.4(10.65)
64.1(.0.11)
61. (1.2()))15)
37.8(10.4%)
33.5(13.1%)
52.6(11.3%)
58.3(10.3%)
30.8(10.5%)
30.8(13.00%
1.0% 1.2%
Social
92.1(10.8%)
92.2(_0.5%)
12.5(1) 2(70.00)8
86.3(11.490
81.9))1))
(1..())))%)
91.6(10.6%)
97. 97.3(10.066)
0.6%
Reddit
80.6(J0.0%))
79.5("0.0%)
80. (00.00)))
78.6 18..(1)
(0.2()
78.6(.0.1%)
(8.2(10.11%)
77.1(10.19)
80.2(10.0%)
0.09%
++
4.1%++6.1% 2.0%
0.8%%+
4.20%
3.3%+44.4%
1.8%
3.4%%++4.0%
3.2%%
2.1%6%3
Table 14: Test AUC-ROC scores as in Table 13 for discrete-time graphs
Dataset
JODIE
DyRep
TGN
TCAT
CAWN
EdgeBBnk
TCL.
GraphMixer
DyGFormer
UN V.
51.0(126 7%5)
52.2(125 (28.22%
51.3(127 12)
54.4(13.0%)
53.7(17.198)
89.6(10.0%)
53. (3..(6)))5)
56.8(11.33)
06 65.2(13.59)
10.8% 2%%
US
52.5(16.89))
618(122.68)
(3..
78.6(10.2%)
82.0(10.2%)
35.4 68.4(11.3%)
90.4(10.2%)
89.4(10.0%)
1.07%
UN Tr.
12.9(_12.4%)
50.3(120.4%)
14.0(114.0%)
64.0(13.6%)
85.((11.0%) 67.6(14.5%)
63.7(14.55))
68.6(13.45)
70.7(13.4%)
7.8%
(3.6(10.355)
67.5(11.28)
73:2(10:28))
72.7(11.88) (%)
70.0(12.958)
63.2(10.4%)
04.((12.5)
80.7(10.65)
95.0(112.8%)
2.4%%-+3.97%
Flights
17.4(19.15)
66.0914.35))
69.1(11.05))
72.0(10.0%)
08.0(10.19)
74.6(10.0%)
70.6(10.0%)
70.7(10.0%)
68.8(10.1%)
1.0%
Cont.
05.6(10.16)
(4.0(10-630)
96.0(10-598)
(5.9(10)6%)
86.7(14.15))
03.0(10.95)
(5.7(11.35))
95.2(11-15))
07-7(10.6%)
1.115-+1.280
p
8.3%%
12.9%%
12.3%
1.5%
3.1%
0.6%
1.5%
1.1%
3.49
38

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Published in Transactions on Machine Learning Research (02/2026)
Table 15: Average AUC-ROC performance over five runs for the test set of the continuous-tine datasets, including standard deviations. For discrete- and continuous-time datasels, the average rank of each model is reported in the last row, respectively. The best performance score for each dataset is highlighted in bold.
Eval.
Dataset
JODIE
Dyllep
TGN
TGAT
CAWN
EdgeBunk
TCL
GraphMixer
DyGFormer
Earon
81.0 + 5.1
80.3 + 1.4
67.9
7.1
69.0
1.6
75.7
0.5
82.7
1 0.0
75.1
1 5.2
88.6 + 0.5
84.5 0.6
UCI
86.8 + 1.0
60.2 1 2.8
62.1 1 1.3
56.2
1.4
56.5
1 0.5
72.5 1 0.0
56.3
1 1.0
80.2
1.0
76.7 0.5
MOOC
83.1 + 4.2
79.0 + 4.5
87.4
1.9
70.9
0.8
68.8
+ 1.6
59.8 + 0.0
68.4
+14+14 1.4
70.3
1.2
80.0 9.0
78.3 +
83.7
0.6
82.9
71.3
77.2 + 0.0
87.3
0.3
79.8
Forec.
LastFM
76.3
69.0 14
2.7
65.2
66.3
75.0
0.0
62.5
59.9
78.2
Myket
64.4 = 2.2
61.1 = 2.9
61.2 2.6
37.8
0.5
33.5
52.6 = 0.0
58.3 = 2.2
59.8
+ 0.4
33.8 # 0.9
Social
92.1 + 1.9
92.2 1: 0.7
92.2 1 2.6
92.5
0.5
86.5 1 0.0
84.9 1 0.0
94.7
= 0.5
94.6 - 0.2
97.3 + 0.1
Roddu
80.6 + 0.1
79.5 1. 0.8
80.4 0.4
78.6
0.7
80.2
0.3
78.6
1. 0.0
76.2
1. 0.4
77.1
0.4
80.2 1.1
Avg. Rank
Euron
1.
66.4
0.4
81.3
76.4
UCI
83.3 + 1.4
51.4 7.8
63.0 1,3
59.6 1.5
58.2
0.6
69.1
0.0
60.0
0.9
80.6 +
76.2 0.6
MOOC
84.8 + 3.1
80.7 +: 3.2
88.5 + 1.8
82.3
0.6
70.4
1: 1.3
61.9
1 0.0
72.6 - 0.6
74.4 1.4
81.2 1 8.9
Wiki.
81.8 1. 0.4
78.4 1. 0.4
84.1 0.6
83.5
0.2
71.6
0.8
77.1 1 0.0
85.2 1 0.5
87.8
0.3
80.0
LastFM
68.4
68.1
65.9
78.9
Myket
64.0 +
64.2 2.7
61.1 2.6
57.6
32.5
0.4
52.0
0.0
58.4
59.5
32.8 1.0
Social
91.3 - 2.1
92.7 = 0.5
91.7 3.3
92.6
0.5
87.7
0.1
85.8 = 0.0
95.2 = 0.2
911
0.2
97.3 + 0.1
Reddit
80.6 - 0.1
79.5 + 0.8
80.1 0.4
78.7 = 0.6
80.2
0.3
78.6 - 0.0
76.2 = 0.4
77.1
0.4 4.1
80,2 + 1.1
Avg. Bank
3.1
3.4
5.8
7.6
6.1
5.9
3.9
Table 16: Average AUC-ROC performance five for the test set of the discrete-time datasets, including standard deviation. For discrete- and continouustime datasets, the average rank of each model is reported in the last row, respectively.
Eval.
Dataset
JODIE
DyRep
TGN
TGAT
CAWN
EdgeBBank
TCL
GraphMixer
DyGFormer
UN
510
1.8
51.3
7.1
51.
53.7 2.1
89.6 + 0.0
53.4
56.9 + 1.6
65.2
US L.
52.5
1.8
61.8
57.7
1.8
78.6
+
82.0
4.0
68.4
75.4 +
90.4 + 1.5
89.4 +
UN Tr.
57.7
+ 3.3
50.3
+ 14
54.
1.5
64.0
+ 1.3
67.6 = 1.2
85.6 + 0.0
63.7 + 1.6
68.6 + 2.6
70.7 + 2.6
Furee. Can. P.
63.6 1: 0.8
67.5
1 855
73.2
1.1
72.7
2.2
70.0 : 1.4
63.2
= 0.0
69.5 4 3.1
80.7 1 0.9
85.5 = 3.5
Flights
67.4
+ 2.0
66.0
68.1
1.7
72.6
0.2
66.0
+ 1.7
74.6 + 0.0
70.6 + 0.1
70.7
+ 0.3
08.8 1.0
Cont.
95.6
0.8
96.6
0.3
86.7
0.1
95.2 + 0.2
97.7 0.0
Avg. Rank
4.3
5.3
2.2
UN
73.7 2.4
70.3
4.3
50.1
1.6
89.5
0.0
56.2
US L.
56.3
1.9
79.9
$4.0
2.2
78.5
81.8
4.0
67.5
75.6
90.2
89.4
UN Tr.
66.1 3.0
63.2
2.1
63.1
1.2
61.7
1.3
61.7
1.3
86.4 + 0.0
60.9 + 1.3
66.3 + 2.5
68.3 4 2.3
Pred.
Can. P.
63.9 +: 0.7
66.6
2.5
73.4
3.5
71.6
2.6
68.0
1.0
62.9 + 0.0
68.2 + 3.6
81.2
1.0
97.7 + 0.7
Flights
69.5
2.2
89.0
+ 1.0
68.8
+ 1.6
72.6
- 0.2
66.0
+ 1.7
74.6 4: 0.0
70.6 + 0.1
70.7 0.3
68.8 + 1.0
Cont.
95.5 1: 0.5
95.4
0.2
96.1
0.8
95.4
0.3
83.3
0.0
92.2 1 0.0
94.5
94.1 1 0.2
97.1 = 0.0
Avg. Rank
5.3
5.3
6.3
39

---

The results are Published in Transactions on Machine Learning Research (02/2026)
H.2 Average precision
Average precision scores an additional metric to evaluate experiments in Section 4 comparable to the results using the AUC-ROC score.
Table 17: Mean average precision performance for dynamic link forecasting (window-based) over five runs for the continuous-tinn time datasets. Values in parentheses show the relative change as compared to the average precision performance for dynamic link prediction (batch-based).
Datasei
JODIE
DyRep
TGN
TGAT
CAWN
EdgeBBank
TCL
GraphMiser
DyGFormer
50.8(112.0%)
68.6(15.0%)
71.7(113.5%)
76.00115.190
(1.1()5.5%)
80.8(19.2%) (8.26111.35)
85.3/11 1.67)
10.6%++3344
UCI
87.0(17.2%)
(9.5(121.4%)
(8.2(_2.88)
64.4(16.2%)
61.0(118%)
68.6(15.4%)
65.2(15.5%)
85.3(10.6%)
80.5(.0.2%)
5.7%v.6.4%%
MODC
12.4(11.13))
16.9(10.35))
86.3()0.8%)
82.7(_2.11)
72.3(11.7%)
50.0(12.77)
74.9(14.6%)
74.4([4.5%)
82.1(J0.4%)
2.0%%++..6%
Wiki.
84.1(10.11)
10.9(10.19)
88.5(10.4%)
87.5(10.45%
75.1(10.1%)
73.3(10.3%)
89.2(100.45)
90.8(10.45%)
63.1(70.0%)
0.27
16.7(11.13))
69.4(12.758)
(8.8()1.9%)
72.1(33.0%
(8.2(12.3%)
73.4(10.3%)
70.3(11.87)
10.0(15.45))
80.5(00.7%)
2.2%%++106%
Myket
64.5(11.6%)
63.1(10.99%)
62.8(11.25%
67.9(11.45%
46.8(13.39%)
51.9(11.3%)
58.9(11.08)
60.0(11.5%)
46.1(13.3%)
1.7%%
Soctal
(0.4(11.33))
91 (
93.9(10.8%)
95.0(10.25)
85.64
79.7(11.19))
(6.1
(6..44))455)
97.7(70.3%)
0.6%%++0.4%
Reddit
$0.1(10.0%)
79.2010.9%)
10.0(10
78.0(10011%)
11.39)025%)
73.5(10.2%%)
76.5(10.008)
17.5(10.0%)
62.8(70.19)
1.1%%....19
a+a
3.%6-4.3%
4.8%6*7.9%
1.636+1.66%
3.5%6+44.6%
3.1%
2.1%-=22%%
3.1%==3.5%
2.896+33.356
2.1%%+-4.0%
Table 18: Mean average precision performance for dynamic link forecasting (window-based) over five runs for the discrete-time datasets. Values in parentheses show the relative change as compared to the average precision performance for dynamic link prediction (batch-based).
Dotaset
JODIE
DyRep
TCN
TCAT
CAWN
Edgellank
TCL
GraphMiner
DyClorrmer
62.6(.22.4%)
40.6(126.81)
52.7(10.9%)
52.4(13.4%)
84.2(10.7%)
52.4(11.7%)
54.0(10.19)
62.4((4.0%%
9.4%
US I..
46.0(.4.5%
62.5(114.5%)
58 (2.6) 8%)
71.0(10.3%)
80.7(10.155)
63:2( 63.2()))2%)
77.5(10.1%)
86.3(10.65)
86. 86.1(10.45)
5.4% 1788+90.8
Tr.
62.7(_10.6%
40.4(116.6%%
53.2(19.798)
58.9(11.7%)
50.2(12.4%)
79.0012.680
57.5(12.3%)
65.8(13.0%)
67.1(14.4%)
6.0%
Can. P.
(2.1(11.39)
61.0(11.355
69.9 (0.00)))00
70.8(14.5%)
68.3(1))95)
59.4(1688)
68.2(16.2%)
80.9(14.8%)
(3.399)
5.3% +4.07
Flighta
(5.2()
63.9(144335)
68 3(10.09))
73.6(11.190)
71.0(10.49) 70.4(10.2%%
71.9(11.09)
6u (0.0 756
1,2%%+1.339
Cont.
94.0()0.2%)
05.8(10.355)
87. (0.899)
96.8(10.8%)
88 ((1445)
80.4(10.6%)
96.6(11.8%)
95. (6.7())))55
98.3(10.65))
1.2% 1.33%
6.99%188.9%
10.6%:110.1%
12.5%
3.0%,22.5% 1.6%
1.8%;22.0%
2.1%
19%
4.1%:155.3%
Table 19: Mean average precision performance over five runs for the test set of the continuous-ting datasets, including standard deviations. For discrete- and contimuuus-time datascts, the average rank of cach model is reported in the last row, respectively.
Eval.
Dataset
JODIE
DyRtp
TGN
TGAT
CAWN
EdgeBank
TCL
GraphMixer
DyGFoonner
Enron
80.8
5.3
78.3
68.6
5.6
71.7 1.2
76.0 + 0.7
81.1
78.2 2.9
89.8 + 0.4
85.3 0.6
UCI
87.0 + 1.9
59.5 - 2.3
09.2
+ 1.0
61.4
1.1
61.0
- 0.7
68.6 - 0.0
65.2
= 0.8
85.3 + 0.6
80.5 0.9
MOOC
82.4 = 4.9
76.9 + 4.3
86.3
+ 2.3
82.7
= 0.7
72.3
+ 1.3
59.0 - 0.0
74.9
1 0.7
74.4 4 0.6
82.1 8.7
Wiki
84.1 0.5
80.9
1: 0.4
88.5
1: 0.4
87.5
0.2
75.1
1 1.0
73.3
1 0.0
89.2
0.3
90.8
- 0.2
83.1 1.2
Forec.
Last
76.7
69.4
78.8
3.5
72.1
0.8
0.5
73.4
70.3
6.5
80.5 0.9
Myket
64.5
1.8
63.1
1.5
62.8
2.2
57.9
0.4
46.6
+ 0.2
51.9
58.9
2.6
60.0
+ 0.2
46.1 1.7
Social
89.4
4.7
91.9 1: 1.0
93.9
1: 1.7
95.0
0.3
85.6
1 0.1
79.7 1: 0.0
96.1
1: 0.4
95.8
1. 0.2
97.7 + 0.1
Reddit
80.1 0.3
79.2 0.9
80.6
4: 0.6
78.6
1.0
81.3
+ 0.4
73.5
0.0
76.5 4 0.6
77.5
+ 0.5
82.8 + 0.8
Avg. Rank
3.5
5.9
3.8
5.2
7.2
6.9
5.1
4.0
3.4
Enron
72.1
3.0
69.7
3.7
65.3
1: 3.2
63.2
0.5
66.0
4: 0.5
76.9
0.0
70.2 4: 3.4
82.3
+ 0.6
76.4 0.4
UCI
49.0
71.2
1.1
68.6
65.1
0.6
65.0
69.0
0.8
85.9 + 0.5
80.7
MOOC
83.4
87.0
84.5
0.7
60.7
78.5
0.5
1
82.4
Wiki.
84.1
0.5
80.9 0.3
88.8
1: 0.4
87.9
0.2
75.0 1 1.1
73.1 1:
89.5
0.3
91.2 - 0.2
83.1
1.1
Prod.
Last
77.6
0.6
71.4 1.7
80.3
+ 3.2
75.0
0.7
69.8
+ 0.5
73.2 + 0.0
71.6
6.1
74.1
+ 1.3
81.1 + 0.9
Mylett
63.4
+ 1.7
62.5 + 1.4
62.1
2.3
57.1
0.4
45.1
+
0.2
513 + 0.0
58.3
+ 2.2
59.1
+ 0.2
44.7 1.6
Social
88.3
4.8
91.6 -
93.2
2.1
91.8
0.3
86,2
- 0.2
80.6
0.0
96.2
0.2
95.1
0.1
97.3 0.1
Reddit
80.1
79.2
80.5
0.5
78.6
1.0
73.7
0.6
1
82.7 0.8
Avg. Rank
3.6
6.2
6.1
7.4
3.5
3.5
40

---

Published in Transactions on Machine Learning Research (02/2026)
Table 20: Mean average precision performance over five runs for the test set of the discrete-time datasets, including standard deviations. For discrete- and contimuous-time datasets, the average rank of each model is reported in the last row, respectively.
Eval.
Dataset
JODIE
DyRop
TGN
TGAT
CAWN
EdgeBBank
TCL
GraphMixer
DyGFormer
UN V.
52.6
1.8
49.6
+ 1.9
49.7 + 3.9
52.7
2.6
52.4 2.0
84.2 + 0.0
52.4 + 0.9
54.0 + 1.4
62.4 1.7
US L.
46.0
= 0.9
62.5
1 3.6
58.6 = 2.4
71.0
8.9
80.7 3.7
63.2 + 0.0
77.5
1 4.3
86.5
+ 1.9
86.1 1.0
UN Tr.
52.7
3.0
49.4
0.9
53.2
1.5
58.9
2.7
50.2 1.7
79.0
- 0.0
57.5
1: 1.9
65.8
1 1.9
67.1 2.7
Forec.
Can.
68.2
83.2
Flights
65.2
2.7
63.9
2.8
68.3
73.5
0.3
65.5 1.3
70.4
0.0
71.0
0.4
71.9 + 0.8
69.1 1.8
Cont.
94.0
2.6
95.8
+ 0.4
97.0
0.5
96.8
0.2
88,2
0,2
89.4 + 0.0
96.6
0.4
95.7 + 0.2
98.3 + 0.0
Avg. Rank
7.3
T.T
5.8
3.5
5.7
4.7
5.0
2.8
2.2
UN V.
67.8
1.9
67.8
1 1.7
66.1
1: 3.9
52.3
2.5
50.7 1.4
84.8 + 0.0
53.3 : 1.3
53.9 + 1.7
59.9 1.4
L.
48.2
1.0
73.1
1: 2.2
81.2
2.1
71.2
8.2
80.8 3.5
63.3 1 0.0
77.4 1: 4.5
86.0 + 2.0
85.8 1.0
58.9
59.3
56.2
Pred.
Can.
52.8 0.5
61.8
1.1
68.5
67.7
1.7
63.8
0.0
64.2
2.0
77.2 +
97.1 0.7
Flights
66.7
3.3
66.8
+ 1.6
68.3
= 1.8
72.7
0.2
65.0
1.3
70.5 - 0.0
70.8
= 0.5
71.2 - 0.7
68.6 1.7
Cont.
94.2
1.3
96.5
+ 0.3
96.3
1.1
96.0
0.3
84.5
0.2
88.8 + 0.0
96.0 0.6
94.2 + 0.1
97.7 + 0.1
Avg. Rank
6.5
5.3
4.0
5.0
7.5
4.8
5.7
3.5
2.7
41

---

Published in Transactions on Machine Learning Research (02/2026)
H.3 AUC-ROC Scores over Time
We present the AUC-ROC scores across the lest. time for all models and contintous-lime datasets with average relative change in performance (rightmost column in Table 13) larger than one, i.e. Enron (Figure 15 UCI (Figure 16). MOOC (Figure 17), and LastFM (Figure 18h. We observe that the patterns seen in Figure 5 for the Enron and MOOC datasets extend to all models. For UCI in Figure [6] we can see the AUC-ROC scores for many time windows and comparably fewer batches. This is because the test set for this dataset contains 15% of all temporal edges but two thirds of the whole observation time.
Figure 18 shows that the LastFM dataset contains several outliers in the first half of the test time, where the performance is better compared to the average. These outliers correspond to the peaks in activity shown in Figure g Similar to what can be observed for the one anomaly in the Enron dataset, these peaks in activity lead to many batches but only a small number of time windows. This because these bursts occur a short period time, leading to an overrepresentation of these outliers using the batch-based approach. At the end of the LastFM dataset, fewer edges occur, leading to a less reliable model performance, which is underrepresented in the batch-based evaluation due to the smaller number of edges.
JODIE
DyRep
TCN
1.0
AT/C-ROG
0.5
Ratch
Window
0.0
TGAT
CAWN
EdgeBank
1.0
AUC-ROC
0.0
TCL
CraphMixer
DyCFormer
1.0
AT/C-ROC
0.0
26000
28000
30000
26000
28000
30000
26000
28000
30000
Time (hours)
Time (hours)
Time (hours)
Figure 15: Model performance of Enron datasct over time, which is visualised by the AUC-ROC scores for each batch and time window individually. The time (x-axis) is limited to the test set.
42

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Published in Transactions on Machine Learning Research (02/2026)
JODIE
DyRep
TGN
AUC--OCC
0.5
Batch Window
TGAT
CAWN
EdgeBank
ACC-ROC
0.5
TCL
GraphMixer
DyGFereer
(TC-ROC
0.5
2000
3000
Time (hours)
Time (hours)
Time (hours)
Figure 16: Model performance of UCI over time.
JODIE
DyRep
TGN
ACC-ROC
0.5
Window
0.0
TGAT
CAWN
EdgeBank
AUC-ROC
0.5
TCL
GraphMixer
DyGFormer
AUC-ROC
0.5
700
Time (hours)
Time (hours)
Time (hours)
Figure 17: Model performance of MOOC over time.
43

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Published in Transactions on Machine Learning Research (02/2026)
JODIE
DyRep
TGN
1.0
AUC-ROC
0.5
Window
0.0
TCAT
CAWN
EdgeBank
AUC-ROC
0.5
TCL.
GraphMixer
DyGFormer
AUC-ROC
0.5
34000
35000
36000
37000
38000
34000
35000
36000
37000
38000
34000 35000
36000
37000
38000
Time (hours)
Time (hours)
Time (hours)
Figure 18: Model performance of LastFM over time.
44

---

Published in Transactions on Machine Learning Research (02/2026)
H.4 Investigating Information Leakage
The problem of information leakage can give memory-based models unlair advantage during evaluation because these models obtain more information than non non-memory-basee models due to this leakage. However, whether this leaked information is useful for making better prodictions depends on the data. We assume that the order of the edges within each snapshot plays an important role in many cases where the leaked information useful. The data could, for example, retain an implicit temporal ordering if the data was obtained by coarse-graining a continuous-tinn graph into snapshots. The edges inside the snapshots could also be sorted by some ID, like the node ID of the source node. This would mean that all occurrences of each node source node would be consecutive, making it very unlikely that each node appears again source node after it was already seen in a previous batch of the same snapshot.
In Figure 19 we show the AUC-ROC scores of each batch individually in the evaluated order and highlight the borders of each snapshot with grey dashed lines. We observe upwards trends in the red regression lines for the US Legislators (DyRep, TGN), the UN Trade (all modcls), and the Flights (JODIE, DyRep) datasets. This suggests that these datasets contain edges in an order that simplifies the prediction for the indicated models, given knowledge from previous batches. Thus, shuffling the data within each snapshot should destroy the useful leaked information and lead to a drop in performance. We report the changes in performance between (i) the models that are evaluated based on edges in the order found in the dataset and (ii) the models evaluated on the datasets with the edges inside each snapshot shuffled in Table 21
The tables contain the relative change in performance for both evaluation approaches: the batch- based link prediction and our window-based link forecasting. We observe that the performance of the batch-based approach drops for the above-identified dataset and model combinations, suggesting that the edges are indeed ordered in such way that the earlier batches in snapshot provide information about later batches, making the prediction easier. Our Lime-window-bass approach prevents this information leakage. Thus, the performance after shuffling is similar to the performance without shuffling because no information, whether useful or not, is leaked.
Table 21: Relative change of the performance between test sets with the order of edges within snapshots, provided by the discrete-time datasets and Lest sets with edges shuffled within each snapshot. We compare the evaluation approaches of our window-based link forecasting with batch-based link prediction on all memory-basee models.
(a) AUC-ROC scores
(b) Average precision scores
Model
JODIE
DyRep
TGN
Model Fval
JODIE
DyRep Forec.
TCN
Eval
Foree.
Pred.
Forec.
Pred.
Forre.
Pred.
Foren.
Prod.
Pred.
Forec.
Pred.
UN V.
11.6%
120.0%
.7.1%
121.4%
41.7%
115.3%
V.
44.2%
418.4%
16.1%
120.5%
11.5%
113.1%
L.
10.1%
13.5%
.0.1%
110.9%
10.6%
110.4%
US
10.0%
12.2%
10.1%
111.0%
11.5%
110.5%
UN Tr.
10.2%
113.8%
70.1%
115.5%
13.5%
114.2%
10.2%
110.0%
10.9%
111.4%
13.3%
19.9%
P. 10.3%
14.3%
J4.4%
J0.1%
J14.0%
110.1%
Can.
J0.2%
13.1%
15.3%
10.1%
117.6%
19.1%
Flights
11.8%
11.4%
71.3%
12.0%
10.3%
10.1%
Flights
11.0%
12.0%
10.9%
13.7%
10.4%
10.7%
Cont.
40.9%
11.2%
70.1%
J1.1%
10.1%
J0.2%
Cont.
12.3%
13.1%
10.2%
12.4%
J0.2%
10.6%
P
0.8%
7.4%
2.2%
8.5%
3.4%
8.4%
1.3%
6.5%
2.2%
8.2%
4.1%
7.3%
45

---

Published in Transactions on Machine Learning Research (02/2026)
JODIE
DyRep
TGN
1.0
1.0
1.0
STC-ROC
0.5
0.5
0.5
400
600
800
200
400
600
800
200
400
600
800
Batch Number
Batch Number
Batch Number
(a) UN Vote
JODIE
DyRep
TGN
1.0
1.0
1.0
AUC-ROC
0.5
0.5
0.5
0.0
0.0
0.0
10
15
20
25
0
10
15
20
25
10
155
20
25
Batch Number
Batch Number
Ratch Number
(b) US Legislators
JODIE
DyRep
TCN
AUC--OC
0.5
0.5
0.5
0.0
0.0
0.0
100
200
300
100
200
300
100
200
300
Batch Number
Batch Number
Batch Number
(c) UN Trade
JODIE
DyRep
TGN
AUÇ-ROC
0.5
0.5
0.5
0.0
0.0
0.0
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
Batch Number
Batch Number
Batch Number
(d) Canadian Parliament
JODIE
DyRep
TGN
AUC-ROC
0.5
0.5
0.5
0.0
0.0
0.0
500
1000
1500
500
1000
1500
500
1000
1500
Batch Number
Batch Number
Batch Number
Flights
Figure 19: AUC-ROC score for each batch individually in the order the edges found in cach discrete- time dalaset (except Contacts, since it has too many snapshots for visualisation). Grey dashed vertical lines separate snapshots, i.e. all points within the same dashed lines correspond to the performances of batches of the same snapshot. The red line represents the best-fit line obtained by performing linear regression on the points within each snapshot.
46


Reviews:
[{"review_id": "lEEQ9e5DCW", "reviewer": "Reviewer_3kuv", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "- This paper clearly and concisely introduces the concepts of Temporal Graph Neural Networks (TGNN) and dynamic link prediction (the task of predicting future graph links events from past graph link events).\n- The paper identifies significant methodological flaws that arise from evaluating dynamic link prediction methods using the same fixed-batch-size structure as is typically used to train TGNNs. Specifically, the paper gives a clear description of four major issues which arise from batching events into groups of fixed size rather than fixed duration:\n    - (a) information loss (from batches encompassing very long durations),\n    - (b) information leakage (from splitting the same snapshot time into multiple batches),\n    - (c) inconsistent forecast horizons (which depart from the real-world motivations underlying TGNN evaluations),\n    - And (d) tunable batch size (i.e. allowing the forecasting method to change the evaluation itself to get a better score).\n- The authors introduce empirical measurements that quantify the issues they have identified with the dynamic link prediction approach to evaluation across a variety of evaluation datasets commonly applied to TGNNs.\n- The authors introduce a new evaluation methodology, termed dynamic link *forecasting*, which solves the identified problems of dynamic link prediction by using fixed-duration evaluation batches rather than fixed-event-count batches. They empirically demonstrate the varying degrees of impact that remedying the four identified issues has across a variety of evaluation datasets commonly applied to TGNNs.\n\n\nStrengths:\n* This work is straightforward to follow thanks to the authors’ efforts towards clear exposition through diagrams, clean prose, and well-organized tables and figures.\n* The authors make a thoroughly argued and highly intuitive case for evaluating using fixed-time slices rather than fixed-event-count slices.\n* The authors implement their novel evaluation methodology and evaluate a wide body of TGNN works in the new paradigm, presenting a substantial body of empirical evidence to back up their claims.\n\n\nWeaknesses:\n* The current structure of the manuscript entails substantial repetition of core ideas which, while often instructive, may to some readers feel redundant. In some ways the later sections of the paper are a victim of the success of the introduction in so clearly laying out the issues with dynamic link prediction that when these problems are recapitulated later, the repeated explanations can feel unnecessarily verbose. \n* Though the introduction explains the present paradigm of dynamic link prediction as arising from a need to batch computation, the authors do not provide measurements of the runtime impact incurred by switching to their method of evaluation.", "claims_and_evidence_yn": "Yes", "claims_explanation": "- The authors introduce empirical measurements that quantify the issues they have identified with the dynamic link prediction approach to evaluation across a variety of evaluation datasets commonly applied to TGNNs.\n- They empirically demonstrate the varying degrees of impact that remedying the four identified issues has across a variety of evaluation datasets commonly applied to TGNNs.", "audience_yn": "Yes", "audience_explanation": "The paper addresses a fundamental issue in the evaluation of Temporal Graph Neural Networks. Researchers developing and applying TGNN methodologies should certainly find this work interesting.", "requested_changes": "Requests\n* Clarification of computational cost associated with unbalanced batch sizes during evaluation\n* More consistency in the number of significant figures presented in tables, e.g. tables 2 and 4.\n* Some discussion of the asymmetry/skew beyond the mean and standard deviation statistics of batch size show in Table 3, plus some discussion of whether this is important. From Appendix C, it appears that some distributions have quite extreme spreads of event counts.\n  - If alternative statistics (e.g. the interquartile range) show interesting asymmetrical qualities of event count distributions, it may be nice to include these in the paper. Expanding appendix C with histograms or other distribution-summarizing plots of window sizes for the specific horizon lengths studied in the main body of the paper would also be of interest. However measured, some discussion of the significance of the often-dramatic differences in number of events per time window in the real-world datasets studied could help readers get a deeper appreciation of fixed-time-window evaluation.\n\nFood-for-thought suggestions:\n* As evidenced by the lovingly padded-out appendix, there is a lot of great content that the authors would like to share with the community. To make room for more content, the authors may consider removing some repetitions of the issues identified with temporal link prediction. In particular, Figure 1, the intro text, and section 3.1 all discuss the same problems in somewhat the same way.\n* Offering a little more discussion as to the implications of temporal link forecasting to the design and training of TGNNs (beyond the single sentence given in the last subsection of the conclusion at present) may be of great interest to readers.\n* TMLR does not require novelty for publication, so the authors are free to modify discussion in the Open Challenges In Link Prediction section that emphasizes how novel this work’s approach is and how much more thorough it solves the identified problems as compared to prior works. For example, the authors may consider instead highlighting the complementary strengths of prior works rather than their limitations.", "broader_impact_concerns": "I have no concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "bMeF5bTVRK", "reviewer": "Reviewer_wmFe", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Summary:\nThis paper demonstrates that the widely used batch-based evaluation protocol for dynamic link prediction in temporal graphs systematically distorts temporal information and can lead to misleading model comparisons. By grouping a fixed number of edges into each batch, traditional evaluation introduces information loss in continuous-time graphs, information leakage in discrete-time graphs, and inconsistent prediction horizons due to varying batch durations. Moreover, the batch size effectively becomes a hidden hyperparameter that influences task difficulty. To address these issues, the authors reformulate the task as dynamic link forecasting, where predictions are made over fixed-duration time windows rather than fixed-size batches. This window-based approach preserves true temporal structure, eliminates leakage within snapshots, and ensures consistent evaluation across models. Extensive experiments on 14 real-world datasets and nine state-of-the-art TGNNs show that forecasting yields more faithful and reliable performance estimates, revealing substantial biases in conventional batch-based evaluation.\n\n\nStrengths:\n1. The paper offers a clear and insightful identification of fundamental weaknesses in the traditional batch-based evaluation protocol for dynamic link prediction.\n\n2. The proposed fixed-horizon, window-based evaluation strategy is simple, intuitive, and empirically well-validated.\n\n3. The paper is highly readable and accessible.\n\nWeaknesses:\n1. The level of technical novelty is somewhat limited. While the problem addressed is important and the empirical analysis is thorough, the core methodological contribution--shifting from fixed-size batches to fixed-duration windows--is conceptually straightforward. The work is stronger in its diagnostic and empirical contributions than in proposing fundamentally new modeling or theoretical techniques.\n\n2. The proposed solution focuses on improving evaluation, but does not address information loss or leakage that occurs during training. Since the models are still trained with batch-based temporal ordering, the learned parameters may remain biased, and the resulting models may not fully generalize to temporally coherent test settings. It would be valuable to discuss whether window-based ideas could also extend to training or how training-time biases might impact downstream conclusions.\n\n3. The window-based protocol may face practical limitations in datasets with highly bursty temporal activity. Because the time horizon is globally fixed, certain windows may contain extremely dense interaction bursts, which may result in large memory footprints or potential GPU out-of-memory issues. The paper mentions possible sub-window chunking, but such strategies may still introduce information loss and leakage.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The paper’s arguments are grounded in systematic empirical analysis across 14 diverse temporal graph datasets and 9 representative TGNN models, covering both continuous-time and discrete-time settings. The authors quantify information loss and leakage using NMI, controlled perturbation experiments, and temporal-density visualizations, and they provide direct comparisons between batch-based prediction and window-based forecasting, which strongly support their conclusions. The experimental results consistently demonstrate that batch-based evaluation distorts temporal ordering and can inflate or deflate model performance, particularly for memory-based architectures. The paper also includes well-designed ablation studies, implementation details, and sanity checks that increase credibility. Overall, the evidence is comprehensive, coherent, and sufficient to substantiate the paper’s central claims.", "audience_yn": "Yes", "audience_explanation": "The paper addresses a fundamental and often overlooked issue in the evaluation of temporal graph learning. The discovery that standard batch-based evaluation can introduce systematic information loss and leakage, and thereby misrepresent model performance, is highly relevant to researchers developing or benchmarking temporal GNNs. The proposed window-based forecasting protocol provides a practical and easily adoptable alternative that improves fairness and comparability across models.", "requested_changes": "1. Discuss the limitations arising from training-time information loss and leakage. The proposed solution addresses evaluation-time inconsistencies but does not mitigate the known issues of temporal discontinuity during training. Since models are still trained using batch-based processing, their parameters may remain biased, and this could limit the generalizability of conclusions drawn from the updated evaluation. A dedicated discussion would help quantify the impact of training-time biases and clarify how they should be interpreted in practice.\n\n2. Address the potential memory challenges of window-based evaluation on highly bursty datasets. Because time windows have a fixed temporal span, windows covering periods of extreme edge density may contain very large numbers of events, potentially resulting in out-of-memory errors or substantially higher compute costs.", "broader_impact_concerns": "I do not see ethical issues.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "xiRCrl2YOK", "reviewer": "Reviewer_VJZb", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper identifies four fundamental issues in batch-based dynamic link prediction—information loss, information leakage, inconsistent prediction windows, and the tunability of task difficulty through batch size. The authors propose dynamic link forecasting, which evaluates models using fixed-duration time windows instead of fixed-size batches. They quantify the issues on 14 datasets, evaluate nine TGNNs, and show that batch-based evaluation can substantially distort model performance, especially for memory-based models on discrete-time datasets. Implementations for DyGLib and PyG are provided.\n\nStrengths:\n\n1. Clear identification of overlooked evaluation flaws.\n\n2. Strong empirical study covering many datasets and models.\n\n3. Practical and intuitive alternative evaluation method.\n\n4. Good reproducibility and clear presentation.\n\nWeaknesses:\n\n1. Guidance on selecting forecasting horizons is limited.\n\n2. Training–evaluation mismatch (batch-based training, window-based evaluation) is not fully discussed.\n\n3. Scalability under extreme temporal densities needs more explicit treatment.\n\n4. Interaction with negative sampling strategies is underexplored.\n\n5. Limited discussion on applicability to ranking-based metrics (MRR).", "claims_and_evidence_yn": "Yes", "claims_explanation": "The empirical analyses are thorough, well-designed, and clearly support the core claims. Some secondary aspects (e.g., effect of horizon choice) could be elaborated further.", "audience_yn": "Yes", "audience_explanation": "The results directly influence how TGNNs should be evaluated and interpreted, which is highly relevant to temporal graph learning researchers and practitioners.", "requested_changes": "Although the paper remains strong overall, the following points would benefit from clearer discussion or refinement.\n\n1. Provide more explicit high-level guidelines for selecting h in practice, including: 1) how h relates to timestamp resolution, 2) how to adapt h for highly bursty vs. uniform datasets, 3) typical ranges for common application domains.\n\n2. Add a dedicated discussion on the implications of evaluating models trained with batch-based methods using window-based evaluation.\nClarify what behavior may change if models are also trained with time-window-based updates.\n\n3. Include a short subsection or appendix elaborating on the runtime and memory implications of window-based evaluation in extreme-density scenarios.\n\n4. Comment on or briefly examine how negative sampling interacts with time-window-based evaluation, especially historic sampling.\n\n5. Expand the limitations section to more clearly articulate what aspects do not transfer to ranking-based evaluation and what would be needed to extend the framework.", "broader_impact_concerns": "I do not identify significant ethical risks beyond those typical for foundational methodological work. As a small enhancement, the authors may briefly discuss the implications of more reliable temporal prediction evaluation in sensitive domains (e.g., mobility, communication networks, socio-economic interactions), though no major concerns are present.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)