A Selective Learning Method for Temporal Graph Continual Learning
Authors: Hanmo Liu
Shimin Di
Haoyang LI
Xun Jian
Yue Wang
Lei Chen
Venue: ICML 2025 poster (2025)
Keywords: Data Selection
Continual Learning
Temporal Graph
Primary area: general_machine_learning->transfer_multitask_and_metalearning
TL;DR: A theory-guided temporal subgraph selection and learning method to efficiently update TGNNs.

Abstract: Node classification is a key task in temporal graph learning (TGL). Real-life temporal graphs often introduce new node classes over time, but existing TGL methods assume a fixed set of classes. This assumption brings limitations, as updating models with full data is costly, while focusing only on new classes results in forgetting old ones. Graph continual learning (GCL) methods mitigate forgetting using old-class subsets but fail to account for their evolution. We define this novel problem as temporal graph continual learning (TGCL), which focuses on efficiently maintaining up-to-date knowledge of old classes. To tackle TGCL, we propose a selective learning framework that substitutes the old-class data with its subsets, Learning Towards the Future (LTF). We derive an upper bound on the error caused by such replacement and transform it into objectives for selecting and learning subsets that minimize classification error while preserving the distribution of the full old-class data. Experiments on three real-world datasets show that LTF effectively addresses the TGCL challenge.

A Selective Learning Method for Temporal Graph Continual Learning
Hanmo LIU
Shimin DI Haoyang LI*
Xun JIAN'
Yue WANG
Lei CHEN
Abstract
Temporal Graph Learning
Old Classes
New Classes
Evolving Old
Ignored New
Node classification is key task in temporal graph learning (TGL). Real-life temporal graphs often introduce new node classes over time, but existing TGL methods assume a fixed set of classes. This assumption brings limitations, as updating models with full data is costly. while focusing only on new classes results in forgetting old ones. Graph con- tinual learning (GCL) methods mitigate forgetting using old-class subsets but fail to account for their evolution. We define this novel problem as tem- poral graph continual learning (TGCL), which fo- cuses on efficiently maintaining up-to-date knowl- edge of old classes. To tackle TGCL, we propose selective learning framework that substitutes the old-class data with its subsets, Learning Towards the Future (LTF).. We derive upper bound on the еггоr caused by such replacement and trans- form it into objectives for selecting and learning subsets that minimize classification еттоr while preserving the distribution of the full old-class data. Experiments on three real-world datasets validate the effectiveness of LTF on TGCL.
Data
Class Data
Past
Current
Period
Period
Graph Continual Learning
Temporal Graph Continual Learning
Static Old
Emerging New
Evolving Old
Emerging New Class Data
Class Data
Class Data
Class Data
Static
Current
Current
Period
Period
Figure 1: The differences in temporal graph learning (TGL), graph continual learning (GCL) and temporal graph con- tinual learning (TGCL). At a new period, TGL assumes no data of new classes appear, while GCL assumes static old-class data. TGCL holds neither of these assumptions, thus is more suitable real-life temporal graphs
beddings (Kumar al., 2019; Rossi et al., 2020; Xu et al., 2020; Cong al., 2023; Wen & Fang. 2022: Li & Chen, 2023; Li et al., 2023). The current approaches for process- ing both structural and temporal information in these graphs utilize range of model architectures, including message- passing mechanisms (Rossi et al., 2020; Xu et al., 2020; Wen Fang, 2022), multi-layer perceptrons (MLPs) (Cong et al., 2023; Gardner Dorling, 1998), and transformers (Yu al., 2023; Vaswani al., 2017). A key application of TGL methods is node classification, which is critical task in the analysis of temporal graphs (Rossi et al., 2020; Xu et al.. 2020; Yu et al., 2023). For example, in social net- works, TGL methods classify normal and malicious users based on their interactions.
1. Introduction
Temporal graphs are essential data structures for real-world applications, such social networks (Baumgartner al., 2020) and online shopping (Ni et al., 2019). In tempo- ral graphs, the edges and/or nodes change over time, with these additions or deletions captured as a sequence of events (Yang et al., 2023; de Barros et al., 2023). In recent years, various temporal graph learning (TGL) methods have been developed to extract insights from temporal graphs by in- corporating cemporal-neightol information into node em-
'Hong Kong University Science and Technology, China 'Hong Kong University of Science and Technology (Guangzhou), China 'Southeast University, China 'Hong Kong Polytechnic University, China Northwesterr Polytechnical University, China Shhenheen Institute of Computing Sciences, China. Correspon- dence to: Shimin DI <shimin.diee ctbimin.de@scc..ddu..m edu.cn>>
While TGL methods are effective classifying nodes, they face significant limitation: they assume static of node classes, which does not reflect the dynamic reality of these environments. This static assumption is illustrated in Fig. 1, where node classes under the TGL setting remain unchanged over time. However, real-world scenarios often exhibit an open class setting, where new classes frequently emerge. Like in social networks, new malicious behaviours contin-
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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A Selective Learning Method for Temporal Graph Continual Learning
ually arise, introducing new node classes into the system (Feng et al., 2023). Due the fixed class set assumption, adapting current TGL methods to this open class setting presents efficiency and effectiveness challenges. Updating the model for all classes becomes inefficient as the tempo-
selection objective that minimizes the upper-bound error on the old classes.
The knowledge from the subsets is hard to generalize to the full old-class data. We solve this problem by designing an efficient loss that aligns the distributions of the subset and the full data.
ral graph grows, while fine-tuning the model for only new
classes risks catastrophic forgetting (French & Chater, 2002; Parisi al., 2019; Masana et al., 2023) of older classes, par- ticularly when their data distribution diverges from past instances.
We conduct extensive experiments on real-world web data, Yelp, Reddit, and Amazon. The results show that our method is effective while ensuring high efficiency.
To address the issue of forgetting when fine-tuning TGL models, continual learning (Parisi et al., 2019; Masana et al., 2023) provides a promising solution. Recently, several graph continual learning (GCI.) methods have been pro- posed to preserve old-class knowledge by either regulariz- ing model parameters associated with previous classes (Liu et al., 2021) or replaying representative subsets of old-class data (Kim et al., 2022; Zhou & Cao, 2021; Chen et al., 2021; Wang et al., 2022; Zhang et al., 2022; Feng et al., 2023). However, existing GCL methods struggle to handle open-class temporal graphs. The major limitation is that they assume the seen data will be static in the future, as shown in Fig.1. Such assumption contradicts with the dy- namic nature of temporal graphs, making the model become out-dated for future temporal graphs.
2. Background
Many real-world scenarios are modeled as temporal graphs (Yang et al., 2023; de Barros et al., 2023; Kazemi et al., 2020), such as social networks and online shop- ping networks. In this paper, the temporal graph G E, G is a set of nodes V with labels Y con- nected by time-stamped events E happening among V within the time period T. G follows the distribution G. Each event e = {ue, U2 t) E E is an interaction (edge) between two nodes ue Vr E V at time & E T. can be equivalently expressed as E. Each node i/ E V is related with time and has a time-dependent feature x,.
Suppose the temporal graph has evolved for N time periods {T1, T2,,.... TN }. and the corresponding temporal graphs are noted as (G1, G2,.., GN3 which follow the distribu- tions {91, Fe, ..., GN }. Each period has a new set of classes (Yi, Y2,... ), where Y, nY, = 0, Vi,j S N and + j. For simplicity, we note the old classes at TN as Yold UfYa IneN. Corresponding to the node classes, GN can be separated into GRew
These limitations in current TGL and GCL methods make updating models for open-class temporal graphs a challeng- ing problem, which we define as temporal graph continual learning (TGCL). The challenge in TGCL how to main- tain both the effectiveness and recency of old-class knowl- edge while ensuring high efficiency. To address this, we pro- pose a selective learning method that identifies and learns representative subsets of old-class data in new temporal graphs, named Learning Towards the Future (LTF). While subset selection is a common approach, detailed analysis of how well these subsets represent the full dataset remains limited, especially when learning from the entire dataset is impractical. To address this, we derive an upper bound on the error introduced by approximating the full dataset with a subset. We transform the upper bound into a sub- set selection objective to minimize this error. Additionally, guided by the upper bound, we design a regularization loss that aligns the embedding distribution of the selected subset with that of the full dataset to pursue better performance. Our contribution can be summarized as follows:
(Vnew EnEW ,TN, YN) and Gold = (Vold, Foold TN,, Yata), where GN = G U UN Vold n V = 0 and Egd n ENew # 0. Ex and EN are overlapping at the events connecting between Vald and Vy is worth noting that Gold has the same set of classes as Gx-1, but the data distribution is different due to the temporal evolution. The illustration on relationships among GN-1, G and G and the notation summary are presented in Appendix A.
2. Temporal Graph Learning
In recent years, many temporal graph learning methods are proposed (Parisi et al., 2019; Masana et al., 2023) to extract knowledge from the temporal graphs. Under the fixed class set assumption, at a new period TN, the TGL methods under the node classification task aims to minimize the classifi- cation error of the model on Gold. i.e. the part of GN with only Yoid- Suppose that h is a binary classification hypothesis (model) from the hypothesis space H. with finite VC-dimension, the TGL. objective is formulated as:
We are among the first to investigate how to effectively and efficiently update a model on temporal graphs with emerging new-class data and evolving old-class data, which we term the temporal graph continual learning (TGCL) problem.
Selecting representative old-class subsets is crucial for addressing the TGCL problem. To achieve this, we define
h = arg min c(h (gol))
(1)
kEH
2

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A Selective Learning Method for Temporal Graph Continual Learning
where <(Mlg) Ev (b(v))) + [(,)] is the expected classification error of h on any distribution G, and f(-) is unknown deterministic function that gives the ground truth classification on each U/.
performances. However, these methods primarily target graph snapshots and are less effective for event-based tem- poral graphs (Feng et al., 2023). This gap is first addressed by OTGNet (Feng et al., 2023). which proposes to replay important and diverse triads (Zhou et al., 2018) and learn class-agnostic embeddings.
Early TGL. works (Wu et al., 2021; Skarding et al., 2021) integrate events of temporal graphs into a sequence of snap- shots, which loses fine- fine-grained continuous-ting time information. Thus recent TGL methods preserve events as the basic train- ing instances (Yang al., 2023). As the pioneers, JODIE (Kumar et al., 2019) processes and updates the embeddings of each node based on their related events by using recur- sive neural network (Alom et al., 2019). CTDNE (Nguyen et al., 2018) and CAW (Wang et al., 2021a) aggregate the information through random walks on the events. TGAT (Rossi et al., 2020), TGN (Xu et al., 2020) and TREND (Wen & Fang, 2022) apply the GNN-like message-passing mechanism to capture the temporal and structural informa- tion at the same time. More recently, there are also works using the multi-layer perceptrons (Cong et al., 2023) or transformers (Yu et al., 2023) to understand the temporal graphs. Other than structure designs, temporal learning techniques like the temporal point process (Trivedi et al., 2019; Wen & Fang, 2022) are also integrated into the TGL methods to better capture the temporal dynamics.
3. Methodology
TGCL problem takes more realistic temporal graph setting that considers both the appearance of new classes and the evolution of old-class data. At a new period Tv, TGCL requires the model to learn the new classes from GN" and maintain the old-class knowledge from Gold;
(aggmin(( NEH
(3)
h
Compared with the TGL problem at Eq. (1), the TGCL problem additionally minimizes e(h (y Besides, TGCL maintains more recent old-class knowledge from Gold dif- fering from GN-1 in the GCL problem at Eq. (2).
In this work, we focus on how to achieve both effectiveness and efficiency in minimizing c(hlggh)) and directly mini- mize ((h|g as most continual learning works do. We follow common strategy by selecting and learning subset G of G To obtain an optimal performance, we first derive an upper bound on the error introduced by approxi- mating G with G in Sec.3.1. We then transform this theoretical bound into a tractable optimization problem to facilitate subset selection in S.c.3.2. Lastly, this error fur- ther minimized during learning by aligning the distribution of G with Gold as detailed in Sec.3.3. The framework of LTF is illustrated in Fig.2.
2.2. Graph Continual Learning
As new classes continuously emerge for real-life temporal graphs, how to efficiently learn new classes without forget- ting the old knowledge (French & Chater, 2002) becomes an important problem. For Euclidean data like images, the forgetting issue has been addressed by many continual learn- ing methods (Parisi et al., 2019; Masana et al., 2023). The common approaches include regularizing the model param- eters, replaying the subsets of the old data, or adjusting the model parameters. Recently, some GCL methods are trying to connect continual learning to dynamic graphs (Tian et al., 2024). The objective of the GCL problem is:
3.1. Classification Error Upper-bound
A small classification error e ((ggg on G%yd is essen- tial for the model effectiveness. Selecting and learning G C Gyy assumes that minimizing <(h(gga)) will also minimize e(hlggdd) While heuristics can help align these errors, a theoretical analysis connecting them is lack- ing. We address this gap using domain adaptation theory (Redko et al., 2020a; Ben-David et al., 2010) and show that <(h (gg can approximate c(hlgg))) with upper-bounded additional error.
hy arg min e(hlggrm)) + E(h19N-1). kEH
where Grew and GN-1 are distributions of Gaee and G -N- and the former term is for learning new-class knowledge while the latter one is for maintaining old-class knowledge. To reduce the cost of learning Gx-1, most of the GCL methods try to use subsets of GN-1 i to approximate its error, where the subsets are selected by the node influence (Zhou & Cao, 2021) or the structural dependency (Chen et al., 2021; Kim et al., 2022; Zhang et al., 2022), or generated via auxiliary models (Wang et al., 2022). TWP (Liu et al., 2021) takes a different approach by preventing the impor- tant parameters for classification and pessaae-passsngg from being modified. SSRM (Su et al., 2023a) aligns distribu- tions between old and new class data distributions for better
Based on Lemma 3 from (Ben-David et al., 2010) (see Appendix C), the classification disagreement of any two models h and h' on any two data distributions is upper- bounded by the discrepancy between those two distributions. Then, the boper- on the classification error of Gold can be derived as the following theorem:
Theorem 3.1. Let gold gguh be the distributions of G and G Let h E H be a function in the hypothesis space
3

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A Selective Learning Method for Temporal Graph Continual Learning
Gy-
GN
Ty-1
Weighted
Lowest 202
Optimize
Enror Minimization laxf-)
(+(()
x(-)
Contribution
Iw
G
Distribution Aligmment Rax()
Extract Embeddingg
Contribution
Lowest (araco
GW
Input
To Distribution
hy
)MMD(
Time
Select Another Node
Figure 2: The selective learning framework of LTF on old-class data. From G Gg is greedily selected by having the lowest classification error (-) and distribution discrepancy jMMMD(-), while G is greedily selected only by the lowest )M) Afterwards, G is learned by minimizing the classification error and aligning the distribution with GNm.
H and heyb be the function optimized on ON The classifi- cation error on gold then has the following upper bound:
Base Algorithm. In minimizing (h (gg] it infea- sible to obtain higu from each possible GN for selection. Therefore we approximate hi with hv that is optimized hy-1 is
min (hlgg)))
I min (hhg119 h, 93
(4)
bEH
GN-1- This is a reasonable approximation, readily available and GN closely resembles the full data Gold by sharing the same class set Youd and being tem- porally proximate. With hige substitued by hy-1, based on the inequality in (Ben-David al., 2010), ( is expanded to: ((gl)) S <(hgg)) 1 + ((hx11198 As c(hN-11gTh)) is unrelated to the sub- set, we focus on minimizing e e(hgr, hN-11g which requires aligning lige with hw-1- Because have depends on G we select G that minimizes e(hN-119N'') to match the behaviors of hgve and hN- This simplifies our selection problem to:
1 dHH )NDh) + e(h, Tuu @
2
where dHAH (9a: Gb) = 2 2SuPHERAN PP (h(ve) 1] Promse, (h(v))) = 1]] measures the HAH divergence between the distributions Go and Gb, and e(h, (D(D) := BaeD(h(z) * (x(x)] is the expected prediction differences h and h' on D.
The proof is given in Appendix C. Following Theorem 3.1, there are three criteria to ensure that /t achieves a lower error on Gold by finding a suitable G
Small error e(hevb g indicates that ligub learned on subset G is also predictive the entire old data Goldd
gzub = arg min chN dHaN(OR gaub). (5) gzzb
Small distribution difference dzAH (( gzub) indicates that the subset G is diverse enough represent the entire old class data Gold,
Due to limited available observations in reality, we trans- form the distribution-leva error c (g pirical error E(-) on the finite subest G
into the em-
Small error (h, Rega gzrl) indicates that h. classifies Gguh similarly as high,, which guarantees that the knowl- edge of high can be transferred h.
((N
Σ (HEN))
Lote (IN-1 (6)
By relaxing c(hlgold to the upper bound in Eq. (4), we convert the original problem into selecting subset G (Sec. 3.2) and updating the TGCL model h (Scc.3.3).
Ssub
where (.ts()) is the classification error like the mean square error. Similarly, we estimate duan (gola gaub) by the square of the mean maximum distribution (MMD) (Gretton et al., 2006) on the finite sets Gold and G
3.2. Subset Selection
Theorem 3.1 specifies three criteria for selecting & from Goldd. Since is unknown during selection, third criterion omited in following analysis. The remaining two cri- teria for representative G are: 1) low c(hsuh Gold), reflecting strong predictive performance on Gold and 2) low dHAR (gold, goub), ensuring close alignment with the distribution of G Next, we introduce how we transform these two criteria into a tractable optimization problem for selecting representative Gzub.
(G.
Σ k(ve,u))
G. V...EGG.
2
k(v).u))
Σ
k(v,,u));
Gal D,EGoiNeEG.
Gbl2
VL.N.EG.
where k(...) is the kernel function, Go and Go are adopted for simplifying notations. To evaluate the kernel values, we

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A Selective Learning Method for Temporal Graph Continual Learning
take a common practice to replace the raw data by their embeddings (Su et al., 2023b; Shi & Wang. 2023; Redko et al., 2020b), which are extracted by hx-1 and noted as dAMD (GN', (C
witness function j(-) is expressed as:
j(vz) = ajds (vr) + +MMDD(B)),
where is the same as in Eq. (8). Afterwards, we greedily select the nodes with the smallest j(-) from G to Ggy untill the buffer is full.
With above estimations, the selection objective of GN in (5.(5) is transformed into:
Graub = arg
min I smm Gy cog + BADD (G
aē(hN-11Gxg) (8)
Cost Reduction. During greedy selection, estimating B GGold GN poubliy-i has a high computational com- plexity of [[ + IGx))))), which limits its applica- tion to large data sets. Thus, we propose to evenly partition Gold into groups of size p. |G > p > m, resulting in W -F partitions. We then greedily select 1/w of Ggyh from each partition and join them as the final subset. The complexity of selecting G&y from each partition is reduced to O((Gg))) + |G
Gold Gou (hN),
where a is a weight hyper-parameter and m is the memory budget for GNy. A larger m brings a better estimation but also increases the computation complexity.
Greedy Algorithm. Directly optimizing the selection ob- jective in Eq. (8) is infeasible due to its factorial time com- plexity. However, it can be proven to be monotone sub- modular function, allowing greedy optimization with guar- anteed approximation to the optimal solution.
Based on the triangle inequality of dxaH(;-) (Gret- ton al., 2006), this partition procedure enlarges the second term of Eq. (8) to dHAH(9N gNrh) S dHan(gN G + dHa NN.w (NN for each parti- tion Gold should be similar to Ggld As the partitioned data can remain a large size for the subset selection, the random partition can well satisfy this requirement.
The first term ((hx-1/G3()) is linear to the clas- sification error of each instance, thus it is directly monotone submodular.
N.w Gold To reduce this additional error, NN ae
Following the proof in (Kim et al., 2016), MMD (GM G hN-1) is also monotone submodular function with respect to G provided k(tz,u,) satisfies 0 I k(v,, ue) (tnx00//1ar/112200711130 13)) Vee, Ue E GV e4 * u4- This requirement is met with a properly parame- terized kernel, and we use the Radial Basis Function kernel (Schölkopf et al., 1997) in practice. Thus, Eq. (8), as a sum of two monotone submodular functions, itself monotone submodular based on the theory in (Cook et al., 2011). Consequently, as per (Nemhauser et al., 1978), (8) can be efficiently approximated by greedy algorithm, achieving an error bound of (1 - 1/e) relative to the optimal solution.
3.3. Model Optimization
After selecting an optimal subset from Sec. 3.2, we trans- form Eq. (4) into a concrete learning objective to train an effective model h with Giy... Because hive is deter- mined after the subset is selected and Gold fixed, the first term e < (gXd) of Eq. (4) cannot be further opti- mized and is omitted. We minimize d g2th) by enclosing the embedding distributions of both data sets extracted by h -Dvn-D et al., 2010; Su et al., 2023b; Shi & Wang, 2023; Redko et al., 2020b), i.e., minimize dHaN(GN I By replacing the population terms with their estimations, the objective of learning G is ē(h, hrgh (Gx))) + dMMD(GG) G
To implement the greedy algorithm, we derive the witness function j(-) to evaluate how adding one node to Graub af- fects the value of (8). The function j()) is summation of two separate witness functions j.t-(-) and jMMDD()). corre- sponding to ((h--1G and & (Gold G.y.). Since the classification error is summation over node-wise losses defined in (6) jet=((;)) lass lat, u )). On the other hand, jMMD(.) can be derived from Eq. (7) as:
As we avoid learning Godd for efficiency reason, we substi- tute Gold with its similarly distributed subset G C Gold gaim as gold. To satisfy this requirement, G is selected by solely minimizing its distribution discrepancy with Gold,
G = arg min |C Sm' Cx""CG"
PAEDDGGT G (10)
(MMD(U))
Σ B
k(y,, un IIN
(9)
S N
2
Σ
where m is the memory budget for G A larger ml improves the estimation but also increases the computation complexity. G can be selected by greedily finding the nodes with the lowest j.MD(.) defined in Eq. (9). We fur- ther reduce the selection cost of G by data partitioning,
G
where k(V,, w/(h) notes the kernel calculated by the node embeddings extracted from the model h. Then, the overall
5

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A Selective Learning Method for Temporal Graph Continual Learning
Table 1: Data statistics
Amazon (Ni et al., 2019). Yelp, business-to-busings tem- poral graph from 2014 to 2019, treats businesses in the same category as nodes of the same class, with user interactions creating events. The graph is divided into five periods, each representing a year, with three new business categories in- troduced each year. Reddit, a post-to-post temporal graph, treats subreddit topics as classes and posts as nodes, User comments create events, with every 24 days forming a pe- riod and five new subreddits introduced each period. Ama- zon is constructed similarly to Yelp, with 20-day periods and three new businesses per period. The temporal graph transformation mechanism is similar to OTGNet (Feng et al., 2023), but adapted to our unique problem definition. Dataset statistics are summarized in Tab. with additional details in the Appendix G.
Data Set
Yelp
Reddit
Amazon
# Nodes
19,918
13,106
84,605
# Events
2,321,186
310,231
875,563
# Timespan/ Period
1 year
20 days
24 days
# Periods
5
3
# Classes / Period
3
5
3
# Total Classes
15
15
9
similar to G After substituting Gogdd with GN",, the
learning objective is transformed to:
Lata " GGg1))) (h) E(h/ GN +oda)dddddGGGg .N (gu [b);
(11)
where E(h, (G is written as ((MGG))) since both terms are equivalent in making ls perform like hggh.
Backbone Model. As LTF is agnostic to TGL model de- signs, we select the classic model TGAT (Rossi et al., 2020) and the state-of-the-ar model DyGFormer (Yu et al., 2023) as our backbone models. TGAT uses the self-attention mech- anism to aggregate the temporal neighbor information and embed the nodes. DyGFormer applies the transformer struc- ture and uses the structural encoding to embed the nodes.
In practice, the complexity of calculating (h) is O([GGT] + 13), which
drrMD (Grm, (N) is much higher than O(GN*)) |] of the classification error calculation. So that we further simplify its format to improve the efficiency. To ensure that GN the target distribution of Gzub during optimization, gradients of G from being pack-propagated. Following this stop gradient design, the first and third terms in & (+) definition at Eq. (7) are omitted, since Giim is not learned and the self-comparison within G is meaningless. After this simplification, the complexity is reduced from [( + |GNN))?) I)²) to O[ [ I),
stop the
Baselines. First, we select three classic continual learning models that are adaptable to the TGCL problem, which are EWC (Kirkpatrick et al., 2016), LwF (Li & Hoiem, 2018) 8) and iCaRL (Rebuffi et al., 2017). EWC and LwF use regularization losses to prevent forgetting the old class knowledge while not using the old class data. iCaRL selects the representative old class data based on the closeness to the mean of the embeddings. For the GCL methods, we select the replay-based methods ER (Zhou & Cao, 2021), SSM (Zhang et al., 2022), OTGNet (Feng et al., 2023), and URCL (Miao et al., 2024). Besides, the naive baselines of learning the full GN (Joint) and learning only the G (Finetunc) are included. Joint is the upper-bound for performance with the lowest efficiency, while Finetune is the opposite.
and dRADD ( (Grm GRrll)) is optimized by:
Last (Geub Gesm h)) =-s
Σ M)r,s)uu.)l)) E
M+EG*m
where s = 3/1G// -GNTM and sg(+) means stopping the gradients from back-propagation.
Finally, by including the objective of learning GNe, our total objective of updating h at TN is:
Evaluation Metric. The average precision (AP) and aver- age forgetting (AF) on each set of classes within period are used to evaluate the model performance. In G.. there are sets of classes {Yi,..., YnJ. and the model's precision on each of them is Pn.i. Vi S n. Then AP at period T, is calculated as AP,, := E PR.s. To evaluate the forget- ting issue at Tu, we use the precision difference between the current method and Joint (19P5) as the forgetting score for Y;, which is Fn,i paint Pa,i- Then the AF at period T, is calculated as AF, := R- - Di=1 Fn..- For simplicity, we omit the subscript N for APN and AFx as they reflect the final performance. A higher value of AP is better, while a lower value of AF is better. To evaluate the efficiency, the average training time per epoch (abbreviated as Time) at the
Leor = G(hhGN + E(h|GT")+ + Blase(Gri" (
where 3 is the hyper-parameter weighting the distribution regularization importance. The pseudo-code of our overall framework is presented in Algorithm at Appendix D.
4. Experiments
4.1. Experiment Setup
Data Set. evaluate our method using three real-world datasets: Yelp (dat), Reddit (Baumgartner et al., 2020), and
'Our code and data are available at https:: //gt:::///tttt/ com/1 iuhanmo321 BECI_ITF..iit.
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A Selective Learning Method for Temporal Graph Continual Learning
Table 2: The comparison between LTF and the baselines methods. The best and second best results are noted in Bold and Underline. Joint and Finetune are excluded from the notations.
TGAT
DyGFormer
Method
Yelp
Reddit
Amazon
Yelp
Reddit
Amazon
APT
AF,
Time
APP
AFL
Timel
APt
AFL
Timel|
|
APt
AFL
Time!]
APT
ARL.
Timel|
AP1
AFL
Timel
Joint
0,0810
58.37
0.1378
50.50
00.4477
128.71
0.0813
95.11
0.1255
70.64
10.0500
177.38
Finetune
0.0141
0.0843
9.11
0.0312
0.1550
14.93
0.0340
0.1408
65.81
(0.0172 0.0800
14.43
0.0360
0.1433
20.58
00.0551
0.1517
88.34
LWF
0.0209 0.0620
13.90
0.0439 0. 0.1091
23.67
0.0303 0. 0.1024
102.92
0.0399
0.0386
26.03
0.0469
0.0944
37.53
0.00763
0.0856
155.03
EWC
0.0443 0.0408
9.19
0.0467
0. 1384
14.95
0.0524 0. 1.51
68.37
0.0601 0.0295
14.24
0.0521 0. 1046
20.20
0.1005 0.0832 89.32
iCaRL
0.0607 0.0198
11.57
0.0602 0.0860
19.22
0.0699 0.0794 70.03
0.0558
0.0214
18.31
0.0917
0.0248
26.34
0.0945
0.0775 92.36
ER
0.0521 0.0332
11.63
0.0622 0.0783 19.07
0.0799 0.0617 69.06
0.0546
0.0276
18.49
0.0771
0.0386 26.65
0. 1026 0.0650
92.11
SSM
0.0552 0,0232
11.82
0.0308
0. 1203
82.99
0.0723
0.0912 145.27
0.0560
0.0235
18.27
0.0723
0.0641 26.09
0013
0.0568
92.15
OTGNet
0.0648 0,0236
35
0.0868
0.0518 49.42
0031 0.0459 709.49
URCL
0,0562
0,0303
11.57
0.0726
0.0649
20.13
0.0915
0,0431
70.32
0.0584
0.0216
20.13
0.0902
0.0284
27.58
0.1089
0.0566 93.43
LTF
0.0682 0.0195
25.05
0.0871
0.0474
36.16
0.1110 0.0165
72.94
0.0681
0.0096 51.80
0.1133
0.0081
58.56
[0.1253 0.0383
101 006
PodSt
Yep
Roddi
ferace
Aeaoy gre (99)
R22
344
Paraare
500
Figure 3: The average precision (AP) of LTF and the base- lines at each period based on TGAT.
Figure 4: The average forgetting (AF) of LTF and the base- lines at each period based on TGAT.
N's update is recorded, as it accumulates the most data and the most time-consuming.
tation to DyGFormer non-trivial. Naive approaches like Joint and Finetune face efficiency and effectiveness issues; Joint requires long training times, while Finetune performs worse than other baselines. Existing continual learning methods partially address TGCL,, achieving higher APs (lower AFs) than Finetune with significantly lower time costs than Joint. Regularization-basse methods are gener- ally weaker than selection based methods, highlighting the importance of data for updating old knowledge. However, performance gap remains compared to Joint. OTGNet improves subset selection by ensuring importance and di- versity, outperforming other baselines but suffering from high time complexity. LTF, with its theoretical guarantees, achieves better performance than OTGNet with lower time costs. On DyGForee, LTF outperforms OTGNet across all datasets. Full results with standard deviations are provided in Appendix I.
Implementation Details. The experiments are run on Nvidia A30 GPU. The implementation of backbone mod- els follow the code provided by DyGLib (Yu et al., 2023). TGAT contains two layers, and each layer has 4 attention heads. DyGFormer contains two layers, and each layer has 4 attention heads. The number of temporal neighbors is 10 and they are selected based on their freshness. We use single 2-layer perceptron to classify all the nodes of the period, which is called glass-incremental setting in continual learning. For all data sets, dropout rate is 0.4, learning rate is 0.00001, training epochs for each period is 100, and batch size is 600. Early stop is applied when validate AP does not improve for 20 epochs. For the selection based methods, 1000 events are selected for each class data at each period of Reddit and Amazon, and 500 for Yelp. Additionally, for LTF, the size of G is set to 500 for all data sets, and data partitioned to have around 10000 samples in each part. The reported results are averaged over 3 random seeds. For all data sets, each period is split into 80% training, 10% validation, and 10% test. The testing data are not seen in training and validation.
4.3. Ablation Study
Selection and Regularization Components. In Tab.3, we evaluate the impact of each LTF component. The key terms of our selection objective in (8) are error é(-I-) and distri- bution d which are represented by Err. and Dist. respectively. We also analyze the effect of adding Idst(-) to the training objective. The first two lines of Tab. 3 show that neither selection component alone is sufficient to find an effective subset. Yelp and Reddit rely more on distribution similarity, while Amazon benefits from lower error. Com-
4.2. Main Experiments
The overall comparison of LTF with other baselines is shown in Tab.2, with performance trends in Fig.3 and Fig. 4. OT- GNet modifies TGAT with a unique structure, making adap-
7

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A Selective Learning Method for Temporal Graph Continual Learning
Table 3: Ablation study on the selecting and learning components of LTF. The applied components are noted with Y. The
best and second best results are noted in Bold and Underline.
Component
TGAT
DyGFormer
Select [Leam
Yelp
Reddit
Amazon
Yelp
Reddit
Amazon
Em: Dist.
APT
ARL
Timel|
APt
ARL
Time]
API
AFL, Timel/
APT
AFL.
Timel|
APT
AFI.
Timel|
APt
AFI
Time.
0.0438
0.0439
0.0559
0.0736
0.1063 0.0185
0.00467
0.0309
0.0807 0.0407
10.1203
0,0456
0.0565
0.0322
11.79
0.0640
0.0695
19.28
0.0592
0.0684 67.77
0.0543
0.0266
18.51
0.0863
0.0350 27.12
0.1161
0.0465 90.18
Y
YYY
0.0654
0.0215
0.0866
0.0447
0.1004 0.0078
0.0618
0.0155
0.0939 0.0272
0.1231 0.0366
Y
Y
0.0682
0.0195
25.05
0.0871
0.0474
39.16
0.1110
0,0165
72.94
0.0681
0.0096
51 10080
0.1134
0.0081
58.56
0.1253
0.0383
101.06
Average Precision (AP)
CX
F12
0:12
0.18-
0:10-
0:10-
0.08
0.08
0.00
6000
0.01
0.31
0/34
19
1.
6.8
0:07
160
ton rare
750, 1860
500
yelo
amazon
Figure 5: Sensitivity on the key hyper parameters based on TGAT.
Table 4: Ablation study on the partition methods when selecting the subsets. The reported values are AP.
The impact of a. a balances error and distribution in selecting G in Eq. (8). Across values [0.25, 0.5, 1, 2. 4], Yelp and Reddit favor smaller weights, while Amazon prefers larger ones, aligning with the ablation study. Op- timal performance occurs around a 1 for all datasets, confirming the importance of both error and distribution in subset selection.
Partition
TGAT
DyGFormer
Method
Yelp
Reddit Amazon|
Yelp
Reddit Amazon
Kmeans
0.0598 0.0754 0.0929
0.05569 0.0912 0.1104
Hierarchical
0.0613 0.0792 0.0897
0.0621 0.0987 0.1091
Random
0.0682 0.0871 0.1110
0.0681 0.1134 0.1253
The impact of B. B controls the weight of (asr()) during subset learning. Despite favoring distribution in selection, Yelp and Reddit require low / for regularization, while Amazon needs higher value. This suggests that distri- bution is crucial for generalizing subset knowledge, with (-st()) enhancing its effect during learning.
bining both improves performance across all datasets and backbones. After selecting the most effective data, incorpo- rating (-) further enhances performance. The additional optimization time is less significant for denser graphs, es- pecially in Amazon, where new class data dominates. Full results are provided in Appendix J.
Size m of G As G is the major carrier of the old class knowledge, its size m is an important factor for the performance. Following the setup of the main experiment, the memory size is set to [250, 500, 750] for Yelp, and [500, 1000, 1500] for Reddit and Amazon. With the increase of memory size, the performance continuously improves, which is consistent with the intuition.
Data Partition Approaches. We reduce selection com- plexity by partitioning old-class data and prove that an opti- mal partition should preserve distribution. Tab. 4 examines different partition methods. Selecting subsets without parti- tioning exceeds GPU memory limits (24G on Nvidia A30), making performance untrackable. Among intuitive methods, random partitioning is more effective, as k-means Hier- archical clustering alter data distribution of each partition, conflicting with theorem requirements. The study on the impact of partition size is included in the Appendix K.
Size m' of G m' affects the quality of distribution approximation in Eq. 10. It can be seen Amazon requires larger size, while 500 is effective enough for Yelp and Reddit. This is because the distribution of Amazon is more complex and requires larger sample size to approx- imate.
In addition to the effectiveness study, we also evaluated the eeeeiency--efformmane tradeoff by varying m and m in Tab. 5. Results show that increasing either m or m consistently improves average precision (AP), at the cost of longer training time. This trend is expected due to the (mmm') complexity introduced by the regularization loss.
4.4. Sensitivity Analysis
In Fig. 5, we evaluate the sensitivity of our method over the essential hyper-parameters on TGAT. The results on DyGFormer are in Appendix L. The empirical analysises are listed as follows, which apply to both backbones:
8

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A Selective Learning Method for Temporal Graph Continual Learning
Notably, the full LTF model (with both subgraph selection and regularization) achieves the highest accuracy among all continual learning baselines, but also incurs additional runtime due to regularization. However, since our selection and regularization modules are decoupled, the regulariza- tion can be disabled when efficiency a priority. In such cases, the selection-only variant (No Reg. for m') still out- performs existing replay-based methods with comparable runtime, offering flexible trade-off between performance and efficiency.
More Complex Datasets To evaluate the scalability and robustness of our approach under more challenging condi- tions, construct two new large-scale benchmarks, Reddit- Large for more data updates and Reddit-Long for longer period durations:
Reddit-Large comprises 344,630 nodes, 4,962,297 edges, and spans 16 time periods, with novel classes introduced per period, totaling 32 classes.
Reddit-Long consists of 558,486 nodes, 5,323,230 edges, and spans time periods, each covering 180 days. each period, new classes are introduced, resulting in a total of 24 classes evenly added over time.
Table 5: Sensitivity analysis on the tradeoff by varying m and m' on Yelp dataset and DyG- Former backbone.
Setting
AP1
Time (s) +
We evaluate several baseline methods alongside our pro- posed LTF framework. As shown in Table 7, despite the increased difficulty in data updates and durations, LTF main- tains competitive performance in terms of both predictive accuracy and runtime, outperforming other continual Iearn- ing baselines such as Finetune and iCaRL when paired with the TGAT backbone.
Varying (size of G
250
0.0434
34.99
m 500
0.0681
54.30
m 750
0.0713
72.31
Varying ml
(size of Geim)
Best Baseline
0.0601
14.24
m' 0 (No Reg.)
0.0618
18.51
Table 7: Performance comparison across Reddit-Large and Reddit-Long datasets.
m' = 250
0.0624
36.70
m' 500
0.0681
54.30
nn' -50
0.0693
71.88
Reddit- Large
Reddit-
Method
AP
Time |
AP
Time $
Joint-TGAT
0.02042
107.73
0.0734
174.02
4.5. Case Studies
Finetune-
0.00237
6.37
0.0113
54.16
iCaRL-TGAT
0.00747
14.71
0.0354
60.03
In this sections, include experiments on special questions of our problem, including the necessity of TGNNs in solving the proposed problem, and how more complex datasets may affect the performance of LTF.
LTF-TGAT
0.01043
37.21
0.0499
110.35
5. Conclusion
The necessity of TGNNs. As node embeddings are the key media of selecting data and classifying nodes, here we study whether the embeddings along can support the whole training process, rather than using the topological structures. As shwon in Tab. 6, the MLP backbone, which only uses the node embeddings, is not able to achieve good performance on even under the joint setting. This shows that the topological structures are essential for the TGCL problem, and the TGNNs are necessary solve it.
This paper introduces a novel challenge of updating mod- els in temporal graphs with open-class dynamics, termed temporal graph continual learning (TGCL.. Unlike exist- ing problems, TGCL necessitates adapting to both emerg- ing new-class data and evolving old-class data, requiring model updates to be both effective and efficient. Our pro- posed Learning Towards the Future (LTF) method addresses TGCL by selectively learning from representative subsets of old classes, a strategy substantiated by thcoretical analysis. Experiments on real-life datasets show that LTF effectively mitigates forgetting with minimal additional cost.
Table 6: The comparison of AP across different backbone models and TGCL methods.
MLP
TGAT
DyGFormer
Joint
0.0184
0.1477
0.1500
Finetune
0.0160
0,0340
0,0551
LTF
0.0171
0.1110
0.1253

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A Selective Learning Method for Temporal Graph Continual Learning
Acknowledgements
2010. doi: 10. 10.10007/1109944099-555444 URL https:
Lei Chen's work partially supported by National Key Research and Development Program of China Grant No. 2023YFF0725100, National Science Foundation of China (NSFC) under Grant No. U22B2060, Guangdong- -ong Kong Technology Innovation Joint Funding Scheme Project No. 2024A0505040012, the Hong Kong RGC GRF Project 16213620, RIF Project R6020-19, AOE Project AoE/E- 603/18, theme-based project TRS T41-603/20R, CRF Project C2004-21G, Guangdong Province Science and Tech- nology Plan Project 202350505030011 I, Guangzhou munic- ipality big data intelligence key lab, 2023A0300012, Hong Kong ITC ITF grants MHX/078/21 and PRP/004/22FX, Zhujiang scholar program 2021JC02X170. Microsoft Re- search Asia Collaborative Research Grant, HKUST-Webbin joint research lab and 2023 HKUST Shenzhen-Home Kong Collaborative Innovation Institute Green Sustainability Spe- cial Fund, from Shui On Xintiandi and the InnoSpace GBA. Xun Jian's work is partially supported by the Fun- damental Research Funds for the Central Universities No. D5000240167.
Chen, X., Wang, J., and Xie, K. Trafficstream: streaming traffic flow forecasting framework based on graph neural networks and continual learning. In
Zhou, Z. (ed.), Proceedings of the Thirtieth International
Joint Conference Artificial Intelligence, IJCAI 2021, Virtual Event / Montreal, Canada, 19-27 August 2021, pp. 3620-3626. ijcai.org, 2021. doi: 10.24963/UCCII. 2021/498. URL https: wttpd/.oo...........60 ijcai (/cai.2021/44 2022/2222299
Cong, W., Zhang, S., Kang, J., Yuan, B., Wu, H., Zhou, X., Tong, H., and Mahdavi, M. Do we really need complicated model architectures for temporal net- works? In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net, 2023. URL https: // //openrevier ew wwt///fffee wett//dffid=ayyPcOOSSS
Cook, W., Cunningham, W., Pulleyblank, W., and Schrijver, A. Combinatorial Optimization. Wiley Series in Dis- crete Mathematics and Optimization. Wiley, 2011. ISBN 978111803139.. URL https: //books google. com. sg/ /btps/ooss iitokkksiddtttt1iWWMMg..
Impact Statement
This paper presents work whose goal advance the field of Machine Learning. There are many potential societal consequences of our work, none which feel must be specifically highlighted here.
de Barros, C. D. T., Mendonça, M. R. F,, Vieira, A. B., and Ziviani, A. A survey embedding dynamic graphs. ACM Comput. Surv., 55(2):10:1-10:37, 2023. doi: 10.1145/3483555 URL 1 1145/3483595.
References
URL httptttt//// /www://wwwww///.////w/.../ http://wwwwwwwlco....e www.yyelp...mmmaaseeeeeeeee
Di, S. and Chen, I. Message function search for knowl- edge graph embedding. In Ding, Y., Tang, J., Se- queda, J. F,, Aroyo, L., Castillo, C., and Houben, G. (eds.), Proceedings of the ACM Web Conference 2023, WWW 2023, Austin, TX, USA, 30 April 2023 4 May 2023, pp. 2633-2644. ACM, 2023. doi: 10. 1 05573543300.35585444 URL https:///oi.....
Alom, M. Z. Taha, M., Yakopcic, C., Westberg, S., Sidike, P. Nasrin, M. S., Hasan, M., Essen, B. C. V., Awwal, A. A. S., and Asari, V. K. A state-of-the-art survey on deep learning theory and architectures. Electronics, 2019, URL https: //api. semanticschott Caapso/oo//ooouppp/ 115606413.
10.
Baumgartner, J., Zannettou, S., Keegan, B., Squire, M., and Blackburn, J. The pushshift reddit dataset. In Choudhury, M. D., Chunara, R., Culotta, A., and Welles, B. F. (eds.), Proceedings of the Fourteenth International AAAI Conference on Web and Social Media, ICWSM 2020, Held Virtually, Original Venue: Atlanta, Georgia, USA, June 8-11, 2020, pp. 830-839. AAAI Press, 2020. URL httpt: //os www.o..saaa......o...a..a......a index phpp Cichp////waa
Di, S., Yao, Q., and Chen, Searching to sparsify tensor decomposition for n-ary relational data. In Proceedings of the Web Conference 2021, WWW '21, pp. 4043-4054, New York, NY, USA, 2021. Associa- tion for Computing Machinery. ISBN 9781450383127. doi: 10.1145/3442381 0341944442288334483... URL. ht. /doi. 11111/.1115/4444250 3449853.
Di, S., Zhang, Y., Yao. Q. Zhou, X., and Chen, L. Effi- cient latent-based scoring function search for n-ary re- lational knowledge bases. ACM Trans. Knowl. Discov. Data, 19(2):34:133.22 2025, doi: 10.1145/3707644 URL httpst::: /tt.///o...oo/////// https/////oo..rg/////// 37777477444
Ben-David, S., Blitzer, J., Crammer, K., Kulesza, A., Pereira, F., and Vaughan, J. W. theory of learning from different domains. Mach. Learn., 1911-1):15
10

---

A Selective Learning Method for Temporal Graph Continual Learning
Feng, K., Li, C., Zhang, X., and Zhou, J. Towards open temporal graph neural networks. In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenRe- view.net, 2023. URL https: /ttp::////ppeeeeeeeeeee net.
Jin, G., Liang, Y., Fang, Y., Shao, Z., Huang, J., Zhang, J., and Zheng. Y. Spatio-temporal graph neural networks for predictive learning in urban computing: A survey, IEEE Transactions on Knowledge and Data Engineering. 2023.
Kazemi, S. M., Goel, R., Jain, K., Kobyzev, I., Sethi, A., Forsyth, P., and Poupart, P. Representation learning for dynamic graphs: a survey. J. Mach. Learn. Res., 21(1),
French, R. M. and Chater, N. Using noise to com- pute error surfaces in connectionist networks: A novel means of reducing catastrophic forgetting. Neural
jan 2020. ISSN 1532-4435.
Comput,, 14(7):1755-176,, 2002. doi: 10.1162/ 089976602600287000 URL https:: org//. 1162/08997660260000
Kim, B., Koyejo, O., and Khanna, R. Examples not enough, learn to criticize! criticism for interpretability. In Lee, D. D., Sugiyama, M., von Luxburg, U., Guyon, I., and Garnett, R. (eds.), Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain, pp. 2280-2288. 2016.
Gao, S., Li, Y., Zhang, X., Shen, Y., Shao, Y., and Chen, L. SIMPLE: efficient temporal graph neural network train- ing at scale with dynamic data placement. Proc. ACM doi: 10.1145/3654977. https: /doi.dd..////// woo.o..r...oooooooooooooooo.oooo
Manag. Data, 2(3):174, 2024.
Kim, S., Yun, S., and Kang. Dygrain: An incre- mental learning framework for dynamic graphs. In Raedt, L. D. (ed.), Proceedings of the Thirty-Firs: International Joint Conference Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pp. 3157-3163. ijeai.org, 2022. doi: 10.29933/UCAL2222) 24963/4963331 438. URL https: htap:://doiii http/oiooorgooooo wwt.o//./....../11111 2022/438.
Garcia-Durán, A., Dumancic, S., and Niepert, M. Learn- ing sequence encoders for temporal knowledge graph completion. In Riloff, E.,, Chiang, D., Hockenmaier, J., and Tsujii, J. (eds.), Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, Brussels, Belgium, October 31 November 4, 2018, pp. 4816-4821. Association for Computational Linguis- tics, 2018. URL nttps://ach http://aaaaanttot.....oo. org/ 01861516/.
Kirkpatrick, J., Pascanu, R., Rabinowitz, N. C., Veness, J., Desjardins, G., Rusu, A. A., Milan, K., Quan, J., Ramalho, T., Gtrbssk-BBrwinnke
Gardner, M. W. and Dorling, S. Artificial neural networks (the multilayer perceptron) review of applications in the atmospheric sciences. Atmospheric environment, 32 (14-15):2627-2636, 1998.
A., Hassabis, D., Clopath, C., Kumaran, D., and Hadsell, R. Overcom- ing catastrophic forgetting neural networks. CoRR, abs/1612.00796, 2016.
Gretton, A., Borgwardt, K. M., Rasch, M. Schölkopf, B., and Smola, A. J. A kernel method for the In Schölkopf, B., Platt, J. C., and Hofmann, T. (eds.), Advances in Neural Information Processing Systems 19, Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems, Vancouver, British Columbia, Canada, December 4-7, 2006, pp. 513-520. MIT Press, 2006. URL bttps::/ppptt /ttp::///cccceiggs.. neurips dc wc/paper e9 @ html.
Kumar. S., Zhang, X., and Leskovec, J. Predicting dy- namic embedding trajectory in temporal interaction net- works. Teredesai, A., Kumar, V., Li, Y., Rosales, R., Terzi, E., and Karypis, G. (eds.), Proceedings of the 25th ACM SIGKDD International Conference Knowledge Discovery & Data Mining, KDD 2019, Anchorage, AK, USA, August 4-8, 2019, pp. 1269-1278. ACM, 2019. URL tnttpss://oo
two-sample-problen
doi: 10. 02211445/322550.33333838 org/10/ 01..0..115//2225500 3330895.
Li, H. and Chen, L. Early: Efficient and reliable graph neural network for dynamic graphs. Proc. ACM Manag. Data, 1(2), jun 2023. doi: 10. 1453358993088 URL https:
Hamilton, W. L., Ying, Z., and Leskovee, J. Inductive representation learning on large graphs. In Guyon, I., von Luxburg, U., Bengio, S., Wallach, H. M., Fergus, R., Vishwanathan, S. V. N., and Garnett, R. (eds.), Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA. pp. 1034-1034, 2017.
/ //doi. org /10 10.100001 45 /
Li, Y., Shen, Y., Chen, I.., and Yuan, M. Zebra: When tem- poral graph neural networks meet temporal personalized pagerank. Proc. VLDB Endow., 16(6):1332 1345, 2023. doi: 10.147783333110335831555 URL ht https:////// /www. vldb. wwd.borggeeee wttb.orggg/vllb///ooo 6 332-11- .dd..

---

A Selective Learning Method for Temporal Graph Continual Learning
Li, Z. and Hoiem, D. Learning without forgetting. JEEE Trans. Pattemn Anal. Mach. Intell., 40(12):2935-2947, 2018. doi: 10. 10.1199/PAMM220112773300 URL https: //doi. wwt//o...oooooooooo.oo/.......w/ 110...111//PAAAAA 2017 011772777388
set functions-i. Mathematical programming. 14:265- 294, 1978.
Nguyen, G. H., Lee, J. B., Rossi, R. A., Ahmed, N. K., Koh, E., and Kim, S. Continuous-time dynamic net- work embeddings. In Champin, P., Gandon, F,, Lal- mas, M., and Ipeirotis, P. G. (eds.), Companion of the The Web Conference 2018 on The Web Conference 2018, WWW 2018, Lyon France. April 23-27, 2018, pp. 969-976. ACM, 2018. doi: 10.1145/3184556 3191526. URL https: http:://ddi..ogg///. 1145/ 3184558. 019.523119526.
Li, Z., Jin, X., Li, W., Guan, S., Guo, J., Shen, H., Wang, Y., and Cheng, X. Temporal knowledge graph reason- ing based on evolutional representation learning. In Diaz, F. Shah, C., Suel, T., Castells, P., Jones, R., and Sakai, T. (eds.), SIGIR '21: The 44th International ACM SIGIR Conference on Research and Development in Information Retrieval, Virtual Event, Canada, July 11-15, 2021, pp. 408-417. ACM, 2021. doi: 10.1145/ 3402933..466263., URL https: //t///do///o /tt///i.oog//../////////// org/10. ////3444483333342663 3462963.
Ni, J., Li, J., and McAuley, J. Justifying recom- mendations using distantly-laelled reviews and fine- grained aspects. In Inui, K., Jiang, J., Ng, V., and Wan, X. (eds.), Proceedings the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference Natural Language Processing (EMNLP-UCCLL)) pp. 198-197, Hong Kong, China, November 2019. Association for Computational Linguistics. doi: 10. 10.186533v1/D19-1100 1018.
Liu, H., Yang, Y., and Wang, X. Overcoming catastrophic forgetting in graph neural networks. In Thitty-Fifth AAAI Conference Artificial Intelligence, AAAI 2021, Thirty-Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Fleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, pp. 8653-8661, AAAI Press, 2021, doi: 10.1609/ AAAL.335100.10499 URL https:://ssee.. http:::/doo..oooo 17049.
URL
Parisi, G. I., Kemker, R., Part, J. I.., Kanan, C.,, and Wermter, S. Continual lifelong learning with neural networks: A review. Neural Networks, 113:54-71, 2019. doi: 10. 1016L..FUUNET:201..0000000 URL https::/t/////cc /doi. org/10. j. neunet. 2019.01.0000 01.02..
Liu, H., Di, S., and Chen, L. Incremental tabular learning on heterogeneous feature space. Proc. ACM Manag. Data,
((1::18:1-18:1, 2023, doi: 10/1145/388868. URL https: //w.i//oii//// org/ 10. wtwp://...1111.1.1111 10111111518555
Rebuffi, S., Kolesnikov, A., Sperl, G., and Lampert, C. H. icarl: Incremental classifier and representation learn- ing. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA. July 21-26, 2017, pp. 5533-5542, IEEE Computer Society, 2017. doi: 10. 10.1100/CVPR.2207..55. URL https://doi org/ 10. 11w11109//vv...
Liu, H., Di, S., Li, H., Li, S., Chen, L., and Zhou, X. Effec- tive data selection and replay for unsupervised continual learning. In 40th IEEE International Conference Data Engineering, ICDE 2024, Utrecht, The Netherlands, May 13-16, 2024, pp. 1449-1463. IEEE, 2024. doi: URL httph::///// //op:::://d....// 10. 00.11099/CDDEE000442200400000000 2024. 00119.
Redko, I., Morvant, E., Habrard, A., Sebban, M., and Ben- nani, Y. A survey on domain adaptation theory. CoRR, abs/2004. 118299 2020a. URL URLhttps:/aarxiv.co abs 2tts/200..1183
org/10. 1109 11w.00111101///E11111100 CTt///IDEE611150
Masana, M., Liu, X., Twardowski, B., Menta, M., Bag- danov, A. D.. and van de Weijer, J.
learning: Survey and performance evaluation image classification. IEEE Trans. Pattern Anal. Mach. Intell., 45(5)35513-5533, 2023. doi: 10. 10.1102/7 3213473. URL https://dol org/ 1109/ TPAMI 2022. 3213473.
Redko, I., Morvant, E., Habrard, A., Sebban, M., and Ben- nani, Y. A survey on domain adaptation theory. CoRR, abs/2004.1 1189, 2020b. httpttss: /ttp:///xxvvvooooee abs Abs/2004.1188
Rossi, E., Chamberlain, B., Frasca, F. Eynard, D., Monti, F., and Bronstein, M. M. Temporal graph net- works for deep learning on dynamic graphs. CoRR, abs/2006. 10637, 2020. URL abs/2006.10631
Miao, H., Zhao, Y., Guo, C., Yang, B., Zheng, K., Huang, F. Xie, J., and Jensen. C. S. A unified replay-based continu- ous learning framework for spatio-temporal prediction on streaming data, 2024. URL abs/2404. 14999.
Schölkopf, B., Sung. K. K., Burges, C. J. C., Girosi, F. Niyogi. P., Poggio, T. A., and Vapnik, V. Comparing support vector machines with gaussian kernels to radial
Nemhauser, G. L., Wolsey, L. A., and Fisher, M. L. An analysis of approximations for maximizing submodular
12

---

A Selective Learning Method for Temporal Graph Continual Learning
basis function classifiers. IEEE Trans. Signal Process., 45(11))2758-276) 1997. doi: 10.1 109/9966500022 URL https: http:////oo..o.....eeeo//e//eeee www.://///....///////.//// 100111199770 /78. 650102.
Wang, Y., Chang, Y., Liu, Y., Leskovec, J., and Li, P. Inductive representation learning in temporal net- works via causal anonymous walks. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, http///ppeeeeeeeeeeeeeeeeeeeeeep htt.tttpss/oppeeeriiiieeeeee id-KYPZ4YsCP3
Shi, and Wang, H. A unified approach to domain in- cremental learning with memory: Theory and algorithm. CoRR, abs/2310. 0as/2310.11244, 12244, 2023. doi: 10.48550/ARXIV, 2310.12244. URL htttps://oi... /tte::/dooiioooo org.i.org//i wtt.oo////.1..0000 arxiv. 2310. 12244.
2021a. URL ht
net/forum? forum?
Wang, Z., Di, S., and Chen, L. Autogel: An automated graph neural network with explicit link information. In Ran- zato, M., Beygelzimer, A., Dauphin, N., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, 2021b.
Skarding, J., Gabrys, B., and Musial, K. Foundations and modeling of dynamic networks using dynamic graph neural networks: A survey. IEEE Access, 9: 79143-79168, 2021. doi: 10.1109/ACCESSS.2001. 3082932. URL http:s:/ddoiooogo/ ACCESS. 2021. 3082932.
December 6- 64, 2021, virtual, pp.
Wen, Z. and Fang, Y. TREND: temporal event and node dynamics for graph representation learning. In Lafor- est, F. Troncy, R., Simperl, E., Agarwal, D., Gio- nis, A., Herman, I., and Médini, L. (eds.), WWW '22: The ACM Web Conference 2022, Virtual Event, Lyon, France, April 25 29, 2022 pp. 1159-1169 ACM, 2022. doi: 10.1 10.114573485447:551222 / /oo.do.orrg. org. /10 10. 004445/445444444 3512111
Su, J., Zou, D., Zhang, Z. and Wu, C. Towards ro- bust graph incremental learning on evolving graphs In Proceedings of the 40th International Conference on Machine Learning, ICML'22.. JMLR.org, 2023a.
URL https:
Su. J., Zou, D., Zhang, Z., and Wu, C. Towards bust graph incremental learning on evolving graphs. In Krause, A., Brunskill, E., Cho, K., Engelhardt, B., Sabato, S., and Scarlett, J. (eds.), International Conference on Machine Learning, ICML. 2023, 23-29 July 2023, Honolulu, Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pp. 32728-32748. PMLR, 2023b. URL https: httpttp::/ppocceediggee mlr.
Wu, 7., Pan, S., Chen, F., Long. G., Zhang, C., and Yu, A comprehensive survey on graph neural networks, IEEE Trans. Neural Networks Learn Syst., 32(1):4-24, 2021, doi: 10.1109/NNNSS
URL https:// 2020 2979386.
press/v202/ wtt//au2aaaaaaa.. httm. html.
Xu, D., Ruan, C., Körpeoglu, E., Kumar, S., and Achan, K. Inductive representation learning on temporal graphs. In 8th International Conference on Learning Representations, ICLR 2020. Addis Ababa, Ethiopia, April 26-30, 2020. OpenReview.net, 2020. URL https: / //openreview.o net. www.moii-uuuaarar het.://orrummiddrrrelll////lt
Tian, Z., Zhang, D., and Dai, H. Continual learning on graphs: A survey. CoRR, abs/2402.06330, 2024. doi: 10. 10.4850/ARXXV.24000003.. URL https://doi. //doi. 06330.
org/10.
Yan, X., Song, T., Jiao, Y. He, J., Wang, J., Li, R., and Chu, W. Spatio-temporal hypergraph learning for next POI recommendation. In Chen, H., Duh, W. E., Huang, H., Kato, M. P., Mothe, J., and Poblete, B. (eds.). Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR 2023, Taipei, Taiwan, July 23-27, 2023, pp. 403-412, ACM, 2023, doi: 10.1145/ 1539618.3591770 URL https: http://ooo..o/g////// 1145 005553533618... 3591770.
Trivedi, R., Farajtabar, M., Biswal, P., and Zha, H. Dyrep: Learning representations over dynamic graphs. In International Conference on Learning Representations, 2019. URL
id-HyePrhRSKk.
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., and Polosukhin, I. Attention is all you need. In NeurlPS, pp. 5998-6008, 2017.
Wang, J., Zhu, W., Song, G., and Wang, L. Stream- ing graph neural networks with generative replay. In Zhang, A. and Rangwala, H. (eds.). KDD '22: The 28th
Yang, L., Adam, S., and Chatelain, C. Dynamic graph representation learning with neural networks: A survey, CoRR, abs/2304.05 055299 2023, doi: 10.48550/ARXIV. 2304.05729, URL https: doii www/10.....0. 48550/ arXiv 2304. 05729.
ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Washington, DC, USA, August 14
18, 2022, pp- 1878-1888. ACM, 2022. doi: 10.
(145/2534678.3359933 URL https: http//doooooo/o 10.1145/35344 3539336.
Yu, L., Sun, L., Du, B., and Lv, W. Towards better dynamic graph learning: New architecture and uni-
13

---

A Selective Learning Method for Temporal Graph Continual Learning
fied library. In Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., and Levine, S. (eds.), Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurlPS 2023, New Orleans, LA, USA, December 16, 2023, 2023.
Zhou, Z.,, Huang, Q. Wang, B., Hou, J., Yang, K., Liang, Y., and Wang, Y. Coms2t: A complementary spatiotem- poral learning system for data-adaptive model evolution. CoRR, abs/2403.011788, 2024. doi: 10.48550/ARXIV. 2403.01738. URL https:: htt.:/oo.oogooooooooooo/oo 48550/
arXiv. 2exiv..403..o 2403. 01738.
Zhang, X., Song, D., and Tao, D. Sparsified subgraph mem- ory for continual graph representation learning. 2022 IEEE International Conference on Data Mining (ICDM), pp. 1335- 1340, 2022. doi: 10.1 N..100/CDMM4844.2022 00177.
Zhou, F. and Cao, C. Overcoming catastrophic for- getting graph neural networks with experience re- play. In Thirty-Fifth AAAI Conference Artificial Intelligence, AAAI 2021, Thirty-Thin Conference Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, pp. 47 4714-4722, AAAI Press, 2021. doi: 01w.1/009AAAAL135555.. //doi. ////oi.org/100 1699 aaai. v35.5.16512.2222.
URL https:
Zhou, H., Zheng, D., Nisa, I., loannidis, V., Song, X., and Karypis, G. Tgl: a general framework for temporal gnn training billion-scale graphs. Proc. VLDB Endow,, 15(8):1572 15800, apr 2022. ISSN 2150-8097. doi: 10. 14778835299337352292422 URL https: org/ 3529342.
Zhou, L., Yang, Y., Ren, X., Wu, F., and Zhuang, Y. Dy- namic network embedding by modeling triadic closure process. In Mcllraith. S. A. and Weinberger, K. Q. (eds.), Proceedings of the Thirty-Secone AAAI Conference on Artificial Intelligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and the 8th AAAI Symposium Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2-7, 2018, pp. 571-578. AAAI Press, 2018. doi: 10.1609/AAALV3211. 11257. URL https: tettss://don /ttp:://ool..ooo www.o.ooo.....ooooooooooooooooee aaai. 732i1.11257,
Zhou, Z., Huang, Q. Yang, K., Wang, K. Wang. X., Zhang, Y., Liang, Y., and Wang,
Maintaining the status quo: Capturing invariant relations for OOD spatiotemporal learning. In Singh. A. K., Sun, Y., Akoglu, L., Gunopulos, D., Yan, X., Kumar, R., Oz- can, F., and Ye, J. (eds.), Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2023, Long Beach, CA. USA, August 6010, 2023, pp. 3603-3614. ACM, 2023. doi: 10. 1145/3580305 3599441 URL attps:/ doi.orgg 10.114553580300 3599422..
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A Selective Learning Method for Temporal Graph Continual Learning
A. Important Notations
In contrast, we focus on the continual learning problem that tackles the challenge of selecting new data subsets effi- ciently fine-tune the past model, ensuring its effectiveness and preventing forgetting at the new period.
The important notations used in the paper are summarized in Tab. 8 below. The relationships among GN-1, Gr and NN" are illustrated in Fig.
Some recent continual learning works have also applied the domain adaptation theory to their research, which are UDIL (Shi & Wang, 2023) and SSRM (Su et al., 2023a). However, both of them differ largely from ours. UDIL focuses automatically finding the most suitable hyper- parameters for the losses to best balance the model stability and plasticity during learning new datasets. SSRM directly minimizes the distribution discrepancy between old and new data. Our work takes an orthogonal direction from them by selecting the most representative subset from the old class data. Besides, our TGCL problem differs from the previous continual learning settings in the considering the evolving old-class data.
Table 8: Important Notations
Notation
Meaning
G~9 g
Temporal graph that follows the distribution g
V,E,T,
Nodes V. events E, time period ' and class set Y of
(Me, (4,))
An event E that links nodes ue I/ E V E
The node and feature z at time
Ty. Tw
The latest period N and past period n < N
h he H
Model h from hypothesis space 76
(())0()
Classification error on distribution and finite set
dwam(()
Discrepancy between two distributions
dx)M(()
Estimated Maximum Mean Discrepancy
C. Proofs of Theorems
We first introduce and prove the important Lemma 3 that is originally proposed in (Ben-David et al., 2010):
@x-1
Ga
Yau
Lemma C.1. For any hypothesis h, h' E H and any two different data distributions D, D',
Yy
Ty-1
TN
(e (')) - -(h, (/ DD)) - duAn((,D))
(12)
2
Figure 6: An illustration on the relationships among GN-1+ Goddd and Gnew Gold and G DO NOT overlap over nodes, but DO share the events connecting old and new class nodes.
where e(h, h' (D) == EeED(h(x) + W(x)] is the expected prediction differences of h and h' on D, and
dHAH(D, 2 sup |PreeD(h(z) + k'(x)] h.
B. Additional Discussion on Related Works
Praed (M()) # N (x)]
Besides the related works in TGL discussed in the main content, we provide additional discussions other TGL variants in this section. Firstly, the efficiency issue in TGL is addressed by redesigning the training framework (Zhou et al., 2022; Gao et al., 2024), sampling the representative nodes (Li & Chen, 2023), and integrating the random walk with temporal graph neural networks (Li al., 2023).
is the discrepancy between the two distributions.
Proof. By definition, we have
dHan(D,D)) = sup [PaED(h(a) # 1((x)]
ANEEN
-PEED (h(x) # h'(z)]l
2 sup (e(h,h''p) - e(h, K'DD')
Beyond simple temporal graphs, research has also explored temporal hyper-graphs (Yan et al., 2023), spatio-temporal graphs (Jin et al., 2023), and temporal knowledge graphs (Li et al., 2021; Garefa-Duráa et al., 2018). 8). However, these methods typically assume a fixed set of node or entity labels and still encounter the forgetting issue when adapting to new classes, making them foundational but limited backbones for studying the TGCL problem.
ANEE
- > 2 (D) c(h,N/'')
(13)
Based on Lemma C. Theorem 3.1 can be prove as follows:
Theorem 3.1. Let gold 9gub be the distributions of Gold and Grab, Let h H be a function in the hypothesis space H and hegh be the function optimized on Goub, The classifi- cation error on gold then has the following upper bound:
There are also works addressing the OOD generalization problem in temporal graphs (Zhou et al., 2023; 2024), which address a fundamentally different problem from ours. These works aim to improve model performance on test datasets that have distributions differing from the training datasets.
min chll S min NEH
c(h sub (ggg
1 + ddAn S.g...g.g.. ggaa)) 2 + chh, Jigu (gab).
9
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A Selective Learning Method for Temporal Graph Continual Learning
Algorithm 1 Pseudo Code
tain the errors and embeddings of all nodes. When selecting G from each partition, it takes O(m/W) for loss esti- mation and O(rm/) / for distribution estimation, which finally gives O(m/W (//WWor +rm/W2 For GN", we only need O 2 for distribution estimation. Because different partitions can be processed parallel, the overall selection complexity is O( + m)/W + r(m + m'))
1: Input: GN,, GN" -N-1
2: G < Uh. GN t Q
3: Partition G into parts with sizes p, resulting in W
TIGA// 1/11 parts N,w) / w=1
W 4: for GN E {GN, Iw=1 do
5: Select Grub size m/W by optimizing Eq.(8)
Learning: When learning G the complexity for error (m) and that for distribution alignment is (mm''). When learning G the complexity is O(GNN")) (1). So the overall learning complexity is O(mm' + |G
6: Select Guim of size m/W by optimizing (10)
7: GNO + GN U Geub G <- GN U N
8: end for
9: hN = arg arg mingen ((hGG + E(h|Gg")
(G 1h
G. Data Set Details
10: return hn
Yelp Yelp a business review dataset that contains a large amount of reviews on different businesses. When buiding Yelp data set, regard the businesses as the nodes to construct the temporal graph. The business categories are used as the class labels. From 2015 to 2019, we take each of the five years as one period of temporal graph. The reviews from the same user within a month create events among the bussinesses they are evaluating. For each period, we select the largest three categories the new classes and include corresponding businesses into the temporal graphs from then on. We extract word embeddings on the reviews of each business with GloVe-2004 and average these 200- dimension embeddings to get the initial node features.
Proof. From the triangle inequality in (Ben-David et al., 2010) and Lemma C.I,
<(hlgh I Ji,
c(h = "eh,,iNng + e(hiv (9N c(hh, (gob))
te(h,h (
S Le(hN + (e Tgga (9 elh, high Righiig (g
S <c(hivoog + 1 + c(h, (ggb).
dn ( 2
Reddit Reddit is online forum dataset that contains large amount of posts and comments different top- ics. When buiding Reddit data set, we regard the posts as the nodes to construct the temporal graph, following the paradigm of (Hamilton et al., 2017). The post topics are used as the class labels. We take January 1st 2017 as the start date and construct the temporal graphs of 20 days period. The comments from the same user within 5 days create events among the posts they are commenting one. There are three periods of temporal graphs created. For each period, we select the topics that have generally even number of posts as the new classes. We extract word embed- dings on the comments of each post with GloVe-200k and average these 200-dimension embeddings get the initial node features.
As this inequality applies for all h H and G% the minimum of the left side is always less than the minimum of the right side.
D. Pesudo Code of LTF
The pseudo code of the Learning Towards the Future (LTF) method is presented in Algorithm below.
E. Definition of RBF Kernel
Definition (Radial Basis Function Kernel (Schölkopf et al., 1997)). Consider the radial basis function kernel IK with entries k,, k( xy)) exp(->/lıı; zyy1) evaluated on a sample set X with non-duplicated points i.e. Dy + V,, xy E X. The off-diagonal kernel entries ka,, i A.. monotonically decrease with respect increasing ?.
Amazon Amazon is a product review dataset that contains large amount of reviews on different products. When buid- ing Amazon data set, we regard the products as the nodes to construct the temporal graph. The product categories are used as the class labels. Starting from January 1st 2016, we take every 24 days as one period of temporal graph. The re- views from the same user within 5 days create events among the products they are reviewing. There are three periods of temporal graphs created. For each period, we select the
F. Complexity Analysis
Note that the sizes of Gold, G.vbb and G as and m',
and Goldd is partitioned into W groups, our time complexity is analyzed as follows:
Selection: For each partition, we first need O(r/W) to ob-
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A Selective Learning Method for Temporal Graph Continual Learning
Table 9: The performance of different methods on the TGAT backbone. The reported values are the mean and standard deviation of AP, AF and Time.
TGAT
Method
Yelp
Reddit
Amazon AF]
AP
AF.
Time
AP1
AFL
Time
APR
Time_
Joint
0.0810=0.0033
58.37=0.60
0.1378#0.0031
50,50=0.50
0.1477=0.0014
128.71=1.40
Finctune
0.0141#0.0045
0.0843+0.0000
9.11=0.10
0.0312#0.0051
0.1550+0.0000
14.93=0.14
0.03-40=0.02)
1.1408200000
65.81=2.60
LWF
0.0209+0.0050
0.0620=000028
13.90=0.22
0.0439#0.0057
00.091
23.67=0.44
0.0303++0.0097
0.102400.0105
102.9243.92
FWC
0.0443+0.0142 0.0408+0.01 78
9.1920.15
0.0467+0.0063
0.1384+0.01 36
14.95=0.14
0.0524+0.0292
0.1152=0.0363
68.37+3.69
iCaRL
0.0607+0.0035
0.0198+0.006
11.57=0.14
0.0602+0.0076
0.0860=0.02777
19.22=0.21
0.0699=0.0127
0.0794=0.0145
70.03=0,48
ER
0.0521+0.0098 0.0332+0.0108
11.63#0.15
0.0622+0.0146
0.0783+0.0157
19.07=0.13
0.0799=0.01448
0.0617=0.0293
69.06#3.11
SSM
0.0552+0.0070 0.0232+0.01 10
11.8240.21
0.0308#0.0068
0.1203=0.0143
82.99=2.23
0.0723=0.0164
0.0912=0.0077 0076
145.27+3.78
OTGNet*
0.0648+0.0120 0.0236*0.0133 39
316.15=17.13
0.0868+0.0071
0.0518+0.0013
49.42=5.55
0.1031+0.00259
0.0459=0.0232
709.49=42.81
URCL
0.0562+0.009 0091 0.0303++0.008
11.57+0.13
0.0726+0.0140
0.0649#0.00 71
20.13+0.55
0.09155+0.006
0,0431#0.0138
70.32+2.1 19
LIF
0.0682#0.0108 0.0195++.0130 25.05=00.37
0.0871+0.0052 0.0474+0.0097 39.16+0.62
0.1110=0.0011 0.0165#0.0041
72.94=2.17
Table 10: The performance of different methods the DyGFormer backbone. The reported values are the mean and
standard deviation of AP, AF and Time.
DyGFormer
Method
Yelp
Reddit
Amazon
API
AFL
Time
APT
AFL
Time
AP1
AFL
Time!
Joint
0.0813:00.000
95.11=2.04
0. 0.1256=0.0140
70.64:1.22
0.1500+0.0054
177.3844.27
Finctune
0.0172=0.000 0000000000000000
0.0800=0.0000
14.43+0.40
0.0360=0.0008
0.1433+0.0000
20.58=0.39
0.0551#0.0154
0.1517=0.0258
88.34=0.85
LWF
0.0399#0.0000 0079 0.038620.000
26.03=0.37
0.0469=0.0107
0.0944+0.0112
37.53+0.90
0.0763+0.0207
0.0856=0.0189
155.03+2.31
EWC
0.0601=0.0074 0074 0.0295=0.011
14.24=0.17
0.0521=0.0190
0.1046:0.0198
20.20=0.14
0.1005:0.0105
0.0832=0.0135
89.32=1.15
iCaRL
0.0558#0.00 0095 0.0214=0.0155 0156
18.31=0.29
0.0917=0.0095
0.0248+0.0125
26.34=0.24
0.0945#0.0255
0.0775#0.03%
92.36=1.03
0.0546:0. 0066 0.0276:00. 0094
18.4940.88
0.0771=0.0172
0.038610.0170 26.65=0.30
0.1026:0.0029
0.0650=0.0057
92.11=0.97
SSM
0.0560#0.0009 0.0235:0000044
18.27+0.29
0.0723=0.02466
0.0641#0..3300
26.09=0.559
0.1063+0.0197
0.0568=0.0170
12.15=1.44
OTGNNet*
URCL
0.058440.0064 0.0216+0.0000 0083
20. 1 3
0.0902=0.01 0.0284+0.0182
17.58
0.1089+0.0110 0.0566+0.01
93.43+2.45
LTF
0.0661 0.0096=0.0077
51. 01.800
0.113920.0089 0.0081:0.0120
58.56#1..1 1.17
0.1253#0.0139
0.0383=0.0121
201.06+3.55 3.50
Awnag Teeken (48)
Forgtingg (4F)
J005
221
L77
CMC
UPQ
Figure 7: The average precision (AP) of LTF and the base- lines at each period, based on DyGFormer.
Figure 8: The average forgetting (AF) of LTF and the base- lines at each period, based on DyGFormer.
3 products that have generally even number of reviews as the new classes. We extract word embeddings on the re- views of each product with Vlo and average these 200-dimensio embeddings to get the initial node features.
search as well, whose names and values are: Weight of regularization loss (LwF, EWC): 10.1, 0.5, 1, 2]; Size of exemplar set (iCaRL, ER, SSM, OTGNet): 1000 for Red- dit and Amazon and 500 for Yelp. which are the same as ours for fair comparison; Number of maintained neighbors (SSM): [S, 10, 20]; The other hyperparameters of OTGNet (Feng et al., 2023) are searched in the same range as re- ported in the original paper. The searching is performed on hyperopt package with 10 iterations.
H. Selection on the Hyper-parameters
The hyperparameters related to the backbone models are selected within the reported range of DyGFormer (Yu et al., 2023) based on the experience. We do not conduct further tuning on the backbone performance. The hyperparameters of our method are selected by grid search. The searching ranges and results of important hyper-parameters are re- ported in Sec. 4.4, with standard deviation reported as well. The hyperparameters of the baselines are selected by grid
I. Full results on Main Experimetns
In this section, we present the results, including standard deviations, for Tab. 2 in See. 4.2. The detailed results for TGAT are shown in Tab. 9, and those for DyGFormer are
17

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A Selective Learning Method for Temporal Graph Continual Learning
provided in Tab. 10. The results demonstrate that LTF not only performs well across all three datasets but also has relatively low standard deviation, indicating the stability of the method. The standard deviation for Finetune goes to smaller than digits for most datasets because its forgetting issue is sever and at the end of increments the model stably forgets most of the knowledge.
Table II: Comparison of Different Partition Sizes.
Size
10000
5000
2500
k-Means
0.1104
0.1555
0.0994
Hierarchical
0.1091
0.1063
0.1002
Random
0.1253
0.1147
0.1027
Besides, the per period performances of all methods based on DyGFormer are shown in Fig. 7 and Fig. 8. Because OTGNet is not compatible to DyGFormer, we exclude it from the presentation. The results show that LTF consis- tently outperforms the other methods in terms of AP and AF across all periods.
robustness of LTF on addressing TGCL.
M. Future Directions
While this work focuses on node classification, similar challenges in integrating newly introduced, differently- distributed data are prevalent in other temporal graph tasks, such as link prediction (Di et al., 2021; Wang et al., 2021b; Di & Chen, 2023; Di et al., 2025) with new user profiles or content categories in social networks. By establishing robust approach for handling open-class dynamics, our framework lays essential groundwork for future research. Additionally, selecting data under various scenarios (Liu et al., 2024) has also been trending recently, it is worth exploring how to extend our method to these scenarios.
J. Full Results on Ablation Study
The results of the ablation study in Tab. with the standard deviation are shown in Tab. 12 and Tab. 13. The results demonstrate that the proposed LTF consistently outperforms the baselines across all datasets and metrics. The standard deviation of LTF is relatively low, indicating the stability of the method.
K. Additional Study on Partition Number
In order for random partitioning to preserve the original embedding distribution, the size of each partition should be larger than a threshold. Statistically, based on the Dvoret- Aky-Kiefer-Wolfowitzz (DKW) inequality, each partition should have 1152 samples to guarantee that the randomly sampled subset can approximate the population distribution with 95% confidence and 0.04 approximation error. Com- pared with the size of our dataset (60k samples for each old class within period in Amazon), this threshold is signifi- cantly smaller and can be easily satisfied. our experiment, we randomly partition the dataset into parts containing samples each, which sufficient to represent the original embedding distribution.
We further study the impact of different partition sizes based on DyGFormer backbone and Amazon datasets, whose AP results are presented in Tab. 11. Performance decreases as the number of partitions increases, primarily because fewer samples in each partition result in higher selection errors. On the other hand, random constantly outperforms other clustering methods, which is consistent with our anal- ysis that keeping the original distribution is important for effective selection.
L. Sensitivity Analysis on DyGFormer
The additional sensitivity analysis results on DyGFormer is shown in Fig. 9. The same conclusion as in Sec. 4.4 can be drown from this set of results. This further validates the
18

---

A Selective Learning Method for Temporal Graph Continual Learning
Table 12: Ablation study on the selecting and learning components of LTF based on TGAT with standard deviations. The
applied components are noted with Y. The best and second best results are noted in Bold and Underline.
Component
TGAT
Select
Learn
Yelp
Reddit
Amazon
Err.
Dist.
(ase(.)
AP-
AF
Timel
APT
AF
Time
APT
AF
Time!
0.0438+0.0117 0.0439+0.0136
0.0579=0.0060 0.073620.0064
0.1063#0.0016 0.0185+0.0033
0.0565#0.0093
0.0322+0.0101
11.79=1088
0.0640=0.0055
0.0695=0.0073
19.28=0.77
0.0592=0.0019
0068440.0041
67.77+2.05
Y
0.0654+0.0104
0.0215+0.01
0.0866=000044
0.0447=0.0067
0.1004+0.0023
0.0078+0.0032
Y
Y
Y
0,0682+0.0108
0.0195+0.0130
25 0540.37
0.0871=0,0052 0.0474=0.0097
39, 16.0.2
0.1110=0.0018
0.0165#0.0041
72.9442.17
Table 13: Ablation study on the selecting and learning components of LTF based on DyGFormer with standard deviations.
The applied components noted with Y. The best and second best results noted in Bold and Underline.
Component
DyGFormer
Sclect
Learn
Yclp
Roddit
Amazon
Emr. Dist. (.
AP1
AFL
Time!
AP
AFL
Time!
APT
AFL
Time.
Y
0.0467=0.007 0.0309H0.0079
0.0807#0.008+
0.0407=0.0220
0.1203#0.0172 0.0456:2.0131
0.0543+0.00 0056 0.026620.0076
18.51=1.13
0.0863+0.00R
0.0350=0 02211
27.12+2.02
0.1161=0.0167 0.0465#0.0126
90.18+2.52
0.0618#0 0060 0.0155#0.0082
0.0939+0.000
0.0272:4000119
0.1231#0.0108 0.0366+0.0117
0.0661 0.0796 51.000..55
0.1134+0.0089 0.0001=0.0120
58.56+1117
0.1253#0.0139 0.0383#0.0121
101.06+3.50
Average Precision (AP)
0.50
0.14
0:32
0.12
0.10
0.20
0.10
0.6-
0.38
010
016
000
0.0
0.1
608
250/500
1500
reddit
Figure 9: Sensitivity the key hyper-parameten based on DyGFormer.
19


Reviews:
[{"review_id": "P19X4ObEwD", "reviewer": "Reviewer_CBnU", "summary": "This paper identifies the challenge of effectively and efficiently updating newly introduced classed in temporal graph node classification. To address this, the authors propose a novel optimization objective that dynamically integrates the loss distribution of both old and new categories over time. Additionally, by substituting the old distribution with subgraphs, the problem is transformed into a subset selection task, which is efficiently optimized through greedy, partitioning, and approximation techniques.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate the reviewer's efforts in reviewing our paper. We thank the reviewer for recognizing our novel problem, well-developed method, and rigorous experiments. Our responses to the valuable feedback are presented below:\n\n**W1**: Given various efficiency improvements in the proposed method, the trade-off to effectiveness is still unclear.\n\n**Reply**: \nOur approximation techniques **greedy selection algorithm**, **partitioning strategy**, and **regularization set simplification** are crucial for making the training and selection phases computationally feasible. Without these approximations, it would be practically impossible to run the experiments under limited resources.\n\n- **Greedy selection** avoids exhaustive searches which have factorial time complexity, making them intractable for real-world graphs.\n- **Partitioning**, as analyzed in the paper, significantly reduces memory requirements. Without it, subset selection could demand over 100 GB of RAM, which is prohibitive in most settings.\n- During training, we **simplify the regularization dataset** from $G^{old}_N$ (full old-class data) to a subset $G^{sim}_N$ $(|G^{old}_N| >> |G^{sim}_N|)$, greatly reducing the regularization loss complexity. This simplification is necessary to prevent GPU memory overflow and failed experiments.\n\nDespite these constraints, we conducted **further analysis to empirically characterize the trade-off between effectiveness and computational efficiency** by varying the sizes of selected subsets $m$ (for $G_N^{sub}$) and $m'$ (for $G_N^{sim}$). The backbone model used is DyGFormer, and the dataset is Yelp.\n\n**Effect of Varying $m$:** $G_N^{sub}$ is the major carrier of old-class knowledge, a larger $m$ will improve its knowledge quality yet takes more training time. Below experiments validate our claim, where increasing $m$ improves average precision (AP) and linearly increasing the training time.\n\n|$m$|AP|Time(s)|\n|-|-|-|\n|250|0.0434|34.99|\n|500|0.0681|54.30|\n|750|0.713|72.31|\n\n**Effect of Varying $ m' $:** \n$G_N^{sim}$ approximates the distribution of $G_N^{old}$, which helps generalize the learnt knowledge from $G_N^{sub}$. A larger $m'$ leads to a better distribution approximation at the cost of more training time. \nExperiments support our claim on $m'$: larger values improve AP at the cost of longer training time, again approximately linear due to the $ O(mm') $ complexity of the regularization loss.\n\n|$m'$|AP|Time(s)|\n|-|-|-|\n|Best baseline|0.0601|14.24|\n|0 (No Regularization)|0.0618|18.51|\n|250|0.0624|36.70|\n|500|0.0681|54.30|\n|750|0.0693|71.88|\n\nIt is also worth noting that although our method achieves the best results among all baselines, this comes with an additional time cost due to the regularization term. However, since our **selection and regularization modules are independent**, users with stricter efficiency requirements can disable the regularization component. Our selection-only setup still achieves **state-of-the-art performance** while maintaining comparable time costs to other replay-based baselines.\n\n---\n**Q1**: Why use MSE instead of Cross-entropy for classification loss?\n\n**Reply**: We employ MSE loss due to its strong theoretical alignment with domain adaptation theory. The key quantity in this framework, i.e., the $\\mathcal{H} \\Delta \\mathcal{H}$ divergence measures disagreement between hypotheses[1]. MSE naturally captures this disagreement by penalizing squared geometric distances between model outputs. In contrast, cross-entropy focuses on prediction confidence (log-probabilities), making it less sensitive to inter-hypothesis disagreements.\nAdditionally, MSE’s bounded gradients lead to more stable optimization and better adherence to generalization bounds in domain adaptation.\n\n---\n**Q2**: What are the limitations of the proposed method?\n\n**Reply**: Our method is limited in two points: \n\n1. **Task Scope**: Our current work focuses on the node classification task within temporal graphs. While this is an important and under-explored area, it is equally critical to address the continual learning problem on other key temporal graph tasks such as link prediction, which may pose different challenges to our approach. We discussed this limitation in Appendix M.\n\n2. **Class Dynamics Assumption**: We assume that each node is associated with a single, static class label throughout its lifetime. However, node labels can also change over time in real life. For example, in epidemic transmission networks, an individual may transition between different states (e.g., infected to recovered), which our current formulation does not accommodate. Capturing such class-switching behavior is also important.\n\n---\n**Q3**: More repeated experiments are needed.\n\n**Reply**: We agree with the reviewer that more repeated experiments are needed to address concerns about the influence of randomness in the results. We will conduct additional experiments and report the results in the final version of the paper.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "Yes.", "experimental_designs_or_analyses": "Yes. All experimental frameworks were rigorously validated through specific statistical method, and cross-verified against benchmark datasets, with detailed robustness checks documented in Evaluation Section and Supplementary Materials.", "relation_to_broader_scientific_literature": "This study make a meaningful contribution to the existing body of knowledge in the related literature.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n1. The paper identifies the issue of label updates in temporal graphs.\n2. The proposed TGCL method is relatively efficient and effective.\n\nWeaknesses:\n1. The combination of partitioning, greedy, and approximation techniques improves efficiency in subset selection and optimization. However, it is unclear whether eliminating these approximations would lead to a significant accuracy improvement.", "other_comments_or_suggestions": "N/A.", "questions_for_authors": "Please refer to the Other Strengths And Weaknesses section for detailed inquiries.\n\n1. Why is the classification loss in line 207 implemented using MSE instead of cross-entropy?\n2. The paper does not discuss the limitations of the proposed method.\n3. Further repeated experiments need to be conducted, addressing concerns about the influence of randomness in the results.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RYQ69dfYeL", "reviewer": "Reviewer_j9Pq", "summary": "In this paper, the authors propose the novel problem of temporal graph continual learning where new classes can emerge in a temporal graph. To solve this task, the authors proposed the learning towards the future framework and derive theoretical insight into the upper bound of error due to graph subsampling. The authors tested this approach with two backbone models across three real world datasets and demonstrated improved performance when compared to existing continual learning approaches.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer's efforts in reviewing our paper. We thank the reviewer for recognizing our novel learning paradigm and the good correspondence between theory and experiments. Our responses to the valuable feedback are presented below:\n\n**Q1**: Experiments on datasets with a longer duration of periods and larger scales are expected to reflect real-world scenarios.\n\n**Reply**:\nWe appreciate your suggestion on applying a more realistic dataset with longer periods and larger scales. \nOur datasets are mined and constructed by ourselves, and we have prepared a larger dataset **Reddit-Long**, which has the duration of **180 days per period, 558,486 nodes, 5,323,230 edges, and 24 classes evenly added over 4 periods**. This is larger than Yelp (our largest dataset) and has a longer duration than Reddit and Amazon. Due to the larger scale of data, we will report the comparison results later in this rebuttal period.", "claims_and_evidence": "Yes, the claims in the paper is backed by empirical evidence and theoretical insights.", "methods_and_evaluation_criteria": "The methodology is sounds and the evaluation is correct.", "theoretical_claims": "yes, there are theoretical claims in the paper and proof was included in Appendix C. The proof look correct to me.", "experimental_designs_or_analyses": "The experimental designs look correct to me, more dataset detailed were provided in Appendix G.", "relation_to_broader_scientific_literature": "This work is related to two areas in graph learning: temporal graph learning and graph continual learning. In this work, the authors combined the ideas from both literature to propose this new setting of temporal graph continual learning which has its challenges different from the two fields. To my knowledge this is a first work in this area and might open up future directions for research.", "essential_references_not_discussed": "The essential references are discussed.", "other_strengths_and_weaknesses": "Overall, I think the paper proposes a novel learning paradigm for temporal graph and focuses on the classification task which is under-explored in the existing literature. The theoretical claims of the paper is also supported by proof and the experimental results. One potential weakness is that usually for newer classes to emerge, it would naturally occur over a long period of time, two out of three datasets are rather short in timespan which is less than a month thus it would be interesting to see results on datasets with longer duration and at larger scale similar to Yelp dataset or larger.", "other_comments_or_suggestions": "None", "questions_for_authors": "For the datasets, did you process and collect them yourself for the labels or did you find it from prior work? If you have mined them, is it possible to collect a larger set to test over longer period of time?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "OmF4PBksty", "reviewer": "Reviewer_bJ1k", "summary": "The paper defines Temporal Graph Continual Learning (TGCL) as the problem of node classification on dynamically evolving graphs, where new unseen classes emerge, and old-class data distributions shift over time. Existing methods struggle with catastrophic forgetting when updating models in such settings, as they either retrain on all past data, which is computationally expensive, or focus only on new data, leading to the loss of old knowledge. To address this, the authors propose a selective learning framework that retains only a subset of old-class data, ensuring efficient updates while maintaining knowledge of past classes.\n\nThe proposed method derives a theoretical upper bound on the classification error of a model trained on a subset of old-class data instead of the full dataset. This bound is then used to guide two key components: a subset selection strategy and a model optimization approach. The subset selection process aims ensure that the selected data maintains a similar distribution to the full old-class dataset. The optimization derives a computable learning objective from the theoretical upper bound. Since directly optimizing these objectives is computationally intractable, the authors propose approximations and greedy algorithms to ensure scalability.\n\nExperiments are conducted on three real-world datasets (Yelp, Amazon, and Reddit), which are transformed into time periods where each period introduces a new set of classes that do not overlap with previous ones. Two state-of-the-art temporal graph learning models are used as backbones, and the proposed selective learning method is applied to optimize their performance. The approach is tested against multiple continual learning baselines, including both regularization-based and replay-based methods.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate the reviewer's efforts in reviewing our paper. We thank the reviewer for recognizing our novelty, sound theory, and good presentation. Our responses to the comments on motivation and more comprehensive experiments are presented below:\n\n**Q1**: Clarify the motivation, especially on why using graphs to handle the proposed tasks.\n\n**Reply**:\nWe appreciate the suggestions on enhancing our motivation.\nTo directly validate that TGCL method is necessary to address our task, we add a naive MLP backbone using only word embeddings as input (with parameter size matched to TGAT), which is also a common practice in GNN research.\n\nWe compare MLP with TGNN backbones (TGAT & DyGFormer) on Amazon using Joint (full-data training), Finetune (new-class-only training), and LTF (ours). The AP results show that the MLP backbone performs **significantly worse than TGNNs (TGAT or DyGFormer)**, demonstrating the necessity of graph-based models for the task.\n\n||MLP|TGAT|DyGFormer|\n|-|-|-|-|\n|Joint|0.0184|0.1477|0.1500|\n|Finetune|0.0160|0.0340|0.0551|\n|LTF (ours)|0.0171|0.1110|0.1253|\n\nWhile our datasets are used as proof-of-concept benchmarks, they are carefully chosen to reflect key challenges in real-world settings. To further reinforce our motivation, we present two additional application scenarios where TGCL is highly applicable:\n\n1. **Attack Identification in Cybersecurity**\n   - **Nodes**: Network entities (e.g., IP addresses, devices)  \n   - **Edges**: Communication or interaction logs  \n   - **Classes**: Cyberattack types (e.g., phishing, ransomware, DDoS)  \n   - **Description**: Attack patterns evolve continuously, with new attack types emerging and existing ones adapting to evade detection. Modeling interactions over time is crucial to understanding and classifying these behaviors.\n\n2. **Illegal Behavior Detection in Social Networks**\n   - **Nodes**: Users  \n   - **Edges**: Historical interactions (e.g., messaging, reposting)  \n   - **Classes**: Misconduct types (e.g., hate speech, fraud, misinformation)  \n   - **Description**: As user behavior evolves and social norms shift, new categories of harmful behavior emerge, often in subtle and adaptive ways. Capturing both user history and temporal interactions is essential for effective detection.\n\n**Q2**: Evaluation over longer sequences of incremental updates\n\n**Reply**:\nWe thank the reviewer for highlighting the importance of learning on a longer-sequence dataset. To evaluate the scalability of our approach in settings with significantly more incremental updates and larger scale, we constructed a new dataset, **Reddit-Large**, consisting of **344,630 nodes, 4,962,297 edges, and 16 time periods**, with **2 new classes introduced per period (32 classes in total)**.\nReddit-Large represents a substantial expansion over our previous largest dataset, Yelp, featuring **3× more time periods, 2× more classes, 20× more nodes, and 2× more events**.\n\nOur results below demonstrate that our method remains robust and effective as the task complexity increases.\n\n||AP|Time|\n|---|---|---|\n|Joint-TGAT|0.02042|107.73|\n|Finetune-TGAT|0.00237|6.37|\n|iCaRL-TGAT|0.00747|14.71|\n|LTF-TGAT (ours)|0.01043|37.21|\n\n---\n**Q3**: More analysis on efficiency versus accuracy trade-off\n\n**Reply**: Please kindly refer to our reply to Reviewer **CBnU W1**.\n\n---\n**Q4**: Additional experiments on other backbone models and temporal graph tasks\n\n**Reply**:\nWe thank the reviewer's suggestions on further validating our method. Our responses are presented below:\n\n1. **More Backbones**:  \n   To further assess the generality of our method, we incorporate **GraphMixer** [1]—an MLP-based model designed for temporal graphs—as an additional backbone. The experimental results show that our method continues to outperform existing baselines even with this new architecture, further supporting the robustness and versatility of our approach.\n\n||Yelp||Amazon||\n|---|---|---|---|---|\n||AP|Time|AP|Time|\n|iCaRL-GraphMixer|0.0627|3.17|0.0817|23.17|\n|LTF-GraphMixer (ours)|0.0714|7.25|0.1241|42.99|\n\n[1] ICLR 2023 Do We Really Need Complicated Model Architectures For Temporal Networks?\n\n2. **Other Temporal Graph Tasks**:  \n   \n   The Temporal Graph Benchmark raises link prediction and node property prediction tasks. These settings also exhibit continual learning characteristics—e.g., in **user–item interaction networks**, new items appear over time, requiring the model to connect users to new items while remembering their old preferences.\n\n   While these tasks can often be framed as **binary classification between node pairs over time**, adapting our framework to such settings would require task-specific modifications. Given that **all prior graph continual learning studies** have centered on classification tasks, we believe extending our method to prediction tasks is an important but **non-trivial direction** that goes beyond the current paper’s scope. We have discussed this as part of future work in **Appendix M**.", "claims_and_evidence": "The key paper claim is that the proposed methodology is both efficient and effective. \n\nThe results demonstrate an enhancement in terms of precision and forgetting compared to the current state-of-the-art. However, from an efficiency perspective, the results are contradictory and difficult to interpret. \n\nThe only three datasets and the only two backbone models used in the experiments make it even more difficult to assess the claims, in particular the one about efficiency. \n\nThe low number of periods, and the low number of new classes per period makes it difficult to assess how the proposed methodology actually retains old-class knowledge. This, in addition to the not-clear efficiency gains, makes the impact of the method hardly supported by the provided evidence (at least when considering reasonably complex validation scenarios).\n\n#POST REBUTTAL:\nI have appreciated the additional experiments and clarifications as regards a non-graph CL baseline and on longer experiences.\nHowever, the response was unconvincing as regards the reasons for deferring a more compelling empirical analysis on temporal benchmarks to future work. Also, the discussion with other reviewers highlighted a somewhat misleading focus of the paper, as the proposed approach relies of maintaining the full graph and uses a definition of forgetting which does not align with standard CL practice. These argument, together with the lack of further debate with the Authors, led me to maintain my score.", "methods_and_evaluation_criteria": "The proposed methods are well-grounded in the principles of continual learning and align with the problem of handling evolving node classes in dynamic graphs. \n\nThe evaluation criteria, are consistent with standard practices in continual learning research.\n\nThe validation setting chosen for assessing the soundness of the methodology (i.e., classifying business categories on Amazon and Yelp, and subreddit topics on Reddit) does not appear to be a compelling example of a problem requiring effective structural propagation over a temporal graph. The Authors do not explain why a temporal graph continual learning approach is needed to solve the problem at hand.\n\nAll things considered, I would expect to see a baseline using a non-graph-based class-incremental-learning method leveraging the average word embedding (which, in this work, serves as the initial feature vector for the nodes) to check whether the methodological structure proposed in the paper is necessary for the problem at hand.\n\nExperiments cover short-term continual learning (only a few time periods), while performance over long time periods remains unexplored while effective long medium-long range propagation is key in temporal graph processing.", "theoretical_claims": "Theorem 3.1: The proof is seemingly correct.", "experimental_designs_or_analyses": "The experimental design, apart from the critiques to the chosen problem, is acceptable.\n \nA sensitivity analysis of the various hyperparameters is present, as well as the ablation study. \n\nA more detailed analysis on the computational time is missing. From the given tables, it is impossible to assess which percentage of precision is possible to give up in order to obtain a time improvement. For example, in the Yelp dataset with DyGFormer, a ~13% increase in average precision costs ~260% more time. \n\nAdditionally, the hyperparameters m and m’ are not put in relation to the training time.", "relation_to_broader_scientific_literature": "Prior approaches in graph continual learning tackle concept drift and memory trade-offs through meta-learning, task replay, and Bayesian updates, aiming to balance stability and plasticity in evolving interactions. Similarly, this paper applies subset selection and distribution alignment to maintain relevant old-class knowledge in temporal graph learning, much like how a replay memory or structural distillation can be used to retain past knowledge. This paper generalizes the idea to evolving graph structures addressing the challenge of evolving node classes in temporal graph learning and continual learning, where existing methods assume a fixed class set or static old-class data. Traditional approaches rely on parameter regularization or random replay to mitigate forgetting, and are not specific to dynamic graphs. This work introduces a selective learning framework that optimizes subset selection using a theoretical classification error bound, ensuring representative old-class retention while adapting to new classes. By aligning subset distributions with the full dataset, it tries to improve knowledge retention more effectively than heuristic replay methods.", "essential_references_not_discussed": "There are no evident omissions.", "other_strengths_and_weaknesses": "The paper is generally well written and fluent in reading.", "other_comments_or_suggestions": "None at this stage (in addition to the requests for clarification below).", "questions_for_authors": "1)\tMotivation for using graphs:\nCould the Authors clarify why a temporal graph continual learning approach is specifically necessary for the selected tasks (classifying business categories on Amazon and Yelp, and subreddit topics on Reddit)? In particular, how would the approach compare against a standard class-incremental (non-graph-based) continual learning method applied directly to the average word embeddings?\n\n2)\tLong-term continual learning:\nHave the Authors evaluated or considered how your proposed approach performs over longer sequences of incremental updates (e.g., significantly more time periods)? Can the Authors discuss if the approach can maintain effectiveness and efficiency as the number of classes grows substantially, and provide (empirical) evidence or reasoning to support this?\n\n3)\tEfficiency versus accuracy trade-off:\nCould the Authors provide a detailed analysis or insights into how performance (average precision and forgetting) scales with computational time? Specifically, what are the trade-offs in terms of hyperparameter settings (such as subset sizes m and m') when balancing computational efficiency against precision gains?\n\n4)\tAdditional experiments\nIt is hard to reach general conclusions given the small number of datasets and backbone models considered (and the relative simplicity of the former). The submission would substantially gain strength if the Authors can provide additional experiments from standard temporal tasks, such as those in the Temporal Graph Benchmark, and possibly extending the backbone models considered.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KfS4UeIAmh", "reviewer": "Reviewer_hR2z", "summary": "This paper introduces Temporal Graph Continual Learning (TGCL), a novel problem setting that tackles the challenge of updating models on dynamic temporal graphs, where both new-class data emerge and old-class data evolve over time. To address this, the authors propose Learning Towards the Future (LTF), a selective learning framework that strategically replaces the old-class data with subsets. The authors derive an upper bound on classification error and formulate an optimization objective that minimizes error while preserving the original data distribution. Furthermore, a regularization loss is introduced to align the embedding distributions of the selected subsets with the full dataset.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate the reviewer's efforts in reviewing our paper. We thank the reviewer for recognizing our comprehensive coverage of the problem and method, detailed analysis and experiments, and clear presentation. Our responses to the comments on motivation, problem setting, and experiment are presented below:\n\n### Problem Setting and Motivation\n\n**W1**: More concrete TGCL application examples are preferred to enhance the motivation.\n\n**Reply**:\nPlease kindly refer to our reply to Reviewer **bJ1k Q1**.\n\n---\n**W2,Q1,Q2**: The problem setting is not clear enough, like the availability of old class data in new periods and whether nodes change their labels.\n\n**Reply**:\nWe thank the reviewer for highlighting the need for a clearer explanation of our problem setting. Below, we provide the necessary clarification:\n\nIn our setting, consider a temporal graph $G_{N-1}$ at period $N-1$, whose node classes form the set $Y_{old}$. As the graph evolves into $G_N$ at the next period, new labels $Y_{new}$ emerge and bring in new nodes. \nAt the same time, **nodes from $Y_{old}$ also appear in $G_N$**, but their data distribution is different from $G_{N-1}$ due to temporal and structural changes.\nAdditionally, we assume that **each node retains a fixed class label across time**.\nIn our paper, we illustrated this setting in **Fig. 6 at Appendix A**.\n\nThis reflects real-world dynamics such as **user behavior graphs**, where new users join over time and existing users remain active. Here, the node classes may correspond to behavior types, with **new types emerging** while **old ones continue to recur**. And user behavior is often **persistent**, with users maintaining their behavior types over time.\n\n---\n**O1**: Why is subset selection necessary for model training?\n\n**Reply**:\nThe subset selection and learning is necessary in three key points:\n\n1. **Efficiency**: Replaying all previously seen data is computationally expensive. Subset selection significantly reduces the training time while maintaining competitive performance, as also evidenced in our comparison against Joint training in Tab. 2.\n\n2. **Effectiveness**: Among various continual learning strategies, subset replay has consistently shown strong performance in preserving prior knowledge. Our experiments in Tab. 2 support this finding, where subset-based methods (Last 6 lines) are generally better than non-subset methods (LwF and EWC).\n\n3. **Generality**: Our selection method is model-agnostic and can be easily applied to a wide range of temporal graph learning architectures, making it flexible and future-proof.\n\n---\n### Experiment\n\n**O2**: Comparison with more SOTA continual learning baselines.\n\n**Reply**: We add a SOTA graph continual learning method TACO [1], which learns a coarsened old-class graph at a new period to achieve efficient update. We perform better because their coarsening procedure overly simplifies the evolving old-class distribution at a new period.\n\n||Yelp||Amazon||\n|---|---|---|---|---|\n||AP|Time|AP|Time|\n|TACO-DyGFormer|0.0591|18.59|0.1030|91.67|\n|LTF-DyGFormer (ours)|0.0681|51.80|0.1253|101.06|\n\n[1] NIPS 2024 - A TOPOLOGY-AWARE GRAPH COARSENING FRAMEWORK FOR CONTINUAL GRAPH LEARNING\n\n---\n**Experiment Deaign and Analysis**: The data segmentation approach requires clarification and experiments on a smaller training data ratio are suggested.\n\n**Reply**:\nOur segmentation strategy follows a **standard time-based approach** widely adopted in the graph continual learning literature. Importantly, we address a common limitation in prior work by explicitly modeling the **reappearance of old-class nodes in later periods**, which better reflects real-world temporal dynamics where class distributions evolve over time.\n\nTo validate that **training data ratio does not affect our conclusion**, we conduct experiments on a lower train ratio of **train/val/test = 60%/20%/20%**. Results show that fewer training data reduces the overall model performance, yet our method still achieves the best performance over other baselines.\n\n||Yelp||\n|---|---|---|\n||AP|Time|AP|Time|\n|Joint-DyGFormer|0.0808|57.42|\n|TACO-DyGFormer|0.0387|11.49|\n|LTF-DyGFormer (ours)|0.0756|24.80|\n\n---\n**Q3**: Why are the AP values below 0.15 in Tab. 2?\n\n**Reply**:\nThe AP values in Table 2 are below 0.15 primarily due to the **challenging nature of our experimental setting**:\n\n1. **Class Imbalance**: The node classes in our datasets are imbalanced (from $10^3$ to $10^5$ in Yelp), which naturally suppresses the achievable AP scores.\n\n2. **Class-Incremental Evaluation**: We adopt a **single unified classifier** to classify all nodes across time, rather than training separate classifiers per class. This setting, known as **class-incremental learning** in the continual learning literature, is more realistic for deployment but significantly more challenging.\n\nDespite the lower absolute values, this setting provides a fair and rigorous evaluation in realistic, imbalanced scenarios.", "claims_and_evidence": "The problem setting is not clear enough.", "methods_and_evaluation_criteria": "While the TGCL problem is well-motivated, the paper does not clearly define a concrete real-world scenario where this setting would be directly applicable. Additionally, how the datasets are partitioned for experiments raises concerns about the realism.", "theoretical_claims": "No.", "experimental_designs_or_analyses": "As mentioned earlier, the segmentation approach may not accurately reflect how new and old-class data evolve in real-world temporal graphs, which could compromise the validity of the evaluation. Additionally, the decision to allocate 80% of the data for training seems quite high, potentially leading to an unrealistically favorable learning scenario.", "relation_to_broader_scientific_literature": "1. LTF extends TGL by introducing the TGCL problem, which accounts for new and evolving classes in temporal graphs, making it more applicable to real-world dynamic environments. \n2. The existing methods assume old-class data distributions remain static, which does not hold for evolving temporal graphs. LTF improves upon GCL by selecting representative subsets that adapt to evolving distributions.", "essential_references_not_discussed": "NA", "other_strengths_and_weaknesses": "**Strengths**\n\n1. The paper provides comprehensive coverage of the proposed problem and method, offering detailed theoretical analysis and experimental validation.\n2. The presentation is well-structured, with clear explanations supported by informative figures and tables, making it easy to follow the key ideas and experimental results.\n\n**Weaknesses**\n\n1. The problem setting lacks a clear real-world application, making it difficult to assess its practical significance. A more concrete connection to real-world scenarios would strengthen the motivation.\n2. While the methodology is well-developed, the problem definition remains somewhat abstract.", "other_comments_or_suggestions": "1. The necessity of using a selected subset for model training should be further clarified.\n2. The paper should include comparisons with sota continual learning baselines to better assess the effectiveness of the proposed method.", "questions_for_authors": "1. Please provide more details on the problem setting. Is old data still available in the new period?\n2. Regarding the dataset, do nodes from previous periods retain their original class labels, or do they evolve over time?\n3. In Table 2, the AP values across all datasets are below 15%. What does this indicate about the model’s performance?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper introduces a novel problem setting called Temporal Graph Continual Learning and proposes a selective learning framework with solid theoretical grounding and empirical validation. While one reviewer strongly supports acceptance, others raise concerns about the clarity of the problem formulation, the necessity of the continual learning framing, and the validity of forgetting metrics. Overall, the paper presents promising ideas but needs better clarification on motivation and alignment with continual learning standards. I will give weak accept for this work.
Decision: Accept (poster)