Future Link Prediction Without Memory or Aggregation
Authors: Lu Yi
Runlin Lei
Fengran Mo
Yanping Zheng
Zhewei Wei
Yuhang Ye
Venue: NeurIPS 2025 poster ()
Keywords: temporal graph learning; future link prediction
Primary area: deep_learning
TL;DR: We revisit the architecture of existing temporal graph learning methods and propose a simple yet effective framework without memory or aggregation for future link prediction.

Abstract: Future link prediction on temporal graphs is a fundamental task with wide applicability in real-world dynamic systems. These scenarios often involve both recurring (seen) and novel (unseen) interactions, requiring models to generalize effectively across both types of edges. However, existing methods typically rely on complex memory and aggregation modules, yet struggle to handle unseen edges. In this paper, we revisit the architecture of existing temporal graph models and identify two essential but overlooked modeling requirements for future link prediction: representing nodes with unique identifiers and performing target-aware matching between source and destination nodes. To this end, we propose Cross-Attention based Future Link Predictor on Temporal Graphs (CRAFT), a simple yet effective architecture that discards memory and aggregation modules and instead builds on two components: learnable node embeddings and cross-attention between the destination and the source's recent interactions. This design provides strong expressive power and enables target-aware modeling of the compatibility between candidate destinations and the source's interaction patterns. Extensive experiments on diverse datasets demonstrate that CRAFT consistently achieves superior performance with high efficiency, making it well-suited for large-scale real-world applications.

Future Link Prediction Without Memory or Aggregation
Lu Yi', Runlin Lei', Fengran Mo², Yanping Zheng': Zhewei Wei 'Remmin University of China, Uniieersité de Montréal
[yilu, runlin_lei, zhengyanping, zhewei]@ruc edu.eedddueo cn fengran www.mootteatl...ommmmmmm
Yuhang Ye
Huawei Poisson Lab, Huawei Technology Ltd.
yeyuhang@huavei.comm com
Abstract
Future link prediction temporal graphs is fundamental task with wide applica- bility in real-world dynamic systems. These scenarios often involve both recurring (seen) and novel (unseen) interactions, requiring models to generalize effectively across both types edges. However, existing methods typically rely on complex memory and aggregation modules, yet struggle to handle unseen edges. In this paper, we revisit the architecture of existing temporal graph models and identify essential but overlooked modeling requirements for future link prediction: representing nodes with unique identifiers and performing target-aware matching between source and destination nodes. To this end, we propose Cross-Attention based Future Link Predictor on Temporal Graphs (CRAFT), a simple yet effective architecture that discards memory and aggregation modules and instead builds on two components: learnable node embeddings and cross-attention between the desti- nation and the source's recent interactions. This design provides strong expressive power and enables target-aware modeling of the compatibility between candidate destinations and the source's interaction patterns. Extensive experiments on diverse datasets demonstrate that CRAFT consistently achieves superior performance with high efficiency, making it well-suited for large-scale real-world applications.
Introduction
Dynamic systems are typically formulated as temporal graphs, where nodes and edges represent
entities and their interactions, and each edge is annotated with a timestamp [TO [5] 47). The prediction of future interactions between entities is defined as future link prediction task in existing studies [9] which is crucial and widely applied in real-world systems [3] 28), such as social networks B.
and collaboration platforms (33. Future interactions be categorized into repeated interactions with historical neighbors and new interactions with previously unconnected nodes 44 For instance, in social networks, individuals often maintain regular contact with close friends while occasionally reaching out to other acquaintances. Similarly, in academic collaboration networks, researchers may frequently publish with long-term collaborators while also initiating projects with new coauthors. Thus, to precisely predict both seen and unseen interactions is important to enhance user experience in different dynamic systems and improve their utility. This dual nature poses nontrivial challenge for future link prediction, demanding models that generalize across both seen and unseen edges.
Yanping Zheng and Zhewei Wei are the corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Batch
node memory
4
t4
d
node embedding
h
MLP
0.5
Aggregation Module
2
f
b2
0.5
t
4
Memory Madule
Figure 1: The general model architecture of existing temporal graph learning methods.
Existing temporal graph learning methods perform future link predictions by adopting one both of the memory and aggregation modules (30 as illustrated in Figure [ The memory module represents node interaction history in compressed memory state, while the aggregation module generates node embeddings by aggregating historical neighbors. For example, TGN (30) uses GRU [6] to update node memory and a graph attention layer for aggregation, whereas DyGFormer [46] omits the memory module and directly applies self-attention over historical neighbors. Although equipped with a sophisticated architecture, these methods suffer substantial performance degradation on recent benchmarks like TGB-Ser [4]. which emphasize unseen edge prediction in real-world scenarios, thus limiting their practical utility. This consistent underperformance may stem from a deeper architectural misalignment with the core demands of future link prediction, prompting critical question: Are memory and aggregation modules truly effective for future link prediction, especially given the need to handle both seen and unseen edge scenarios?
To investigate this question, we identify two essential model capabilittes that are missing from the existing architecture but are key to addressing the challenges of future link prediction. First, the memory and aggregation modules have limited expressive power due the absence of unique node identifiers. They typically operate over historical interaction data, which often lack distinctive node or Therefore, models often struggle distinguish between nodes using 44 This limitation becomes particularly severe in datasets with a low proportion of seen edges, where the model must rely on a more expressive representation of historical interactions to generalize unseen edges. Second, both modules are generally applied to individual nodes in isolation, without modeling how well the candidate destination (i.e., the targel) aligns with the source's 's recent interaction patterns, capability we refer to as target-aware matching. Although some recent methods [46, 38 21 leverage correlation encodings to capture the relation between the source and destination, they primarily focus on the connections between their neighborhoods, rather than directly assessing semantic compatibility between the destination and the source's 's behavioral history. Therefore, the framework designs of these methods not well aligned with the core demands of future link prediction to evaluate how well a destination fits the source context.
edge features [13 17
44
only their edge timestamps
In this paper, we introduce minimalistic architecture that centers on these two essential modeling requirements: representing nodes with unique node identifiers and performing target-aware matching, while discarding the commonly used memory and aggregation modules. Specifically, we propose CRoss-Attention based Future Link Predictor on Temppral Graphs (CRAFT), which employs learnable embeddings to serve as node identifiers and cross-attention mechanism between each can- didate destination and the source's recent neighbors to realize target-aware matching. By integrating these two components, our CRAFT provides strong expressive power and enables direct evaluation of the destination's 's compatibility with the source's 's interaction patterns, making effective for both seen and unseen edge prediction. Overall, main contributions are follows:
We propose CRAFT, a simple yet effective architecture for temporal graph learning. Unlike existing models that rely memory and aggregation modules, CRAFT' is built on essential components tailored for future link prediction: unique node identifiers and target-aware matching.
With strong expressiveness and destination-ccodiiioneee context modeling, CRAFT effectively addresses both seen and unseen edge prediction, addressing the limitations observed in prior work.
Extensive experiments on 17 datasets, including the TGB and TGB-Seq benchmarks, demonstrate that CRAFT consistently delivers superior performance across both types of prediction tasks while maintaining high efficiency, making it well-suited for large-scale real-world applications.

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2 Related Work
Temporal graph learning methods for future link prediction. Temporal graph learning focuses on modeling the evolving patterns of node interactions over time, with future link prediction serving as core task [32]. TGN [30] initially propose the memorr-aggreggee
architecture for temporal graph learning and categorize earlier methods within this architecture, including JODIE [7]. DyRep [35,, and TGAT 42 Among them, JODIE, DyRep, and TGN adopt RNNs 40 in the memory module to update node memory when new edges arrive, and utilize time projection, identity function, and temporal graph attention to aggregate historical information, respectively. TGAT and many subseqent methods generate time-dependent node representations directly by aggregating historical neighbors without the memory module. These methods leverage various techniques to model dynamic interactions, including the MLP-Mixer R4] in GraphMixer [7]. attention mechanisms in TGAT [42) DyGFormer [46). TCL [37], and SimpleDyG 41] as well as temporal point processes (c.g., Hawkes processes [12 244
in TREND [39 and LDG [16]. etc.
Limitations of existing methods on predicting unseen edges. Poursafaei al. 27 are the first to observe the imbalance between seen and unseen edges in existing datasets. They propose a simple heuristic method, EdgeBank, which memorizes historical edges without any learnable components, yet achieves surprisingly strong performance on many benchmarks due to their high ratio of seen edges. To make evaluation more challenging, Huang et al.
133 introduce the TGB benchmark, featuring large-scale datasets and rigorous multiple negative sampling strategy, while some datasets still exhibit excessive seen edges. To fill this gap. Yi et al. designed to evaluate performance on datasets with minimal seen edges. Their findings further revealed that most existing methods struggle to generalize unseen edge. This persistent performance gap between seen and unseen edges motivates us to rethink the architecture of temporal graph learning.
44] propose the TGB-Seq benchmark,
3 Problem Formulation
Temporal Graphs. We define a temporal graph as G = (V, E), where V is the set of nodes, and E is sequence of edges ordered by non-dccreasing timestamps, i.e., E {ee, e Jm with each edge = (us, Us, 44) denoting an interaction from the source node u, to the destination node i at time 4, This graph model is also known "link stream" or "streaming graph" 2 18 Throughout this paper, we use the terms target and destination interchangeably.
Future Link Prediction. Future link prediction aims to estimate the likelihood of an interaction between source node u and destination node e at future time f, given all historical edges before t in the graph G. We follow prior works [ 44 to frame this task as ranking problem, as real-world applications often require identifying the most likely destination from a large pool of candidates. Accordingly, the objective is to rank the positive destination node v higher than sampled negative candidates, conditioned on the source node u and the prediction time L.
Seen and Unseen Edge Prediction. In this paper, we define seen edges as edges that have appeared before the prediction time, and unseen edges as edges that have not appeared before the prediction time. Both seen and unseen edge predictions are common in real-world applications. For instance, users on e-commerce platform may regularly purchase routine products (seen edges) while occasionally buying new items such as clothing (unseen edges). As noted in prior work [44, existing methods perform well seen edge prediction but struggle with unseen edge prediction. Our work addresses both settings, bridging an important gap in the literature, which has predominantly focused on seen edges.
Proposed Methods
In this section, we first introduce how our CRAFT's architecture achieves two essential modeling requirements for future link prediction (Section 4.1 1) representing nodes with unique identifiers to enhance the model expressive power and 2) performing target-aware matching to enable direct assessment of the temporal compatibility between the source and destination. Then, we details on the necessity of these two components in Section 4.2, In Section we analyze the time complexity of CRAFT to demonstrate its superior efficiency and compare it with existing methods.
3

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plu, v1,
p(u, v2,,,2,t)
Learnable node embedding edge representation
14
Prediction Layer
u. v,
(u, v1, L)
(t
(u, V2, t)
Al(er)
((:)))
elapsed time since last activity
(2, U1, t)
u. U2, t)
set target candidates
Feed Forward Network
1/2
11
1/2
cross-attention
Positional
P1
P2
Pa
encoding
Extract recent neighbors
Node Embedding
121
7h
Figure 2: Model architecture of our proposed method, CRAFT: representing nodes with learnable embeddings and performing target- aware matching using cross-attention.
4.1 Model Architecture
The architecture of CRAFT is shown in Figure 2 Given the source u and a set of candidate destinations D = {11, 02, [ at time i, we first extract the & recent neighbors of before t, and look up node embeddings for these neighbors and the destinations. For the i-th neighbor n, of u, we add positional encoding to the node embedding capture the temporal order of these neighbors. Then we adopt a cross-attention module between the candidate destinations and the source's s neighbors to compute the edge representations. To capture the temporal status of the destinations, we encode the elapsed time since last activity these destinations and concatenate it with the edge representations. Finally, we use an MLP to predict the edge likelihoods. We detail the process as follows.
Learnable node embedding unique identifiers. To represent nodes with unique identifiers, we introduce learnable node embeddings that are trained jointly with the model. Such trainable embeddings encode the contextual information from interaction history of nodes, thereby serving as the unique latent identifiers. Specifically, we denote the embedding of node n as e(n) E Rd For the i-th neighbor n, of the source u, we add positional encoding p(i) to the node embedding e(n:) to represent the temporal order of these neighbors. The updated embedding is given by:
e(n:) c(n.) p()),
(1)
where p(i) is also trainable. The positional encoding enable the model to capture the short-term and long-tem interests of the source, which affect the future interactions crucially. Then, we obtain the
embedding sequence of the source's neighbors: S = (ē(n1). @(n2), ... e(mx)) and the embedding sequence of the candidate destinations: D (e(u1) ), e(r2), e(v,)]. Note that these destination
nodes are independent of each other, and we concatenate them only for parallel computation.
Target-aware matching via cross-attention. Considering the inherent requirement of future link prediction to assess the destination's compatibility with the source's historical interaction patterns, we implement target-aware matching through cross-attention between the candidate destinations and the source's 's neighbors. This mechanism allows each candidate destination directly attend the source's 's historical interactions, thus better evaluating the alignment between the destination and the source's temporal preferences. We define the Attention and FFN function 36 as follows:
QK
Attention Q, K, V) -oftmax
VV,
(2)
Vd
FFN(H) GELU + W, + b
(3)

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Our cross-attention module is stacked with multiple layers, and each layer includes multi-head attention network (MHA) and feed-forward network (FFN), The f-th layer calculation is given by:
z ! Attention (H
( SW SWE)).
(4)
E,5
Z = MHA (2- S) + H( = concal 4
z (f-1)
_/ W. + ((11)
(5)
H FFN (0) + (
(6)
where W & Ruxdh W Rdxds and W Rdxda are the projection weight for the i-th head in the l-th layer, where dj = d/h and is the number of heads. H denotes the hidden state of the l-th layer, and H = D. Each layer takes the hidden state of the previous layer as the query, and the embedding sequence of the source's 's neighbors as the key and value. The output of the last layer (()) will be the edge representations of the source and candidate destinations.
After the cross- cross-attention module, encode the elapsed time since last activity of the destination nodes, in order to capture the temporal status of the destinations. The clapsed time is projected to time-context vector Rd by linear layer TimeProjection and then concatenated with the edge representation. Finally, we feed them to an MLP to predict the edge likelihood between the source and the destination. Specifically, the predicted score of the i-th destination node e; is computed as:
Prediction.
ū: MLP (concat (i), TimeProjection (A(()))))
(7)
where At(r;) =t t- t (u:) is the elapsed time between the prediction time and the last activity time of v, t (u,), and (1) is the edge presentation of (u, U, t) generated by cross-atiention module. The TimeProjection function maps the time t R to Rdd by W, t, W. Rdx1, Furthermore, for the scenarios involving excessive seen edges, we encode the repeat time of the candidate edge to capture the inherent repeat patterns in the temporal graph. Here, the repeat time of edge (a, b) refers the number of times edge (a, b) appears in the dynamic graph upon the prediction time. Similar to the elapsed time encoding, we will first project the repeat time by a linear layer and then concatenate with the edge representation before the prediction MLP.
Loss function. We adopt the Bayesian Personalized Ranking loss 29 which is widely used and well-suited for ranking tasks [9). Given source node u interacting with a positive destination node i and negative destination node v at time t, the loss is defined as:[(u, t) = log (ūj Ú;), where iJ and ūū denote the predicted scores for the positive and negative samples, respectively.
4.2
On the Necessity of Learnable Embeddings and Cross-Attention
4.2.1
Learnable Node Embeddings Enable Powerful Expressiveness
Most existing methods generate node representations from interaction data, such as edge timestamps and node or edge features. However, in many real-world temporal graphs, including well-established benchmarks 13
these features are often missing or extremely sparse. This largely because node and edge features are often hard to collect in practice and are not easily aligned across heterogeneous node types 44. Therefore, many models rely purely on edge timestamps, which significantly limits their ability to distinguish between nodes. In the example shown in Figure D existing methods are unable to distinguish nodes a and f because they have identical interaction timestamps and lack unique identifiers.
4 17
Recent approaches 21 38 46) attempt to mitigate this issue by introducing correlation encodings to capture the relation between the k-hop neighborhoods of the source and destination nodes. However, the model's perception is inherently constrained by the choice of k. For example, DyGFormer uses neighbor co-occurrence frequency to model correlations between nodes. But in the example shown in Figure D it cannot distinguish the candidate edge (b, a) from (b, f), since both b and a, and and share two common neighbors, i.e. c and d, and d and respectively. It fails to capture that only the co-neighbors of and have prior interactions (c, d, lo), which is a critical signal of a tightly-knit group structure and essential for making accurate predictions. While increasing k may offer broader context, leads to exponential neighborhood expansion, introducing excessive noise 5 or resulting in memory overhead [44)
5

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independent matching
neighborhood matching
larget-aware matching
UserB
UserC
iPhone
AirPods
iPad
UserB
UserC
iPhone Case
iPhone Case
UserA
iPhone
AirPods
iPad
iPhone
AirPods
iPad
UserB
UserC
iPhone
AirPods
iPad
(a) Modeling UserA and iPhone
(b) Self-ateention among UserA's neighbors and iPhone Case's neighbors
(c) Cross-attention between iPhone Case and UserA's neighbors
Case independently
Figure 3: Illustration of different source-destination matching schemes for predicting whether UserA likely to purchase iPhone Case time Before time t, UserA has purchased iPhone, AirPods, and iPad in chronological order, while UserB and UserC have previously purchased iPhone Case.
These limitations emphasize the necessity of representing nodes with unique identifiers. Similar insights have been observed in the study of the expressiveness of static Graph Neural Networks (GNNs) 20 where the lack of distinctive node embeddings hampers model performance. No- tably, Abboud al. [I] demonstrates that GNNs with randomly initialized node embeddings, which serve as implicit identifiers, can outperform models that rely solely on structural information. There- fore, we introduce learnable embeddings that serve as node identifiers and encode contextual infor- mation, enabling the model to distinguish between nodes even in the absence of explicit features.
4.2.2
Cross-attention Mechanism Enables Target-aware Matching
35 do not explicitly model the relationship between source and destination nodes. As illustrated Figure [ they typically follow common paradigm: first, the memory and aggregation modules are used to encode interaction histories into individual node representations; then, MLP predicts the edge likelihood based on these node representations. This approach models each node's local dynamics independently and neglects the direct matching between node pairs. An exception is DyGFormer [46), which applies self-attention over the combined historical neighbors of both the source and destination nodes, aiming to learn temporal dependencies within and cross the two sets together. While it introduces a degree of cross-node awareness, focuses on the relation between the source and destination neighborhoods and is not explicitly conditioned on the candidate destination. As a result, when the source and destination neighborhoods lack semantic overlap or are heterogeneous in type, the attention signal becomes diluted or misaligned, leading to weak modeling of compatibility between the destination and the source context.
Most existing methods (30 42
To better align with the objective of future link prediction, which involves assessing how well a target node fits the source context, we implement target-aware matching through a simple yet effective between the destination and the source's 's recent neighbors. This allows each
design: cross-attention candidate destination to directly attend the source node's historical interactions and enables the model to capture fine-grained behavioral patterns as well as semantic alignment across entities. Consider the example Figure 3 which demonstrates how different matching schemes perform in predicting whether UserA is likely to purchase iPhone Case at time t. Subfigure (a) illustrates the independent matching mechanism adopted by most existing methods, where the source (UserA) and the destination (iPhone Case) are modeled independently with their respective neighbors. This hinders the model from recognizing the strong connection between iPhone and iPhone case. In (b), the neighborhood matching mechanism adopted by DyGFormer includes both source and destination neighborhoods, but treats nodes uniformly. If UserB or UserC has purchased many unrelated items besides iPhone Case, the semantic connection between iPhone and iPhone Case may be overwhelmed. In contrast, our target-aware matching mechanism, shown in (c), enables the candidate iPhone Case to attend directly to iPhone, effectively capturing their semantic relationship. We empirically compare these matching strategies in Section 5.2 demonstrating the advantages of our cross-attention design.
4.3 Time Complexity Analysis
We analyze the time complexity of performing future link predictions for a batch of source nodes and their corresponding candidate destinations. Let B denote the batch size, & the number of historical

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neighbors considered per node, q the number of candidate destinations per source, d the embedding or feature dimension, and d the average node degree the temporal graph. We compare CRAFT
with four state-of-the-art methods: TGAT 42 TGN B0), GraphMixer 77, and DyGFormer [46].
For TGN and TGAT, we follow common practice and consider their standard configurations: TGN
with one graph attention layer and TGAT with two. The total time complexity generally consists of
two dominant parts: 1) extracting historical neighbors and 2) computing edge likelihoods.
For the extraction of historical neighbors, we consider the common strategy of retrieving the k most recent neighbors 43 30 following the widely adopted implementation in DyGLib [46]. Alternative neighbor extraction implementation are discussed in the appendix. The dominant cost arises from locating the most recent neighbor among all existing neighbors via binary search. taking (log d) per query. Since existing methods typically gather neighbors for both source and destination nodes, this step takes O(B(1 + q) log d). TGAT, which aggregates two-hop neighborhoods via two attention layers, incurs ( + g) + k)) log d). In contrast, CRAFT only considers neighbors of the source, reducing the complexity to O [ log d). This reduction is particularly beneficial in real- world scenarios, where it is common to evaluate many candidate destinations per source, making efficient neighbor retrieval critical for scalable inference.
To compute edge likelihoods, most existing methods compute node representations by aggregating each node's historical neighbors, followed by an MLP for prediction. The aggregation step dominates computation. TGN, TGAT. GraphMixer, and DyGFormer employ one graph attention layer, two graph attention layers, an MLP-Mixer, and a Transformer encoder, respectively, each incurring various computational complexities per node: Okdd), d(kad²), O(kd²), and O(kd2 + k2d).. In contrast, CRAFT computes edge likelihoods directly using cross-attention between destinations and the source's neighbors, requiring O Bgd + Bkdd) for projections and O Bykkd for attention per batch. This approach eliminates the need for neighbor feature projections for each node, significantly improving efficiency, especially when g or k is large.
Table summarizes the results, showing that CRAFT offers superior efficiency in both neighbor extraction and edge likelihood computation. These findings highlight the ad advantage of CRAFT's simple architecture, making it well-suited for large-scale dynamic systems in practical applications.
5 Experiments
In this section, we investigate the effectiveness and efficiency of CRAFT on future link prediction. To fully evaluate the performance of CRAFT on predicting seen and unseen edges, we conduct experiments on 17 datasets, including the TGB-Seq benchmark (44) (ML-20M, Taobao, Yelp, GoogleLocal, Flickr, YouTube, WikiLink), the TGB benchmark 133 (igbl-review, tgbl-comment, tgbl-coin, tgbl-fiihhs)) and six commonly used datasets (wikipedia, reddit, mooc, lastfm, uci Flights). We compare CRAFT with seven state-of- of-the-an art continuous-time temporal graph models, including JODIE [17]. DyRep [35.. TGAT (42), TGN (30, CAWN [38, GraphMixer 7. and DyGFormer [46] The details of datasets and baselines are provided in the appendix.
Negative destination sampling. We adopt the negative destination samples from the benchmarks or randomly sample 100 negatives from all potential destinations. Specifically, for datasets from the TGB and TGB-Seq benchmarks, negative samples are provided by the benchmarks themselves: The TGB benchmark samples 100 or 20 negative destinations for each source node from historical and random negative edges [3). while the TGB-Seq benchmark randomly samples 100 negatives for each source [44]. For other datasets without publicly available negatives, we follow the approach outlined in TGB-Seq to randomly select 100 negative destinations for each source node. Importantly,
Table 1: The big-O notation of the time complexity of different temporal graph learning methods, where only the dominant term is retained for clarity.
Methods
Extract historical neighbors
Compute edge likelihoods
TGAT 42
B(1 + () + k) log d
B(1 + g)k²dd
TGN
30
B(1 + q) log d
B + k)kd²
GraphMixer
((1 + o) log d
B(1 + k)
DyGForeer
46
( + g) log d
B(1 + (kd + k2d)
CRAFT
B log d
Bqd + Bkud + Bqkd
7

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Table 2: MRR scores (%) of CRAFT and baselines on unseen-dominant datasets. The first, second, and third place rankings are highlighted, accordingly.
Datasets
ML-
Taobao
Yelp
GoogleL.ocal
Flickr
YouTube
WikiLink
lebl-review
Lgbl-comannnt
JODIE
21.162073
18.3622.18
69. 31
41.86
46 210
41.67
57. 17.94
41,43a015
DyRep
19.001144
40.03,220
57.69_111
37.73.1:54
38.04 18.04_414
15.122143
42.63
40.0610.
28. 18.90
TGAT
10.47
19.78
23.53
43.56=233
19.64:02:
56.20::211
TON
23,99=029
60.28
69.79=2024
54.13+1197
46.03=6575
55. 16:589
62.94=216
37,48++22
37,90=2.10
CAWN
12.31
25.71
18. 18.26:a0m
48 69.69
47 15
19.30 10
GrahMMixrr
21.97.187
13.96 19
21.31
1onm
58.871911
36.89.119 90
76. 16..71
DyGForeer
21.68:0..0
18.39
49 59.58.2287
46.08 1:44
22.39
67.03
SÜNN-HN
33.12#801
68.58-0221
69.34:2044
62.88:0051
60.15=0020
59.64=021
69.37
35.62+059
55.24+022
CRAFT
35.91 #065
70.68=0022
72.69
62, 40.45
62,34
58, 92.n2
75.48
41.77=00
91.72
Rel. Rep.mm
49.69%
17.25%
4.02%
15.19%
25.74%
0.08%
19.92%
0.82%
20.41%%
Abs Impry. 11.92
10,40
2.81
8.22
12.76
0.05
12.54
0.34
13.55
Table 3: MRR scores (%) of CRAFT-R and baselines on seen-dominant datasets. The first, second, and third place rankings are highlighted accordingly.
Datasets
wikipedia
reddit
mooc
lastfin
uci
Flights
igbl-coin
flii-ftights
JODIE
76.48
77.1621.27
19.91=106
18.49
11.43
20.37+4.18
DyRep
67.42:421
72.33+2.14
17.71
17. 77.666656
14.00
15.6220.47
45.2014400
55.60
TGAT
72.7211.50
18.03
31.55L4.1
24. 1..
31. $1.5010.48
53.9011.09
60, 60.92.10.57
TGN
82.222a0.0
79.25+n.24
39.03=2.53
25.592443
45.2926643
64.24=2.11
58.60=23.0
70.50#200
CAWN
86,07220.s
87.6622.04
27.02:20.5
35. 10.004
66.9620048
80.0622.10
GraphMixer
73.57
70.87+00.8
29.02=0.28
26.76=1.42
42.26+00.9 1.05
75.57=0.27
DyGFormer
88.69
88. 28.70s
42.20=1.31
46.50=0o51
+6.2
84.1 334,46
17.17
SGNN-HN
82.22
87.42
57.25
40.72
57.23
80.80
78.46:10.00
89.03
CRAFT-R
88,25+0.26
89.33
62.32=0.39
50.21
1
13.166
88,47+0225
91.39
ReI.Imprv. -0.50%
0.71%
47.68%
18.73%
-1.96%
-1.15%
17.07%
29.63%
Abs.Impry. -0.44
0.63
20.12
8.71
-1.50
-0.97
12,90
20.89
we perform collision checks to ensure that no positive edges are sampled negative edges for small datasets, which may lead to different results compared to prior works.
Experimental Settings. We follow the evaluation protocol of TGB-Seq and TGB benchmarks for all datasets. We use MRR as the evaluation metric, follow the original split of datasets, or chronologically split the datasets into training, validation, and test sets with 75%, 15%, and 15% of the edges, respectively. We follow the configurations in or 400, accordingly) and learning rate (1e-4) across all methods. The baseline implementation is based the DyGLib library [46]. For fair comparison, the average results of 3 runs reported. Other implementation details are provided in the appendix.
44 46 to use the same batch size (200
5.1 Effectiveness and Efficiency of CRAFT on Future Link Prediction
Experimental Setup. We categorize the datasets into two groups based on their seen edge ratio. For datasets with high ratio of seen edges (referred to as seen-dominant datasets), we apply repeat time encoding, and denote the variant as CRAFT-R. For datasets with minimal seen edges (referred to unseen-dominant datasets), The results for all baselines on the TGB-Seq and TGB datasets are directly taken from previous studies 44 45). Missing entries indicate cases where the model failed due to either out-of-time (unable to complete single training epoch within 24 hours) or out-of-memory on a 32GB GPU.
the default CRAFT model without repeat time encoding.
Effectiveness Evaluation. Table 2 and Table 3 present the MRR scores on unseen-dominant and seen-dominant datasets, respectively, with Rel.Imprr and Abs Ampry. indicating the relative and absolute improvements over the second-best baseline. Overall, CRAFT achieves the best results on a majority of benchmarks, with over 10% relative improvements on 10 out of 17 datasets compared to the second-bee best baseline. These results confirm the effectiveness of our architecture and highlight the value of its two key components: unique node identifiers and target-aware matching, which is opposed to the traditional memory and aggregation modules in the baselines. Specifically, CRAFT exhibits superior performance on unseen-dome dominant datasets, demonstrating that it successfully addresses key limitation of prior models, which often fail on unseen edge prediction. For seen- dominant datasets, CRAFT-R still performs best on most benchmarks, with only minor underperformance (less than 2%) compared to DyGFormer on three datasets. The reason may be attributed to DyGFormer's use of additional heuristies, such as neighbor co-occurrence frequency, which could provide additional gains in these datasets. However, such design increases computational complexity and lead to out-of-time
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Flights
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Figure 4: Test set inference time of CRAFT and baselines on Flights, Yelp and WikiLink.
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Figure 5: Training time per epoch of CRAFT and baselines on Flights, Yelp and WikiLink.
out-of-memor, failures large-scale datasets such WikiLink and tgbl-ffights. In contrast, CRAFT maintains high performance with a simpler and more generalizable architecture.
Efficiency Evaluation. We evaluate the efficiency of CRAFT by measuring both inference and training times on three representative datasets of increasing scale: Flights (IM edges), Yelp (19M edges), and WikiLink (34M edges). T the inference time for CRAFT and baseline methods, showing that CRAFT completes prediction all test edges (each with 100 negative samples) significantly faster than all baselines. Notably, on the larger datasets Yelp and WikiLink, CRAFT requires less than half the time of the most efficient baseline, JODIE, This highlights CRAFT's practical suitability for real-world deployment, where temporal graphs are large and fast inference essential. EigurrBjillustraen CRAFT is the most efficient method overall, with the exception of being slightly slower than JODIE and DyRep on the smallest dataset, Flights. However, as the dataset size increases, the efficiency advantage of CRAFT becomes more pronounced. On the WikiLink dataset, many temporal graph learning methods fail to complete a single training epoch within 24 hours, whereas CRAFT finishes one epoch in just 0.6 hours. Compared to the most efficient baseline, JODIE, CRAFT is 1.5x faster on the WikiLink dataset.
the training time per epoch of CRAFT and the baselines.
5.2 Effect of Learnable Node Embeddings and Cross-attention Mechanism
Experimental Setup. To verify that unique node identifiers and target-aware matching are critical for future link prediction, we incorporate designed learnable node embeddings into existing methods, to explore whether it can results in performance improvements. We choose TGAT and DyGFormer representative methods because they also rely attention mechanisms. The only difference is the matching mechanisms, where TGAT adopts independent matching, while DyGFormer adopts neighborhood matching. After replacing the original node features with learnable node embeddings, we denotes the modified variants as TGAT-LE and DyGFormer-LE. For fair comparison, we also use learnable positional encodings for the source and destination neighborhoods in DyGFormer-Le which is consistent with CRAFT, and we remove the neighbor co-occurrence frequency encoding for DyGFormer-LK Detailed implementations are provided the appendix. We evaluate all methods on three large and challenging datasets with minimal seen edges, GoogleLocal, Yelp, and tgbl-review.
Results. As shown in Figure 6 comparing each method with its LE variant, we observe significant performance improvements, particularly for TGAT-LE, which achieves up to fivefold gains on Yelp. These results show that learnable node embeddings improve the expressive power of these models and are essential for generalizing to unseen edges real-world applications. Despite these improvements, both TGAT-LE and DyGFormer-LE LE still underperform our CRAFT. The performance gap indicates

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DyGFormer
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Figure 6: Evaluating the impact of learnable node embeddings and cross-attention: CRAFT vs. TGFr/eryFormer with and without learnable embeddings (LE).
PosEni
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wikipedia
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Figure 7: Evaluating the impact of positional encoding, elapsed time encoding, repeat time encoding.
again the importance of target-aware matching, which enables the model to directly assess whether the destination node compatible with the source context. These findings confirm that the two crucial components in our CRAFT, learnable node embeddings and cross-attention-bae target-aware matching. are essential for future link prediction.
5.3 Ablation Study: Effect of Positional, Elapsed Time, and Repeat Time Encoding
Experimental Setup. We conduct ablation studies to evaluate impact of three encoding com- ponents in CRAFT: positional encoding, elapsed time encoding, and repeat time encoding. For each study, we remove one component while keeping the others intact, and denote the resulting variants w/o PosEnc, w/o Elapsed, and w/o Repeat, respectively. We evaluate these variants five representative datasets: wikipedia, mooc, uci, tgbl-review, and GoogleLocal.
Results. We find that all three encodings can positively impact the performance of CRAFT. Among them, the elapsed time encoding contributes significantly across all datasets, as it effectively captures the temporal status of each destination node. Positional encoding is especially critical on mooe and GoogleL.ocal, demonstrating its ability to capture fine-grained temporal order and enable the model to effectively learn from sequential dynamics in these domains. Repeat time encoding plays a prominent role wikipedia and uei, which exhibit high proportion of seen edges. While mooe also contains many seen edges, the gain from repeat time encoding is relatively small, possibly because Icarnable node embeddings and target-aware matching already capture the relationships between the source and destination in this case. Overall, these results confirm the necessity of all three encodings in enabling CRAFT to handle a broad range of temporal dynamics effectively.
6 Conclusion
In this paper. we revisit the architectural foundations of temporal graph learning and identify two essential modeling requirements for future link prediction: representing nodes with unique identifiers and performing target-aware matching between the source and destination nodes, which are over- looked in existing methods. Motivated by these observations, we proposed CRAFT, a simple yet effective framework that replaces memory and aggregation modules with learnable node embeddings and cross-attention mechanism. This design equips CRAFT with strong expressive power and capacity to explicitly capture both seen and unseen edge prediction. Extensive evaluations demonstrate the superiority of CRAFT, establishing practical and scalable solution for real-world future link prediction tasks.
relevance, allowing it to generalize effectively to
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Acknowledgements
The work partially done at Gaoling School of Artificial Intelligence, Beijing Key Laboratory of Research on Large Models and Intelligent Governance, Engineering Research Center of Next- Generation Intelligent Search and Recommendation, MOE, and Pazhou Laboratory (Huangpu), Guangzhou, Guangdong 510555, China. This research was supported in part by National Nat- ural Science Foundation of China (No. U2241212, No. 92470128), by National Science and Technology Major Project (2022ZD01 14802). by Beijing Outstanding Young Scientist Program University joint program on Information
No. W..BIJWZYJH11200 SAHH000011100020000 Retrieval. We also wish to acknowledge the support provided by the fund for building world-class universities (disciplines) of Renmin University of China, by Engineering Research Center of Next- Generation Intelligent Search and Recommendation, Ministry of Education, by Intelligent Social Governance Interdisciplinary Platform, Major Innovation & Planning Interdisciplinary Platform for the "Double-First Class" Initiative, Public Policy and Decision-malee making Research Lab, and Public Computing Cloud, Renmin University of China.
and StuawiiRRemme
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A Notation Table
Table 4: Summary of mathematical notations used in the paper.
Symbol
Description
G = (V,
Temporal graph with node set V and edge sequence E
V
Set of nodes in the temporal graph
E
Sequence of edges ordered by non-decreasing timestamps Source node in a potential interaction
u (or ue ug)
(or Ui, Uj)
Destination node in potential interaction
E,
(ui, U2s t4)
An edge denoting interaction from source s; to destination de at time t, Number of recent neighbors considered for each source node in CRAFT Number of attention heads Dimension per attention head, where d, d/h
k
h
dn
At(v)
Elapsed time since last activity of destination node v
(v)
Last activity time of destination node
B
Batch size
q
Number of candidate destinations per source
d
Embedding or feature dimension
d
Average node degree in the temporal graph
B
Time Complexity Analysis
B.1 Other strategies for extracting historical neighbors
An alternative approach for extracting historical neighbors is to maintain fixed-size window of most recent neighbors, as implemented in TGB [3]. This strategy necessitates updating the window by removing the oldest neighbor and adding the new one, incurring cost of O log B) per batch for any temporal graph learning method [13]. For existing methods except CRAFT, this approach is more efficient than maintaining all historical neighbors (Section 4.3) when (1 + q) log d log B. However, this window-base based strategy presents two significant challenges: 1) It requires processing edges in strict chronological order, preventing edge shuffling for sequence-based methods, potentially leading to performance degradation. (We shuffle the training set during CRAFT's training process to learn more robust embeddings for CRAFT.) 2) For datasets with multiple edges occurring simultaneously, this strategy may be infeasible, as the neighbor window could include interactions at the prediction time, rather than before the prediction time, resulting in data leakage.
C Future Link Prediction and Recommendation
Recommendation is often considered special application scenario for future link prediction, as stated in works like JODIE 17 and TGN 30 This is also why many existing datasets used in temporal graph learning come from recommendation systems, such as lastfm (from JODIE for music recommendetrnn recommendation) and tgbl-review (from TGB [3. dataset for e-commerce recommendation curated from Amazon.com) Temporal graph learning covers a wider range of application scenarios, from education (the mooc dataset from JODIE), to transportation (tgbl-flight [3),, ), and transactions (tgbl-coin [3)). In essence, temporal graph learning aims to capture a variety of evolving patterns in real-world dynamic systems, while recommendation is one specific use case. Recommendation focuses bipartite graphs (user-item interactions), while temporal graph learning aims to work general temporal graphs, including both bipartite and non-bipartite graphs.
To further assess the effectiveness of CRAFT, we compare it with two widely recognized recommen- dation methods: SASRec [14] and SGNN-HN (5). on bipartite datasets. Figures and display the MRR scores of CRAFT (and CRAFT-R), SASRec, and SGNN-HN on four small bipartite datasets and five large bipartite datasets, respectively. We observe that CRAFT achieves the best performance on most datasets, except for the Googlel.ccc ocal dataset, where it slightly trails behind SGNN-HN, Gen- erally, CRAFT-R outperforms both SASRec and SGNN-HN on seen-dominant datasets with larger margin, compared to the results unseen-dominant datasets. These results suggest that existing
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SASRec
SGNN-HN
CRAFT-R
90
90
64
53.21
88
55
88
89
62
MRR (%)
86
88
87.42
84.24
45
84
87
58
57.25
40.72
82
86
56.59
40
56
wikipedia
reddit
mooc
lastfm
Figure MRR scores of CRAFT-R, SASRec and SGNN-HN on seen-dominant bipartite datasets.
SASRec
SGNN-HN
CRAFT
42
41.77 64
62:35
73
72.38
72.69
70
60.58
70. 68
36
35.91
MRR (%)
40-
68
35
34.05
34
70
33.12
56
36-
54-
14.18
60.62
32
tgbl-review
GoogleLocal
Yelp
Taobao
ML-20M
Figure 9: MRR scores of CRAFT, SASRec and SGNN-HN on unseen-dominant bipartite datasets.
recommendation methods perform worse than temporal graph learning methods in seen-dominant scenarios, while our proposed CRAFT achieves the best of both worlds.
D Experiment Details and Additional Empirical Study
D.1 Code Availability
The implementation of CRAFT and baselines based DyGLib 46 The implementation of CRAFT and all commands to reproduce the experimental results are publicly available at hhttps
//github wti.ghtb...oolllllee. wwt..ooyle6///AAAA..
D.2 Datasets
In our experiments, we adopt diverse set 17 datasets: seven from TGB-Seq 44 four from TGB [13), and six commonly used datasets in the field. T the key statistics of these datasets for reference. Detailed descriptions of the datasets are available in their respective original papers: TGB-Seq datasets in 44) TGB datasets in [33, wikipedia, reddit, mooc, lastfmm in [17],
in [26). Flights in (27). While other datasets have been proposed in the literature [27]. those with an insufficient number of nodes ensure robust evaluation.
we exclude
D.3 Baselines
We provide a concise overview of the baselines used in our experiments, focusing on their memory and aggregation modules.
JODIE incorporates both memory and aggregation modules. The memory module utilizes an RNN to encode historical interactions into a compressed state. The aggregation (embedding) module generates current node representations by projecting the memory states with a time-context vector.
DyRep employs an RNN for memory state updates, similar to JODIE. leverages temporal graph attention to transform interaction history, using these transformed representations as input for the memory module. The aggregation module simple identity mapping, directly outputting nodes' memory states.
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Table 5: Datasets statistics: seven TGB-Seq datasets, four TGB datasets, and six commonly used datasets. This table is partially adopted from TGB-Seq 44
Dataset
Nodes (users/Items)
Edges
Timestamps
Repeat ratio
Bipartite
Domain
ML-20M
100.785/9.60 646
14,494,325
9,993,250
Movie rating
Taobao
760,617/863
18,853,792
139,171
16.58
E-commerce interaction
Yelp
L.338,6884488 081
19,760,293
14,646,734
25.18
Business review
Googlel.ocal
206,244/267,83
1,913,967
1,771,060
Business review
Flickr
233,836
7,223,559
134
Who- Tho-To-Follow
YouTube
402.422
3,288,028
203
Who-To-Follow
WikiLink
1,361,972
34,163,774
2,198
Web link
Igbl-review
352,636/298.55
4,873.540
6,865
0.19
E-commerce review
igbl-coin
638,486
22,809, ,486
1,295,720
82,93
Transaction
igll-comment
994,790
44,314,507
30,998.030
19.81
Reply network
igbl-flight
18,143
67,169,570
1,385
96.48
Transport
Wikipedia
8,227/1,008 ,000
157,474
152,757
88.41
Interaction
Reddit
10,000/984
672,447
669.066 066
88.32
Reply network
MOOC
7,047/97
411.749
Interaction
LastFM
980/1.000
1,293,103
1,283,614
88.01
Interaction
UCI
1,899
59,835
58,911
66.06
Social contact
Hlghts
13,169
1,927,145
122
Transport
DyGFomer
DyGFormen-lstto pos
Dy@Fommerlast-time
DyGF DyGFoorme-mean-eee pes
myGromeermeanttie
CRAFT
60
51.05
64.97
65.32
35.83
MAR (%)
43.84 45.19
60
40
35.95
22.39
40
14.51
GoogleLocal
Yelp
tgbl-review
Figure 10: Evaluating the impact of learnable node embeddings and cross-attention: CRAFT and more variants of DyGFormer.
TGN uses GRU for memory state updates and temporal graph attention aggregate historical neighbor information for node embeddings. This information encompasses neighbors' memory states, features, edge features, and timestamps.
TGAT pioneered temporal graph attention, employing multiple layers aggregate historical neigh- bors without a memory module.
CAWN extracts temporal random walks for each node and applies anonymization strategy to ensure inductive learning. These causal anonymous walks are then encoded by an RNN to generate node embeddings.
GraphMixer is sequence-based method that simply aggregates historical neighbor information us- ing MLP-Mixer without a memory module. introduces a fixed time encoding scheme, demonstrating superior effectiveness compared to trainable time encoding.
DyGFormer, another sequence- bosee method, utilizes transformer encoder in its aggregation module. computes neighbor co-occurrence frequency between source and destination nodes to capture their relationship in terms of common neighbors.
D.4 Collision Check for Small Datasets
For datasets with small number of nodes (wikipedia, reddit, mooe, lastfm, uci and Flights), we implement collision check throughout the entire training process, including training, validation, and testing phases. This approach enhances compared to the results of the wikipedia and reddit datasets reported in 44 This improvement attributed to the elimination of false positive samples, which prevents model confusion during training and validation.
performance of most temporal graph learning methods
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Table 6: AP scores (%) of CRAFT and baselines on four commonly-adopted datasets.
Dataset
CRAFT
DyGFormer
GraphMixer
TGN
DyRop
JODIE
TGAT
CAWN
wikipedia
98.07=0.10
99.08=0.07
97.28+0.25
98.60=0.10
95.1840.93
96.94z0.30
97.32=0.09
98.80=0.02
reddit
99.32=0.04
99.27+0.05
97.50=0.05
98.71+0.01
98. 28:006
98. 38.50=0.08
98.49=0.00
99. 15+0.01
lastfm
93.93=0.03
92.9910.20
75.99s0.22
78.24+2.39
70.4313.42
69.23a0.75
73.00:0.35
86.9110.09
mooe
96.15=0.01
89.36x0.41
83.51=0.17
91.00+3.75
81.30+1.87
82.18=1.37
86.34=0.49
81.24:0.44
D.5 Implementation of TGAT-LE and DyGFormer-LE
In Section 5.2, we introduce TGAT-LE (TGAT with learnable embeddings) and DyGFormer-LE (DyGFormer with learnable embeddings) to demonstrate the effectiveness of learnable embeddings and the cross-attention mechanism. We provide detailed implementations of these variants below.
TGAT-LE. We replace node features with learnable embeddings without further modifications. While the standard TGAT configuration uses two layers of temporal graph attention, TGAT-LE employs only one layer. Due to the out-of-time issue, TGAT cannot run on the Yelp dataset with two layers [44]. Therefore, we evaluate TGAT with one layer for Yelp, while other TGAT results are directly adopted from Table 2 in the main paper. Notably, TGAT-LE outperforms TGAT even with single layer, demonstrating the strong expressiveness of learnable embeddings.
DyGFormer-LE. In this variant, we replace the original node features with learnable node embed- dings and remove the neighbor co-occurrence frequency encoding scheme. Additionally, replace the time encoding with learnable positional encoding, similar to the approach used in CRAFT. After passing through the transformer encoder, and destination nodes as their respective node representations, following strategy commonly used in Transformer-based sequence models (14). To better differentiate this variant, refer it as DyGFormer-last-pe as it uses the output of the last neighbor from the transformer encoder and adopts positional encoding.
the output for the last neighbor of both the source
More Variants of DyGror.r. An alternative strategy for producing node representations is to use mean-pooling over the outputs of all neighbors from the transformer encoder. Additionally, temporal information captured by positional encoding can, principle, also be conveyed through time encoding. We explore these options and introduce three variants of DyGFormer: 1) DyGFormer- last-time, which uses the last neighbor output with time encoding instead of positional encoding: 2) DyGFormer-mean pos, which uses mean- seea--poolig with positional encoding; and 3) DyGFormer-mean- time, which uses mean-pous mean-pooling with time encoding. For time encoding, we concatenate a time-context vector obtained by projecting the time interval between the prediction time and each historical interaction through a linear layer- with the corresponding node embedding. The results of these variants are shown in Table TO, The performance of these variants varies across different datasets, suggesting that different datasets exhibit varying interaction patterns. For instance, the GoogleLocal dataset benefits from the mean-pooling strategy, possibly due to the consistent preferences of users in this dataset. Nevertheless, we observe that all variants underperform CRAFT, highlighting the superiority of our cross-attentin mechanism.
D.6 Average-Precision Performance Comparison
Recent studies show that MRR is better suited for tasks with multiple negative samples, as it captures the ranking of the positive edge among negatives more effectively. Moreover, many dynamic graph learning benchmarks 13 44 use MRR the primary metric for link prediction tasks. Therefore, we chose MRR as our main evaluation metric. For reference, we also include the AP results Table b which align with the experiments in Section 5atiion5and and highlight CRAFT's superiority.
D.7 Empirical Study: Positional Encoding vs. Time Encoding
In CRAFT, we use positional encoding to capture the temporal order of the source's neighbors. An alternative approach time encoding, which encodes the time interval between the prediction time and the timestamps of historical interactions. We compare the performance of CRAFT using positional encoding and time encoding Figure TT] For time encoding, we concatenate a time- context vector, which is obtained by projecting the time interval through a lincar layer, with the
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PosEnc
TimeEnc
CRAFT
CRAFT-R
CRAFT (BCE)
CRAFT-R (8CE)
88.93
62.32 77
88.10
88.25
60
MRR (%)
75.56
75.60
62.88
74.94
75.11
41.85
41.77
75
42
41.49
62
61.83
86
85.55
19.83
47.69
74
41.27
51.39
85
73
41
61
wikipedia
mooc
Uci
tgbl-review
GoogleLocal
Figure 11: Comparisons of positional encoding vs. time encoding and BPR loss vs. BCE loss.
Table 7: The tuning ranges of hyperparameters for CRAFT.
Hyperparameter
Tuning Range
Descriptions
N Nueighbors
[30, 60, 90, 120]
the number of neighbors used for each source the dropout rate for FFNs and MLPs the dropout rate for attention scores the dropout rate for node embeddings the number of layers in cross-attention
Phidden_
Phidden_dropout dropout
[0.1, 0.2, 0.3, 0.5]
Partn dropout
[0.1, 0.2]
Pomb dropout
[0.1, 0.2]
N Mayers
[1,
node embedding of each neighbor of the source. These concatenated vectors serve as the key and value inputs to the cross-attention module. In the figure, w/o PosEnc refers models without either positional or time encoding (same as in Figure 7 w/ TimeEnc refers to models using time encoding instead of positional encoding, and the original CRAFT (or CRAFT-R) uses positional encoding. We observe that CRAFT with positional encoding and CRAFT with time encoding perform comparably across most datasets. However, CRAFT with positional encoding significantly outperforms CRAFT with time encoding the wikipedia and mooc datasets. This suggests that using time encoding introduces excessive noise in these datasets, whereas the temporal order provided by positional encoding is sufficient for capturing the sequential dynamics.
D.8
Empirical Study: BPR loss vs. BCE loss
Most temporal graph learning methods are trained using the Binary Cross Entropy (BCE) loss, whereas CRAFT adopts the BPR loss. To assess the impact of the loss function, compare the performance of CRAFT trained with BPR loss and BCE loss in Figure [I] The results show that both versions perform comparably across most datasets. Among the five evaluated datasets, only GoogleLocal exhibits performance gap greater than 1% between the two losses. These findings highlight the robustness of CRAFT and indicate that its performance is largely unaffected by the choice between BPR and BCE loss functions.
D.9 Hyperparameters
The hyperparameters for the baselines on the TGB-Seq benchmark, TGB benchmark, and six commonly used datasets (wikipedia, reddit, mooc, lastfm, uci, and Flights) are selected based on the best configurations reported in [4). [13, and[46), respectively. Thanks architecture, it involves only a limited number of hyperparameters. We fix the batch size across all methods, and set embedding size to for small datasets and 128 for large ones. 7 the hyperparameters and their tuning ranges. We perform grid search over these ranges using the validation set to determine the optimal settings. The final hyperparameters for CRAFT, along with the batch size and embedding size per dataset, summarized in Table g
CRAFT's simple
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Table 8: Optimal hyperparameters and embedding size F for CRAFT, and the fixed batch size B on
various datasets.
Dataset
Nneighhors
Phidden_drees dropout
ceett_dropout
Pemh dropont
Mayers
uci
30
0.3
0.2
0.2
200
wikipedia
120
0.1
0.1
0.2
1
200
64
reddit
120
0.1
0.2
0.1
1
200
64
mooe
30
0.1
0.1
0.1
2
200
Flights
90
0.2
0.2
0.2
1
200
64
lastfim
120
0.1
0.1
0.1
1 200
64
GoogleLocal
60
0.2
0.1
0.2
2
200
128
Flickr
90
0.1
0.1
0.2
1
400
128
YouTube
90
0.2
0.2
0.2
2
400
128
Taobao
60
0.2
0.1
0.2
2
400
128
Yelp
60
0.2
0.2
0.2
2
400
128
ML-20M
60
0.2
0.2
0.2
1
400
128
Wikilink
60
0.2
0.2
0.2
400
128
Igbl-review
120
0.1
0.2
0.1
200
128
tgbl-coin
60
0.2
0.2
0.2
200
128
tgbl-comment
60
0.2
0.1
0.2
200
128
igbl-flight
90
0.2
0.2
0.2
200
128
E
Discussion
E.1
Broader Impact
This paper introduces CRAFT, an efficient and effective temporal graph learning method for future link prediction. CRAFT can be applied across range of real-world scenarios, including recommendation on social media, product recommendation on e-commerce platforms, and interaction forecasting in social, financial, and gaming networks. By enabling more accurate and scalable future link prediction, CRAFT has the potential to enhance user experience and improve overall system utility in these domains.
E.2 Transductive and Inductive Future Link Prediction
The transductive setting for future link prediction focuses on forecasting future links for nodes observed during training, while the inductive setting targets predicting links involving previously unseen nodes [30] In this paper, we do not explicitly separate the transductive and inductive tasks. All datasets follow the original training, validation, and test splits provided by existing benchmarks are split chronologically. As result, evaluation naturally encompasses both settings.
CRAFT is primarily designed for transductive future link prediction, it relies on historical in- teractions to learn meaningful node embeddings. In the inductive setting, however, the source or destination node has little to no interaction history- a situation that frequently arises in real-world dynamic graphs, such as when a new user joins a social network or new item is introduced to an e-commerce platform. Without prior interactions, is difficult for any method infer new node's behavioral preferences. This scenario aligns with the well-known cold-starí problem in recommendation systems [31), where common solutions involve incorporating node profile features and estimating similarity with known nodes. We view this inductive scenario distinct challenge from standard future link prediction, which focuses on leveraging interaction history to model node preferences and predict future links based on dynamic behavioral patterns. Addressing the inductive case effectively may require additional assumptions or auxiliary data beyond the scope of this work.
Another perspective on inductive learning is to eliminate training costs by expecting the model to generalize directly to unobserved nodes, assuming these nodes have sufficient historical interactions to infer their preferences. However, as demonstrated in Section [.22, incorporating learnable node embeddings substantially improves the performance temporal graph learning methods by enhancing their expressive power. Moreover, the experimental results in Table and Table 3 show that CRAFT consistently outperforms baselines designed for inductive learning, despite their more complex architectures. While inductive learning remains valuable research direction, argue that learning
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Table 9: Comparison of CRAFT-core with features vs. embeddings.
Datasets CRAFT-core_w. feaatt CRAFT-coreew CRAFTTcore___embee w_tmbed__eeeddd
igbl-flight
86.36
90.61
Table 10: Comparison of the original CRAFT and CRAFT with features.
Method
wikipedia
reddit
mooc
CRAFT
08.2550.226
89.33=0.11 89.42=0.04
62.3220.39 61.03+0.62
CRAFT_add_fen _edt_
88.40#0.39
from historical interactions is a fundamental requirement for future link prediction, which depends on accurately modeling node-specific interaction patterns. Therefore, training CRAFT on all available historical interactions derive meaningful node embeddings offers more effective approach.
E,3
Node and Edge Features
The current version of CRAFT does not incorporate any node or edge features. This decision is motivated by several considerations.
First, most benchmark datasets lack such features. This because node features in real-world dynamic graphs are often incomplete, noisy, and difficult to align across node types, particularly in bipartite and heterogeneous graphs. For example, the GoogleLocal dataset 44, a real-world dataset of restaurant reviews from Google Maps, includes two node types: users and places, whose features (e.g., user profile vs. place attributes like price) cannot be aligned. Furthermore, many features are missing, like the price feature for over 267,00 9,00 out of 267,336 places. These issues explain why many temporal graph benchmarks often lack features. the features are sparse or poor quality, they can introduce noise and degrade performance.
Second, existing studies have shown that interaction data provides more valuable information than node features for link prediction, whether in static graphs 233 or temporal graphs [44. CRAFT, which does not use any features, still achieves superior performance compared to the baselines that incorporate features. This highlights the critical importance of modeling temporal interactions and the limitations of current methods in fully leveraging interaction data.
Third, while node features can differentiate nodes, they cannot capture interaction patterns as effectively as learnable node embeddings. To evaluate the contribution of node features to future link prediction in existing benchmarks, we conduct experiments on the tgbl-flight dataset, which is the only dataset among those we considered that provides node features. We compare CRAFT-core, w embed (which uses learned node embeddings) with CRAFT-core w_feat (which replaces embeddings with raw node features). Here, CRAFT-core denotes the CRAFT model without the repeated time and last elapsed time encodings, which we remove to isolate their effects and focus on the role of node representations. As noted TGB 133, the node features for each airport igbl-fligh include attributes like the ISO region code, longitude, and latitude, which can differentiate nodes. However, Table 9 shows that the node embeddings is more effective than node features CRAFT. This because node embeddings are learned from the interaction data, which better captures nodes' interaction patterns.
That said, CRAFT is flexible and can easily accommodate features if needed. Node features can be concatenated with learnable node embeddings, while edge features can be appended to the source's neighbor embeddings or combined with positional encodings indicate edge types. To demonstrate this flexibility, we conduct a simple experiment in which both node and edge features (when available) are first projected through a linear layer and then concatenated with the learnable embeddings. Table I0 shows that CRAFT add feat performs comparably to the original CRAFT, suggesting that this method can serve as a basic variant of CRAFT for incorporating features when needed. While CRAFT_ade underperforms on mooc. This reinforces our previous point that node features may often lack high quality be less valuable for link prediction.
feat slightly outperforms CRAFT on the wikipedia and reddit datasets,
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E.4 Negative Sampling Strategies
proposed two challenging negative sampling strategies for future link prediction: historical negative sampling and inductive negative sampling. In this work, we adopt multiple negative samples per positive instance and follow the random negative sampling strategy used prior benchmarks 13 44 as using multiple random negatives per sample is sufficiently challenging for the models and provides fair basis for comparison.
Poursafaei al. 27
E.5 Limitations and Future Work
CRAFT is specifically designed for future link prediction and does not directly support other tasks such as dynamic node classification. Our design focuses on modeling the relationship between the destination node and the source node's ' interaction history, without maintaining dynamic node representations over time. To extend CRAFT support dynamic node classification, straightforward approach is to update node embeddiings continuously via gradient descent. This has the potential advantage of enabling single model to support multiple tasks, eliminating the need for training separate models as required in prior work. Exploring such unified and flexible modeling capabilities a promising direction for future research.
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Reviews:
[{"review_id": "E02a3Mmhei", "reviewer": "Reviewer_HCZc", "summary": "The paper introduces a novel method to work on link prediction in dynamic graphs, featuring two components: learnable node embeddings and a \"target-aware matching\", relying on a cross-attention mechanism.", "questions": "- the sampling of negative items is a subject in itself in the Recommender System community. It is shortly/vaguely described here (l262-263). What does \"We adopt the negative samples from the benchmarks\" mean? Is the random selection focusing on a node, or is it global?\n- there are imprecisions in the formalism: the graph model looks like a \"link stream\" model. Is it exactly one, or not? Also, \"since both pairs share two common neighbors\" (l178): in a graph, nodes usually have neighbors, not edges.\n- \"repeat time\" is an important concept in your work, however not defined. What does it mean? What happens to \"repeat time\" if an edge appears irregularly?\n- at the core of the model, there is the hyperparameter k, the size of a candidate set. The value of k is not evaluated, however it should have a tremendous impact on the CRAFT's performance. It seems with the sentence l181 that [4] and [36] deal with experiments on this, but it should probably be expanded. Could you explain what effect you expect k to have?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The paper clearly exposes its aim, and the solution they bring to existing litterature. However, I am afraid that there is a deep problem plaguing the whole paper: authors deal with a problem which is not (exactly) the same as the one presented in the existing litterature. They perform and improve link prediction _for a given node_, while other methods analyse a whole graph and propose to predict links _at the graph level_, which is very different. \nSecond problem (related to the first one): while authors mention in 4.2.2 (and Fig3) the use case of a recommender system scenario, they completely neglect this litterature, while it would clearly be more relevant to their problem, since recommendation focuses on a _candidate user_ with a potential set of items. There are already a large body of works on recommending items in a dynamic setting, with or without graph learning (and with several attempts to encode time as presented here, see Sequential Recommendation¹). But TGN, TGAT and others (JODIE, DyRep) were not meant to work by focusing on a user/node as it is done here. \n\n¹: note that in a recommender system, the candidate set usually is the entire collection of items\n\nIn light of this, all the paper is affected: the Related Work section is far too short or out of scope (1st paragraph), Experiments confront CRAFT to irrelevant methods (or omit relevant baselines), etc.\n\nAlso, in 4.2.1, it is claimed that GNNs are plagued by \"lack of distinctive node embeddings\", sustained by a 2020 paper. The 5-year gap is important here, as most GNNs have been using random/other initial embeddings for years.\n\nMinor remarks.\n\nBibliography: \n- \"Attention is all you need\" as more than one author…\n- use {} to prevent capital letters from being transformed to lowercase (eg, gnns)\n- BPR was published, don't cite arxiv version when possible", "was_revised": true, "final_justification": "updated score after discussion with authors and clarifications.", "rebuttal": "Thanks for your valuable time and constructive suggestions. \n\n> W1. \"authors deal with a problem which is not (exactly) the same as the one presented in the existing literature. They perform and improve link prediction for a given node, while other methods analyse a whole graph and propose to predict links at the graph level, which is very different.\"\n\nThe problem we address is indeed the same as that presented in the existing literature, such as in TGN and JODIE. As stated in TGN: \"In future edge prediction, the goal is to predict the probability of an edge occurring between two nodes at a given time\", which is exactly the task that CRAFT performs — predicting the probability of an edge given its two terminals and a timestamp. \n\nWe are not entirely sure what is meant by \"other methods...predict links at the graph level,\" but we would like to offer the following clarifications that may help address any misunderstandings:\n\n1. **The inputs and outputs are the same for all baselines and CRAFT**. The inputs consist of the time $t$ and nodes $s,d$, and the output is the probability of the edge $(s,d)$ occurring at time $t$. **All baselines, including CRAFT, cannot output the next edge $(s,d)$ given only the time $t$**.\n2. **The focus of all baselines and CRAFT is the same**: modeling the interaction patterns of a **node** using its historical neighbors. For example, recent works [R3] apply a Transformer encoder *on the sequence of historical neighbors* to obtain node representations and then predict the edge score. CRAFT is similar to these works, inferring the node's interaction patterns based on its historical neighbors.\n3. Please distinguish between **continuous-time dynamic graph (CTDG)** and **discrete-time dynamic graph (DTDG)**. Methods usually process each static graph as a whole separately in a DTDG and then model these graphs as a sequence. However, CRAFT and baselines are all for CTDGs, where the graph is modeled as a stream of edges.\n---\n> W2. \"while authors mention...recommender system scenario, they completely neglect this literature, while it would clearly be more relevant to their problem...\"\n\nWe would like to clarify the relationship between our focus (future link prediction in temporal graph) and the recommendation literature:\n1. **Recommendation is often considered a special application scenario for future link prediction**, as stated in works like JODIE and TGN. This is also why many existing datasets used in temporal graph learning come from recommendation systems, such as lastfm (from JODIE for music recommendation) and tgbl-review (from TGB [R1], a dataset for e-commerce recommendation curated from Amazon.com). \n2. **Temporal graph learning covers a wider range of application scenarios**, from education (the mooc dataset from JODIE), to transportation (tgbl-flight [R1]), and transactions (tgbl-coin [R1]). In essence, temporal graph learning aims to capture a variety of evolving patterns in real-world dynamic systems, while recommendation is one specific use case.\n3. **Recommendation focuses on bipartite graphs** (user-item interactions), while **temporal graph learning aims to work on general temporal graphs**, including both bipartite and non-bipartite graphs. \n4. **Experimental comparison with recommendation methods in Appendix B.8 demonstrates that CRAFT outperforms widely recognized recommendation methods**: Most of temporal graph learning literature (e.g., JODIE and TGN) does **not** specifically review or compare with recommendation literature due to their differences. That said, we recognize the value of recommendation methods as strong baselines, especially in bipartite graph settings. Therefore, we've **compared CRAFT with two recommendation baselines, SASRec and SGNN-HN** in Appendix B.8 and the results demonstrate CRAFT's superiority.\n5. **We will add a review of recommendation literature to our revised manuscript** and provide further clarification of the differences between recommendation and dynamic graph learning. If you have any specific works that you believe should be included or compared in our review, please feel free to suggest them.\n\n---\n> W3. \"it is claimed that GNNs are plagued by \"lack of distinctive node embeddings\", sustained by a 2020 paper. The 5-year gap is important here, as most GNNs have been using random/other initial embeddings for years.\"\n\nThanks for this valuable point. Our emphasis is that dynamic graph learning methods have not fully embraced the idea of node identifiers as static GNNs have. Many still rely on zero features when explicit features are absent, limiting their expressiveness—this is exactly what motivates the use of learnable node embeddings in our CRAFT.\n\n---\n> W4. Minor remarks\n\nThank you for your careful reading and helpful feedback! We will revise the bibliography accordingly.\n\n> Q1. \"What does \"We adopt the negative samples from the benchmarks\" mean? Is the random selection focusing on a node, or is it global?\"\n\nFor datasets from the TGB and TGB-Seq benchmarks, negative samples are provided by the benchmarks themselves: The TGB benchmark samples 100 or 20 negative destinations for each source node from historical and random negative edges [R1], while the TGB-Seq benchmark randomly samples 100 negatives for each source [R2]. For other datasets without publicly available negatives, we follow the approach outlined in [R2] to randomly select 100 negative destinations for each source node.\n\n> Q2-1. \"the graph model looks like a 'link stream' model\"\n\nYes, we focus on continuous-time dynamic graphs, where the graph is modeled as a stream of edges, as defined in most existing literature (JODIE, TGN, DyGFormer[R3], etc.).\n\n> Q2-2. \"Also, 'since both pairs share two common neighbors' (l178): in a graph, nodes usually have neighbors, not edges.\"\n\nTo clarify, in this sentence, we are referring to the nodes b and a, and b and f sharing common neighbors, respectively, rather than saying that the two edges (b, a) and (b, f) share common neighbors. We will revise the sentence for better clarity: \"since both **b and a**, and **b and f** share two common neighbors, c and d, and d and e, respectively\".\n\n> Q3. \"'repeat time'.. What does it mean?\"\n\nRepeat time refers to the number of times an edge appears in the dynamic graph upon the prediction time $t$. Previous studies [R2, R4] have shown that some datasets contain excessive repeated edges, and most methods tend to excel only at predicting these repeated edges. **CRAFT is the first model to effectively address both repeated edges (seen) and new edges (unseen)**, which is crucial for real-world dynamic graph applications where unseen edges are common.\n\n---\n> Q4. \"k, the size of a candidate set...Could you explain what effect you expect k to have?\"\n\nTo clarify, $k$ is **not** the size of the candidate set but rather refers to the number of hops of neighbors ($k$-hop neighbors) considered in existing methods, as mentioned in l175. CRAFT does not consider multi-hop neighbors, i.e., $k = 1$, and outperforms baselines that consider multi-hop neighbors.\n\nThe size of the candidate set (denoted as $q$) does not affect the prediction results of CRAFT or other baselines, but it does impact the evaluation score. **A larger candidate set increases the evaluation difficulty and typically lowers the MRR scores**, as the methods must rank the positive destination among a larger pool of candidates. \n\nTo assess the robustness of CRAFT, we conducted experiments with $q=500$ on the lastfm and wikipedia datasets. As shown in Table 1, CRAFT either outperforms or performs comparably to the best baseline when $q=500$. Notably, the significant superiority of CRAFT over the baselines on lastfm with $q=100$ is also maintained with $q=500$, further demonstrating CRAFT's robustness.\n\nTable 1: MRR with candidate set size $q=500$\n|Dataset|CRAFT|DyGFormer|GraphMixer|\n|-|-|-|-|\n|lastfm|**28.56**|21.20|10.91|\n|wikipedia|69.08|**70.11**|49.98|\n\n---\nWe greatly appreciate your valuable time and insightful comments! Should you have any further questions, we would be happy to discuss further.\n\n[R1] Temporal graph benchmark for machine learning on temporal graphs. NeurIPS'23\n\n[R2] TGB-Seq Benchmark: Challenging Temporal GNNs with Complex Sequential Dynamics. ICLR'25\n\n[R3] Towards Better Dynamic Graph Learning: New Architecture and Unified Library. NeurIPS'23\n\n[R4] Towards Better Evaluation for Dynamic Link Prediction. NeurIPS'22\n\n[R5] Do we really need complicated model architectures for temporal networks? ICLR'23"}, {"review_id": "Ca0rD4RcwS", "reviewer": "Reviewer_Z46w", "summary": "This paper introduces CRAFT architecture, whose most significant differences from the previous models are (1) the introduction of unique node identifiers and (2) the use of cross attention mechanism (coined as target-aware matching in the paper).\nThe one of the strongest motivations of this paper is, the memory or aggregation components commonly used in previous work may not be required, if trainable a trainable node embedding unique for each node is used instead.\nGiven a source node and a set of candidate destinations, it first finds k neighbors for the source node (in the embedding space), sort them by recency, and add trainable positional encodings to node embeddings. Then it applies several rounds of cross attention mechanism, adds elapsed time information, and then finally predicts the score for each candidate destination.\nFrom experiments, it is empirically proven that the suggested CRAFT method outperforms former approaches, while at the same time achieving reduced computational complexity.", "questions": "* Is there a way to obtain node embeddings for unseen nodes? I believe the use of node attributes & aggregation in previous work is mainly for this.", "limitations": "Clarification & discussion on setups where there exist unseen node and unseen edge would be preferred.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n* Large performance improvement introduced by simple change\n* Paper is organized well and easy to understand\n* Analyses are done thoroughly\n\nWeaknesses\n* Some details are not clear: e.g. the formulation of TimeProjection function (I assume it's similar to JODIE's though)\n* I believe it can't handle when a *node* is not present during training, i.e. inductive setup, which is the scenario often discussed in literature.", "was_revised": true, "final_justification": "I read the authors’ response and other reviews, and decided to keep the score.", "rebuttal": "Thanks for your valuable time and constructive suggestions. \n> w1. \"Some details are not clear: e.g. the formulation of TimeProjection function (I assume it's similar to JODIE's though)\"\n\nYes, the **TimeProjection** function is a linear layer that maps the elapsed time $t$ to a vector in $\\mathbb{R}^d$ (as noted in Line 151) via $W_t \\cdot t$, where $W_t \\in \\mathbb{R}^{d \\times 1}$. We will revise the paper to clarify this formulation.\n\n---\n> w2. \"I believe it can't handle when a node is not present during training, i.e. inductive setup, which is the scenario often discussed in literature.\"\n\nThank you for this valuable point. There are two cases where a node is unseen during training but appears in testing:\n\n1. **Case 1:** The new node has no historical neighbors before the prediction time. **Neither CRAFT nor existing baselines can make accurate predictions for this node**, as all methods rely on modeling interaction patterns based on historical data to predict future neighbors.\n\n    In fact, **predicting the next interaction for a new node with no history is a typical *cold-start* problem**. For example, in the recommendation literature, the cold-start problem is often studied separately [R2], with common approaches like learning from metadata of new items [R3] or inferring a new user's preferences through asking the new user's explicit ratings [R4]. Notably, the dynamic graph learning community [R1] has also recognized the difference between the cold-start problem and classic link prediction based on historical interactions.\n\n2. **Case 2:** The new node has historical neighbors before the prediction time. **CRAFT can handle Case 2 as existing methods do**, as it only relies on the embeddings of historical neighbors. To empirically evaluate CRAFT on this, we follow the inductive setup from [R5], where test nodes $S'$ are selected, and all edges connected to them are removed from the training set. The model is then trained on the remaining graph and evaluated on the edges involving nodes in $S'$. As shown in Table 1, **CRAFT consistently outperforms these baselines under this inductive setup**.\n\n    Table 1. MRR Results under the Inductive Setup\n    ||CRAFT|JODIE|TGN|DyGFormer|\n    |-|-|-|-|-|\n    |mooc|**62.66**|27.66|46.46|42.29|\n    |lastfm|**46.28**|19.22|26.44|40.20|\n    |GoogleLocal|**55.83**|24.42|45.03|18.52|\n\nIn summary, both CRAFT and existing methods focus on link prediction based on historical interaction data, a problem highly relevant to real-world dynamic systems and extensively studied. However, existing methods struggle with predicting unseen edges [R1], a challenge that has not been effectively addressed. In this paper, we prioritize addressing this limitation to enhance the applicability of temporal graph learning methods in real-world applications. While we recognize the importance of the cold-start problem, we plan to explore it in future work.\n\n---\n> Q1. \"Is there a way to obtain node embeddings for unseen nodes? I believe the use of node attributes & aggregation in previous work is mainly for this.\"\n\nThank you for this insightful question. One commonly proposed solution [R3] is to incorporate auxiliary node information (e.g., name, description) and learn to project these features into the same embedding space as the node embeddings. However, this approach requires high-quality node features, which are lacking in most existing benchmark datasets. As a result, we cannot verify this method on existing datasets, and previous works also cannot confirm their effectiveness of using node features for link prediction of unseen nodes.\n\nWe recognize that **leveraging node features to address cold-start and general link prediction tasks is an important research direction, and we are actively investigating it**. However, addressing this challenge is non-trivial and will require incremental efforts, such as **creating new benchmark datasets with high-quality node attributes** and **developing models that effectively integrate these features**.\n\n---\n> L1. \"Clarification & discussion on setups where there exist unseen node and unseen edge would be preferred.\"\n\nThank you for your valuable suggestions. We will add the following discussion in our revision:\n\nUnseen nodes commonly arise in real-world dynamic graphs, such as when a new user joins a social network or a new item is added to an e-commerce platform. In these cases, the new node lacks interaction data, making it difficult to predict its future interactions or preferences. This challenge is often referred to as the cold-start problem, where common approaches include leveraging auxiliary node information (e.g., metadata, descriptions) to predict the behavior of new nodes.\n\nUnseen edges are prevalent in dynamic graphs, as new interactions continually emerge. For instance, a user may purchase an item for the first time or follow another user they have not interacted with before. Predicting such unseen edges is challenging, and existing methods often struggle in this area. In our work, we address both unseen and seen edge prediction, filling a critical gap in the existing literature, which typically focuses only on seen edges.\n\nWe hope this clarification enhances the understanding of our approach. If you have any further suggestions, please let us know.\n\n\n[R1] TGB-Seq Benchmark: Challenging Temporal GNNs with Complex Sequential Dynamics. ICLR'25\n\n[R2] Cold-start Recommendation by Personalized Embedding Region Elicitation. UAI'24\n\n[R3] MARec: Metadata Alignment for Cold-start Recommendation. RecSys'24\n\n[R4] Preference elicitation as an optimization problem. RecSys'18\n\n[R5] Towards Better Dynamic Graph Learning: New Architecture and Unified Library. NeurIPS'23"}, {"review_id": "F3reMUULcH", "reviewer": "Reviewer_12t9", "summary": "This paper presents CRAFT (Cross-Attention based Future Link Predictor on Temporal Graphs), an architecture for future link prediction in temporal graphs. The authors identify two critical yet underexplored requirements for this task: incorporating unique node identifiers and enabling target-aware matching between source and destination nodes. Departing from prior approaches that rely on memory and aggregation modules, CRAFT adopts a simpler design composed of two key components: learnable node embeddings and a cross-attention mechanism that aligns candidate destination nodes with the source node’s recent interaction history. This architecture facilitates expressive and adaptive modeling of temporal interaction patterns while maintaining architectural simplicity, enabling effective generalization to both seen and unseen edges.", "questions": "None", "limitations": "None", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "This manuscript presents several strengths.\n\n(S1) The writing is clear and easy to follow.\n\n(S2) The proposed architecture is easy to implement and suitable for unseen future links.\n\n(S3) The baselines and datasets are comprehensive.\n\nNevertheless, this manuscript also has several weaknesses that should be addressed.\n\n(W1) The motivation for unique node identifiers is relatively weak. In real applications of temporal graphs, different nodes should have rich and different features, why these features cannot be used to differentiate nodes? \n\n(W2) I think it is a bit wired that the framework only utilizes learned node embeddings and positional encoding, without utilizing any node features and edge features. Although I noticed that the authors claim many of the benchmark’s datasets lack node features. However, this is not the case in practical scenarios. As the example in your Figure 3, the products ‘iphone/air pods/iphone case’ should have texts, images, and other statistical features if we want to conduct a real next-item- recommendation task. If we assume nodes have no features, how could we know what does a specific node (say node 100) indicate? And how could such a system be useful in practice? Hence, I think the practical utility of the proposed model is rather limited.\n\n(W3) Moreover, how does the model handle newly coming nodes? Since practical temporal graphs will involve not only unseen edges but also unseen nodes as time evolving. The node embeddings are learned during model training. How does the model handle these unseen nodes seems to be a crucial limitation.\n\n\n(W3) The paper claims that the learnable node embedding will enable powerful expressiveness. However, there lacks a theoretical justification that the embedding could improve expressiveness for the temporal prediction task. Theoretical results of static gnns may not be seamlessly transformed into temporal gnns.", "was_revised": true, "final_justification": "Thank you for the author's submission. Appreciate the authors’ efforts and contributions. The final rating reflects a comprehensive evaluation of the paper’s strengths and limitations.", "rebuttal": "Thanks for your valuable time and constructive feedback. \n\n>W1&W2-1. \"If we assume nodes have no features, how could we know what does a specific node (say node 100) indicate?\"\n\nWe use the node identity (e.g., index 100) to represent a node and retrieve its interaction history. For example, $(100, 99, t)$ denotes an interaction between node 100 and node 99 at time $t$. **This is exactly how existing benchmark datasets are structured**, i.e., nodes are treated as ID-based entities, and their interaction patterns are inferred purely from interaction data if no features are available. In fact, **this setup is widely adopted in practical applications.** For example, a large body of work in the recommendation literature, one of the most important applications of future link prediction, focuses on predicting a user's next interaction based solely on interaction data[R5].\n\n---\n> W1&W2-2. \"In real applications of temporal graphs, different nodes should have rich and different features, why these features cannot be used to differentiate nodes?\" \n\nWe agree that high-quality node features can be invaluable for link prediction tasks if available. However, this is not always the case, and we would like to clarify that link prediction models based solely on interaction data are often required in real-world scenarios and present a valuable research challenge.\n\n1. **Node features in real-world dynamic graphs are often incomplete, noisy, and difficult to align across node types, particularly in bipartite and heterogeneous graphs.** For example, the GoogleLocal dataset [R1], a real-world dataset of restaurant reviews from Google Maps, includes two node types: users and places, whose features (e.g., user profile vs. place attributes like price) cannot be aligned. Furthermore, many features are missing, like the price feature for over 267,000 out of 267,336 places. These issues explain why many temporal graph benchmarks often lack features. If the features are sparse or of poor quality, they can introduce noise and degrade performance.\n\n2. **Existing studies have shown that interaction data provides more valuable information than node features for link prediction**, whether in static graphs [R6] or temporal graphs [R1]. CRAFT, which does not use any features, still achieves superior performance compared to the baselines that incorporate features. **This highlights the critical importance of modeling temporal interactions and the limitations of current methods in fully leveraging interaction data.**\n\n3. **While node features can differentiate nodes, they cannot capture interaction patterns as effectively as learnable node embeddings.** We tested this on the *tgbl-flight* dataset, comparing `CRAFT-core_w_embed` (using node embeddings) with `CRAFT-core_w_feat` (replacing embeddings with features). (`CRAFT-core` refers to CRAFT without the repeated time and last elapsed time encodings, which we removed to mitigate their impact.)\n   \n   Table 1. Feature-based CRAFT vs. Embedding-based CRAFT\n   |Dataset|CRAFT-core_w_feat|CRAFT-core_w_embed|\n   |-|-|-|\n   |tgbl-flight|86.36|90.61|\n\n   As noted in TGB [R2], the node features for each airport *tgbl-flight* include attributes like the ISO region code, longitude, and latitude, which can differentiate nodes. However, Table 1 shows that the node embeddings is more effective than node features in CRAFT. This is because node embeddings are learned from the interaction data, which better captures the interaction patterns of nodes.\n\nThat said, we recognize that **leveraging node features for link prediction is an important research direction, and we are actively investigating it**. However, addressing this challenge is non-trivial and will require incremental efforts, such as **creating new benchmark datasets with high-quality node attributes** and **developing models that effectively integrate these features**. In this paper, we focus on modeling node interaction patterns using interaction data, as this remains a valuable and unsolved problem.\n\n**To enable CRAFT to leverage node features, we explore incorporating them by modifying node embeddings.** Specifically, we project edge and node features (if available) by a linear layer and concatenate them with the learnable embeddings. The concatenated features are projected to match the dimension of the embeddings. Table 2 shows that `CRAFT_add_feat` performs comparably to the original CRAFT, suggesting that **this method can serve as a basic variant of CRAFT for incorporating features when needed**. While `CRAFT_add_feat` slightly outperforms CRAFT on the wikipedia and reddit datasets, it underperforms on mooc. This reinforces our previous point that node features may often lack high quality or be less valuable for link prediction.\n\nTable 2. CRAFT with Features\n||wikipedia|reddit|mooc|\n|-|-|-|-|\n|CRAFT_add_feat|**88.40±0.39**|**89.42±0.04**|61.03±0.62|\n|CRAFT_original|88.25±0.26|89.33±0.11|**62.32±0.39**|\n\n---\n> W3. \"how does the model handle newly coming nodes? Since practical temporal graphs will involve not only unseen edges but also unseen nodes as time evolving.\"\n\nThank you for this valuable question. As we mentioned in a related context raised by Reviewer Z46w, **Predicting the next interaction for a new node without any historical interactions is considered a *cold-start* problem**, which is distinct from the classic future link prediction task addressed in this paper and related literature—predicting future interactions by modeling node interaction patterns based on historical data. As a result, neither CRAFT nor any of the baselines can handle this cold-start problem.\n\n**The cold-start problem is typically studied separately from classic future link prediction.** For instance, in the recommendation literature, common approaches include learning from metadata of new items [R7] or inferring a new user's preferences by requesting explicit ratings [R3]. Once the new node has accumulated some interactions, recommender systems can switch to classic future link prediction methods to predict subsequent interactions [R7].\n\nThe dynamic graph learning community [R1] has also recognized the distinction between the cold-start problem and classic link prediction based on historical interactions. Accordingly, recent benchmark datasets (e.g., the TGB-Seq benchmark used in our paper) are designed to include only test nodes that have appeared in the training set. **Therefore, our focus in this paper is on the classic future link prediction task, specifically addressing the limitation of existing methods in predicting unseen edges.** That said, we acknowledge the importance of the cold-start problem and plan to address it in future work.\n\n---\n> W4. \"...there lacks a theoretical justification that the embedding could improve expressiveness for the temporal prediction task.\"\n\nThank you for this insightful question. The expressiveness of temporal GNNs is defined by the ability to map two distinct nodes in a temporal graph to unique embeddings at a given time, i.e., distinguishing between different nodes in a temporal context [R4]. By introducing node embeddings, we provide unique representations for each node, allowing the model to effectively differentiate between nodes based on their embeddings. We will include this discussion in our revision.\n\n[R1] TGB-Seq Benchmark: Challenging Temporal GNNs with Complex Sequential Dynamics. ICLR'25\n\n[R2] Temporal graph benchmark for machine learning on temporal graphs. NeurIPS'23\n\n[R3] Preference elicitation as an optimization problem. RecSys'18\n\n[R4] Provably expressive temporal graph networks. NeurIPS'23\n\n[R5] Neural Collaborative Filtering. WWW'17\n\n[R6] Revisiting Link Prediction: A Data Perspective. ICLR'24\n\n[R7] MARec: Metadata Alignment for Cold-start Recommendation. RecSys'24"}, {"review_id": "JYRXqpaiTQ", "reviewer": "Reviewer_657h", "summary": "This paper introduces CRAFT, which discards memory and aggregation modules for future link prediction on temporal graphs.", "questions": "Please see weakness", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n1. The paper is well-organized and the overall presentation is clear and coherent.\n2. The proposed method achieves strong empirical results on the task considered in the paper.\n\nWeakness:\n1. The roles of the embedding and memory components appear to be quite similar in functionality, yet the paper does not clearly differentiate between the two.\n2. The link prediction task formulation differs from conventional dynamic graph representation learning settings. It remains uncertain whether the proposed method outperforms existing models such as DyGFormer under a standardized task formulation.\n3. In Section 4.3, the number of candidate destination nodes is controlled by a hyperparameter q. The method used to select destination nodes may significantly influence the final results. However, the paper lacks a sensitivity analysis on this hyperparameter.\n4. Although the paper claims that the memory component does not help in handling unseen nodes, the embedding-based approach does not seem to offer any specific mechanism for such cases either. This raises the question of whether the two can, in fact, be treated equivalently.\n5. The paper lacks a concrete case study to visually or intuitively validate its key contributions.", "was_revised": true, "final_justification": "The authors’ responses have addressed all of my concerns. Although I still believe that the embedding based approach, without additional mechanisms, may struggle to handle unseen nodes, overall the manuscript meets the bar for acceptance.", "rebuttal": "> W1. \"The roles of the embedding and memory components appear to be quite similar in functionality, yet the paper does not clearly differentiate between the two.\"\n> \n> W4. \"Although the paper claims that the memory component does not help in handling unseen nodes, the embedding-based approach does not seem to offer any specific mechanism for such cases either. This raises the question of whether the two can, in fact, be treated equivalently.\"\n\nThank you for your thoughtful questions. **While both the embedding and memory components share the goal of representing a node's interaction history in a compressed form, they differ significantly in design and capability.**\n\n**Design**: The memory component typically uses an RNN model to update each node's memory vector when new interactions occur. The memory of each node is initialized as a zero vector and updated by the RNN, which takes the memory and new interaction data as inputs. In contrast, node embeddings in CRAFT are learnable, updated through gradient descent, and directly encode the interaction patterns of nodes.\n\n**Capability**: The memory component struggles with unseen edges (as noted in [R3]), as it does not serve as a unique identifier for nodes, unlike learnable node embeddings. Specifically, when two nodes always interact with other nodes at the same time, their memory become indistinguishable because the RNN input for both nodes is identical, especially when no features are available.\n\nConsider this example (inspired by [R3]): In a temporal graph with two disconnected groups of nodes, Group A and Group B, each node in Group A corresponds to a node in Group B, and they interact identically within their groups. For example, $(A_1, A_2, t)$ in Group A corresponds to $(B_1, B_2, t)$ in Group B. The memory component cannot distinguish between corresponding nodes, such as $A_1$ and $B_1$, because the RNN input for both is the same. However, learnable node embeddings can distinguish between any pair of nodes as they serve as unique identifiers.\n\nThis lack of distinguishability limits the memory component's expressiveness, preventing it from differentiating nodes with similar interaction patterns. This issue is especially critical in datasets with many unseen edges, where the model needs expressive node representations to rank multiple candidates accurately, rather than relying on memorizing seen edges. **To empirically compare the memory component and learnable node embeddings, we conducted experiments using a simple model `Embedding`**, which only utilizes node embeddings. In this model, the probability of an edge $(s,d)$ is predicted using the dot product of the embeddings of nodes $s$ and $d$. Formally, the score for edge $(s,d)$ is computed as:\n\n$$\n\\text{score}(s,d) = \\text{e}(s)^T \\cdot \\text{e}(d), \\quad \\text{where } \\text{e}(s), \\text{e}(d) \\in \\mathbb{R}^d.\n$$\n\nWe compared this model with JODIE, which incorporates a memory component and a simple time projection layer as its aggregation module. As shown in Table 1, **Embedding outperforms JODIE by a large margin, demonstrating the significant capability gap between node embeddings and memory components**.\n\nTable 1: Embedding vs. JODIE\n|Dataset|GoogleLocal|YouTube|Flickr|reddit|Flights|\n|-|-|-|-|-|-|\n|Embedding|**44.81**|**49.76**|**55.03**|**81.02**|**79.84**|\n|JODIE|41.86|41.67|46.21|77.16|20.37|\n\n---\n> W2. \"The link prediction task formulation differs from conventional dynamic graph representation learning settings. It remains uncertain whether the proposed method outperforms existing models such as DyGFormer under a standardized task formulation.\"\n\nThere appears to be a misunderstanding. **The task in this paper is exactly the same as in conventional dynamic graph representation learning settings**, such as those in DyGFormer, TGN, JODIE, etc. Formally, the task is to predict the probability of an edge $(s,d)$ occurring at time $t$ based on the interaction history of $s$ and $d$. **For this reason, we can directly adopt many of the reported results of existing methods from the literature, including those on the TGB benchmark, as evaluated in [R1] by the authors of DyGFormer**.\n\nThe misunderstanding may arise from our use of MRR as the evaluation metric, instead of AP, as in the original DyGFormer paper. Recent studies show that MRR is better suited for tasks with multiple negative samples, as it captures the ranking of the positive edge among negatives more effectively. Moreover, many dynamic graph learning benchmarks [R2, R3] use MRR as the primary metric for link prediction tasks. Therefore, we chose MRR as our main evaluation metric. For reference, we also include the AP results in Table 2, which align with the experiments in our manuscript and highlight CRAFT's superiority over the baselines.\n\nTable 2: AP results\n|Dataset|CRAFT|DyGFormer|GraphMixer|TGN|DyRep|JODIE|TGAT|CAWN|\n|-|-|-|-|-|-|-|-|-|\n|wikipedia|98.07±0.10|**99.08±0.07**|97.28±0.25|98.60±0.10|95.18±0.93|96.94±0.30|97.32±0.09|98.80±0.02|\n|reddit|**99.32±0.04**|99.27±0.05|97.50±0.05|98.71±0.01|98.28±0.06|98.50±0.08|98.49±0.00|99.15±0.01|\n|lastfm|**93.93±0.03**|92.99±0.20|75.99±0.22|78.24±2.39|70.43±3.42|69.23±0.75|73.00±0.35|86.91±0.09|\n|mooc|**96.15±0.01**|89.36±0.41|83.51±0.17|91.00±3.75|81.30±1.87|82.18±1.37|86.34±0.49|81.24±0.44|\n\n---\n> W3. \"In Section 4.3, the number of candidate destination nodes is controlled by a hyperparameter q. The method used to select destination nodes may significantly influence the final results. However, the paper lacks a sensitivity analysis on this hyperparameter.\"\n\nThank you for this insightful point. For datasets from the TGB and TGB-Seq benchmarks, **negative samples are provided by the benchmarks themselves to ensure fairness**: The TGB benchmark samples 100 or 20 negative destinations for each source node from historical and random negative edges [R1], while the TGB-Seq benchmark randomly samples 100 negatives for each source [R2]. For other datasets without publicly available negatives, we follow the approach outlined in [R2] to randomly select 100 negative destinations for each source node.\n\n**Increasing $q$ typically raises the evaluation difficulty and lowers MRR scores**, as methods must rank the positive destination among a larger pool of candidates. To assess the robustness of CRAFT, we conducted experiments with $q=500$ on the lastfm and wikipedia datasets. As shown in Table 3, CRAFT either outperforms or performs comparably to the best baseline when $q=500$. Notably, the significant superiority of CRAFT over the baselines on lastfm with $q=100$ is also maintained with $q=500$, further demonstrating CRAFT's robustness. \n\nWe also experimented with CAWN, which performed third-best on wikipedia and lastfm. However, running experiments with CAWN took over 80 hours to complete, which explains why existing benchmarks typically use $q=100$ to balance efficiency and evaluation thoroughness[R2].\n\nTable 3: MRR with $q=500$\n|Dataset|CRAFT|DyGFormer|GraphMixer|\n|-|-|-|-|\n|lastfm|**28.56**|21.20|10.91|\n|wikipedia|69.08|**70.11**|49.98|\n\n---\n> W5. \"The paper lacks a concrete case study to visually or intuitively validate its key contributions.\"\n\nThank you for this valuable point. We have provided two case studies in Section 4.2 to demonstrate the necessity of our key components: learnable node embeddings and the cross-attention mechanism. Figure 1 shows that even methods like DyGFormer, which aim to improve the ability to distinguish between nodes, fail in a simple example, highlighting the need for learnable node embeddings to provide unique identifiers. Figure 3 compares CRAFT's cross-attention mechanism with existing methods and explains its advantages.\n\nIn response to your feedback, we plan to combine the temporal graph example from Figure 1 with the example in our responses to W1 and W4 into a unified graph. This will further illustrate the limitations of existing methods and the importance of node embeddings. If you have any suggestions, we are happy to discuss further.\n\n[R1] An Empirical Evaluation of Temporal Graph Benchmark. Arxiv'23\n\n[R2] Temporal graph benchmark for machine learning on temporal graphs. NeurIPS'23\n\n[R3] TGB-Seq Benchmark: Challenging Temporal GNNs with Complex Sequential Dynamics. ICLR'25\n\n[R4] Towards Better Evaluation for Dynamic Link Prediction. NeurIPS'22"}]

Author rebuttal:

Meta-review: The paper introduces a novel approach, CRAFT (Cross-Attention-based Future Link Predictor), to temporal graph link prediction, which forgoes the use of memory and aggregation modules commonly used in prior models. Instead, it leverages two key components: learnable node embeddings and a cross-attention mechanism for target-aware matching between source and destination nodes. The proposed method is simple and effective, consistently outperforming a wide range of existing models across 17 different datasets. A primary concern raised by several reviewers is the paper’s handling of cold-start scenarios (where new nodes appear without interaction history). While the authors clarify that CRAFT and existing models cannot handle cold-start problems effectively, a more in-depth exploration or potential solution for these scenarios would have made the paper more comprehensive. In practical applications, such cases are frequent, and addressing them could further solidify the utility of the method.
Decision: Accept (poster)