Towards Continuous Reuse of Graph Models via Holistic Memory Diversification
Authors: Ziyue Qiao
Junren Xiao
Qingqiang Sun
Meng Xiao
Xiao Luo
Hui Xiong
Venue: ICLR 2025 Poster (2025)
Keywords: Incremental learning
Model Reuse
Transfer learning
Primary area: learning on graphs and other geometries & topologies

Abstract: This paper addresses the challenge of incremental learning in growing graphs with increasingly complex tasks. The goal is to continuously train a graph model to handle new tasks while retaining proficiency in previous tasks via memory replay. Existing methods usually overlook the importance of memory diversity, limiting in selecting high-quality memory from previous tasks and remembering broad previous knowledge within the scarce memory on graphs. To address that, we introduce a novel holistic Diversified Memory Selection and Generation (DMSG) framework for incremental learning in graphs, which first introduces a buffer selection strategy that considers both intra-class and inter-class diversities, employing an efficient greedy algorithm for sampling representative training nodes from graphs into memory buffers after learning each new task. Then, to adequately rememorize the knowledge preserved in the memory buffer when learning new tasks, a diversified memory generation replay method is introduced. This method utilizes a variational layer to generate the distribution of buffer node embeddings and sample synthesized ones for replaying. Furthermore, an adversarial variational embedding learning method and a reconstruction-based decoder are proposed to maintain the integrity and consolidate the generalization of the synthesized node embeddings, respectively. Extensive experimental results on publicly accessible datasets demonstrate the superiority of DMSG over state-of-the-art methods.

Published as a conference paper at ICLR 2025
TOWARDS CONTINUOUS REUSE OF GRAPH MODELS VIA HOLISTIC MEMORY DIVERSIFICATION
Ziyue Qiao' Junren Xiao? Qingqiang Sun Meng Xiao Xiao Luo
Hui Xiong
1 School of Computing and Information Technology. Great Bay University
2 AI Thrust, The Hong Kong University of Science and Technology (Guangzhou)
School of Engineering, Great Bay University
*Computer Network Information Center, Chinese Academy of Sciences Department of Computer Science, University of California, Los Angeles (z i joe, junrenxiao1 38, sunisfis geffiigting @ma i com shaow cnic. com, xiaoluočcs, ucla edu, xionghui (a @ust. hk
ABSTRACT
This paper addresses the challenge of incremental learning in growing graphs with increasingly complex tasks. The goal is to continuously train a graph model to handle new tasks while retaining proficiency on previous tasks via memory replay. Existing methods usually overlook the importance of memory diversity, limiting in selecting high-quality memory from previous tasks and remember- ing broad previous knowledge within the scarce memory on graphs. To address that, introduce a novel holistic Diversified Memory Selection and Generation (DMSG) framework for incremental learning in graphs, which first introduces a buffer selection strategy that considers both intra-class and inter-class diversities, employing an efficient greedy algorithm for sampling representative training nodes from graphs into memory buffers after learning each new task. Then, to adequately rememorize the knowledge preserved in the memory buffer when learning new tasks, a diversified memory generation replay method is introduced. This method utilizes a variational layer to generate the distribution of buffer node embeddings and sample synthesized ones for replaying. Furthermore, an adversarial variational embedding learning method and a reconstruction-basee decoder are proposed to maintain the integrity and consolidate the generalization the synthesized node embeddings, respectively. Extensive experimental results publicly accessible datasets demonstrate the superiority of DMSG over sfate-of-the-an art methods. The code and data can be found in https: : / / thub. com jome/j /o1////08811 7/DMSG
INTRODUCTION
Graphs, owing to their flexible relational data structures, are widely employed for many applications in various domains, including social networks (Jiang et al. 2016 Qiao et al., (021)) recommendation
systems (Wu et al. 2022), and bioinformaties (Zhang al. 2021 ( Huang et al. 2025). With the increasing prevalence of graph data, graph-based models like Graph Neural Networks (GNNs) have gained significant attention due to their ability to capture complex structural relationships and those dynamic variants also demonstrate remarkable inductive capabilities growing graph data (Ju et al.) 2024 Pareja et al., 2020 Manessi et al. 2020). However, as the growing graph in Figure I ssoows, added, the associated learning tasks can become increasingly complex. For
when new nodes example, the graph models on academic networks might need to predict the topics of papers in highly dynamic research areas where the topic rapidly emerges, and those on recommendation networks might need to continually adapt to new user preferences. Recent research on the inductive capability and adaptability of GNNs often remains limited a specific task (Hamilton al. 2017 Han et al.) 2021; Qiao et al. 2023) and cannot be readily applied to incremental tasks. Moreover, it is often inefficient to train an entirely new model from scratch every time a new learning task introduced. In recent years, model reuse via incremental learning (Tan et al. 2022; Kim et al. 2022), also known
"Corresponding Authors

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continual learning or lifelong learning, has led to exploring more economically viable pipelines, enabling the model to adaptively learn new tasks while maintaining the knowledge from old tasks.
The main challenge of incremental learning on graphs lies in mitigating catastrophic forgetting. As the graph model learns from a sequence of tasks on evolving graphs, it tends to forget the information learned from previous tasks when acquiring knowledge from new tasks. One prevalent approach to address this issue is the memory replay method, a human-like method that typically maintains a memory buffer store the knowledge gained from previous tasks. When learning new task, the model not only focuses on the current information but also retrieves and re-learns from memory, preventing the model from forgetting what was learned previously as it takes on new tasks. Nevertheless, this method has two major focuses to address on graphs: (1) How to select knowledge from old graphs to form more high-quality memory buffers? Existing methods usually select representative training samples as knowledge. However, determining which nodes in the graph are more representative is difficult and usually a time-consuming process. Furthermore, most methods (Zhang et al. 2022c Wang et al. 2022) select samples all into one same buffer without considering the inter-class differences between various previous tasks, which may degrade the quality of preserved knowledge. (2) How to effectively replay the limited buffer knowledge to enhance the model's memorization of previous tasks? Due to constraints related to memory and training expenses, the samples chosen for the buffer are often limited. Many methods (Zhou & Cao 2021 1 SSu & Wu (023) concentrate on memory selection, neglecting to broaden the boundaries of memory within the buffer, resulting in discount replay. Finding an effective way to replay knowledge from these limited nodes is critical to incremental learning in graphs.
In this paper, we propose novel Diversified Memory Selection and Generation (DMSG) method on incremental learning in growing graphs, devised to tackle the above challenges. we consider that selecting diversified memory helps in Comprehensive Knowledge Reten- tion: we apply a heuristic diversified memory selection strategy that takes into account both intra-class and inter-class diversities between nodes. By employing an efficient greedy al- gorithm, we selectively sample representative training nodes from the growing graph, placing them into memory buffers after completing each new learning task. Furthermore, we explore the memory diversification in memory reply for En- hanced Knowledge Memorization: we intro- duce generative memory replay method, which first leverages a variational layer to produce the distribution of buffer node embeddings, from which synthesized samples are drawn for replaying. We incorporate an adversarial variational em- bedding learning technique and reconstruction-Bee based decoder. These designed to preserve the integrity and strengthen the generalization of the synthesized node embeddings on the label space, ensuring the essential knowledge is carried over accurately and effectively.
2 closses
dlasses
classes
Incremantal learning
Incramentoi learning
CDUN
Cheiifee
GNN
Choetier
GNN
Chestifer
B,
8
Graph Modal
Growing graph
Figure I: growing graphs, where nodes with distinct labels are shaded in various colors. The number of classes expands as the graph grows, causing increasingly complex classification tasks.
An example of incremental learning in
The main contributions can be summarized as follows: (1) We propose a novel and effective memory buffer selection strategy that considers both the intra-class and inter-class diversities to select repre- sentative nodes into buffers. (2) We propose a novel memory replay generation method on graphs to generate diversified and high-quality nodes from the limited real nodes in buffers, exploring the essential knowledge and enhancing the effectiveness of replaying. various incremental learning benchmark graphs demonstrate the superiority of the proposed DMSG over state-of of-the-art methods.
(3) Extensive experiments on
2 PROBLEM FORMULATION
In this section, we present the formulation for the incremental learning problem in growing graphs. Generally, growing graph is represented by sequential of m snapshots: G (G', G2 Go.... Gm)
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Memory Selection
Variational layer di
Broadening Diversity Memory Replaying
Buffers
N 1efl.?? xf)
diversity
GNN
Classifier
RRP
seleting intra diversity
G²
Growing
Parameter sharing
New maining nodes
Gradient reversal layer
Reconstructed
GNN
Classifier
H D(. ha)
c
MISE
CGSS
Newly parameters
Consolidating Generalization
6²
Training on New Task
Maintaining Integrity
Figure The framework DMSG. In this instance, the graph model underwent training on a 2-class node classification task on G Two new classes of nodes are added to G' to form G?. Certain nodes of the previous two classes are first selected into buffers. Then, the model is further trained on two new classes of nodes and buffers to perform incremental learning.
and each snapshot corresponds to the inception of a new task, represented as T= Tm) Each graph G is evolved from the previous graph G .... G C G¹, ", 2.... m.. and each learning task T is more complex than the previous task T,-1. This paper specifies the learning tasks to classification tasks and followss the class-incremental learning setting, i.e., the number of classes increases alongside graph growth, increasing the task complexity. continuously learn model f(0) on T. For the t-th step, the task T incorporates training node set Ve with previously unseen labels (i.e., novel classes), where each vertex v; E V has the label ys y", and y {yí ..., yx is the set of novel classes. The task T is to train the f()) u/ > - )od to ensure it can infer well on the current novel classes while preventing catastrophic forgetting of the inference ability on previous classes.
this scenario, we aim
Jointly Incremental Learning. This is straightforward solution for the problem, which collects training nodes of all classes of previous tasks train f0) in each step. This treats the accumulated tasks (T) T ..., T'} whole new task and retrains the model from scratch. However, this solution inefficient because it leads to redundant training of labeled nodes and creates computational challenges due the growing graph size.
Memory Replay for Incremental Learning. This method offers a more practical solution. Instead of gathering all previous training nodes, it maintains buffers B that store a small yet representative subset training nodes for each class of previous tasks. The objectives can be formulated as follows:
= Σ (f((n))).)) NEEV*
Σ Σ ((f(vu:0),gk)
J=1 NNEB,
Memory replay on previous tasks
where L is the loss function the accumulated all class set, K =U'' is the number of previous classes, the a balance second term ensures the representative training nodes from previous classes included in the current training phase, efficiently mitigating the risk of catastrophic forgetting of previous classes. Also, the size of B, is much smaller than the total node number of class j. Thus, the number of training nodes required is significantly lower than joint training, leading to substantial increase in efficiency.
and By is the buffer for the j-th class. The
METHODOLOGGY
Without loss generality, we choose the plain GCN model followed by a classifier head as the backbone of (0), which encodes each node in graphs into embedding and probability Pi- As shown in Figure 2 initially, this model was trained on the graph G1. When the f-th task introducing classes arrives. we first extend new parameters (highlighted the yellow segment) into the last layer of the classifier, ensuring the output probabilities encompass the previous and newly introduced classes. To facilitate continual training of f()), we leverage the memory replay
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framework, which incorporates both the Heuristic Diversified Memory Selection (Section 3.1 and the Diversified Memory Generation Replay (Section (.2).
Motivation. Consider p( as the true data distribution of graphs from prior t tasks, and ((B<t) as the data distribution encapsulated within the memory replay buffers B sampled from G't-- To understand the efficacy of the buffer diversity in incremental learning scenarios, we engage in theoretical examination to indicate that a high diversity within ensures that the empirical loss (()
over B closely mirrors the total expected loss (()) over p(Grt).
Theorem 1. Let the loss function C(0,a) x)) be B-Lipschitz continuous in respect the input Under this condition, the discrepancy between the expected loss under the true data distribution 2( and that under the replay buffer distribution g(B<1) is bounded follows:
w)] (Bon((B..) [C(0, e)]l S 3- W(P(G
(2)
where ((p, q) denotes the Wasserstein distance between distributions and defined by: W(p. infzer(na)) B(n )' and [p, (p.q) q) represents the set of all possible joint distri- butions (couplings) that can be formed between p and q.
Assume that both (G2z) and (B<r) follow Gaussian distributions with means μp, My and covariance matrices Ep. Eg respectively. Thus, the squared 2-Wasserstein distance between two Gaussian distributions is given by:
(3) Since the Σ measure the distribution diversity and B<g is the subset of G<t and is typically less diverse (detailedly analyzed in Appendix [A.I). Assuming the sampling strategy is unbiased upon means, the Be more diversified, Mn + Epp. leading the Wasserstein distance decreases. Based on Theorem [ the discrepancy between the expected loss under true distribution and the buffer distribution becomes less, making the optimization on the buffer more closely approximate the optimization on all previous graph data.
W2 Ep),N( E,)) = Il, p,ll² Tr(E, E2, E,, -,,
3.1 HBURISTIC DIVERSIFIED MEMORY SELECTION
Based on the above motivations. For memory selection, to ensure that the selected nodes are adequately diverse with respect to the classification task, consider the two perspectives: P1: the nodes within the same buffer should exhibit sufficient diversity to faithfully represent disparate regions of their corresponding areas. Also, P2: the inter-class distance between nodes residing in distinct buffers should be maximized to facilitate the model to delineate clear classification boundaries. Thus, we introduce the concepts of antra-iiversity and inter-diversity for the buffers. Our goal is to select the buffer B, corresponding to the i-th class of training nodes based on the following criteria:
K
B: = arg max A(C B.CC, VEB.
Mv,B,).
K
J=
intra-diveriity
inter-diversity
where C, is set of i-th class of training nodes, A(u, B,, GO) denotes the distance measure between node and B, in the current graph G which we define the L2-norm distance on probabilities between node and its closest node in B, While the measure can be defined as any topological distance, such as the shortest path, we use probability distance because offers finer resolution, reduced noise towards tasks, and computational efficiency. The first term quantifies the intra- ditra-iiversity within the buffer B,, reflecting the variations among its own nodes, while the second term quantifies the inter-diversity between B3 and other buffers, illustrating the differences between the nodes of B; and those belonging to other buffers.
Heuristic Greedy Solution. However, achieving this objective for selecting different classes of buffers is an NP-hard problem. This kind of problem is usually addressed using heuristic meth- ods (Hochbaum 1996). Thus, we introduce a greedy algorithm to sample representative training nodes when new tasks are introduced. Specifically, suppose y = -KK+ C is the training nodes of t-th task and C, is the training set corresponding to the i-th novel class. We have previously selected buffers {B, K in previous tasks, where K and the numbers of previous classes and
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novel classes, respectively. Then, the greedy selection strategy is defined in the Algorithm| 1 where (D,,)) EvEB, (A(u, x- E Lj=1,j A(v, B,)) is the set score function defined the buffer set B; of the i-th class, Ap(e(B, is the gain of f choosing v into B, and u* is the chosen node using the greedy strategy. In greedy Algorithm the core idea is make the currently best choice of buffer nodes at every step, hoping to obtain the global optimal solution for the objective Eq Eq through this local optimal choice.
Below, we give a Proposition of approximation guarantee of our greedy algorithm.
Algorithm 1: Heuristic Buffer Selection
Input:
(B; | 1=1-
// buffers of previous tasks.
Proposition 1. (Greedy Approximation Guaran- tee of Algorithm 1). The greedy Algorithm 1 that sequentially adds elements to an initially empty set based on the largest marginal gain LB under a cardinality constraint provides solution B; that is at least (1 2 times the optimal solution, i.e.,
{C} J-Ji -+ // training node sets of
K+n
novel classes of current tasks.
f(0). // Model after trained on the
(t (1-1))th task.
Output: {B. K+* {B,) // updated buffers.
/ Initializing
+/
1 Create empty buffer {B.)
f( (1-2) S(OPT),
2 for from K + to K +
(5)
Select one node with highest output probability on the i-th label from C into B, via f(0).
where OPT represents the optimal solution of the buffer set B,.
end
/+ Greedy Selecting.
Proof. The above Proposition can be de- rived from the Greedy Approximation Guar- antee for Monotonic and Submodular Func- tions (Nembauser et al. 1978) (proof can be found in Theorem 2 in the Appendix), given that our function f is both monotonic (from Lemma ① and submodular (from Lemma 2 The greedy algorithm is guaranteed to produce solution that least (1 _) times the optimal solution. D
5 repeat
for from K + to K + do
Ap (.) = D(B, Uv) D(B)), 2" = arg maxc, (B, ())B)
Add v* into B, end
10
until b nodes are sampled each buffer;
Time Complexity Analysis. For each buffer of the t-th task, there are b sampling steps where b is the size of the buffers. Each sampling can be done in O((K + n) |C; )), by determining distances and making comparisons. Thus, the overall complexity of selecting each buffer is Olb(K + +n) (CI).
Note that (the buffer size) and + n (the total number of classes up to /-th task) are typically much smaller than C,), ensuring the efficiency of the algorithm.
3.2 DIVERSIFIED MEMORY GENERATIVE REPLAY
During training for the t-th task T', the stored representative nodes in the buffers J,KK from previous t tasks are also recalled to reinforce what the model has previously learned, known as memory replay. However, the limited buffer size still presents challenges: C1: the stored knowledge may constrained and might not encompass the full complexity of previous tasks, leading potential bias in replaying, and C2: the training process become difficult as the model may easily overfit to the limited nodes in the buffers, undermining its ability to generalize across different tasks. Thus, proposed the Diversified Memory Generation Replay address the above problems.
Broadening Diversity of Buffer Node Embeddings. Specifically, the embeddings of the buffer nodes first subjected to variational layer, which aims to create more nuanced representations that encapsulate the inherent probabilistic characteristics of nodes. Let 2; E IR² denote the embedding of node i; Bj, 1 E < K, where h is the hidden dimension. Specifically, treat the nodes in the buffers as the observed samples Vos drawn from the ground-truth distribution of the previous nodes:
K
-
U
U
(2.)
(K xb
Vol-
(6)
J=1 EE,,
(2. The node variable ~ is drawn from the variational network layer qo (Z|z) with parameters @.. Specifically, do. outputs the mean and variance of the node embeddings distributions respectively,
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expressed Z a Liner layer followed with a Relu activation layer. Then we use the reparameterization technique to sample from A(Z", _"), expressed as 7 2 + Z O c, where Z IRA and is drawn from standard normal distributions. Thus, we define the generated samples as Vge- The variational operation augments the diversity of observed buffer nodes Vol. empowering the model explore more expansive distribution spaces.
= = (Z) and Z" -% (Z), where & (.) is the identity function and g3 (.) is
Maintaining Integrity of Synthesized Embeddings. Then, we further propose maintain the integrity of these variational node embeddings to prevent them from deviating too far, which im- plies that while the generated embeddings should exhibit diversity, they must remain similar to the ground-trun ones. Specifically, we adopt an adversarial learning strategy. We introduce an auxiliary discriminator, D: : R + RR' with parameters Qd, tasked with distinguishing the original embeddings and the variational embeddings of nodes. In contrast, the model is learned to generate diversified variational node embeddings from the original ones, meanwhile ensuring the authenticity of synthesized variational node embeddings. Thus, the learning objective is defined as follows:
LMISE min Ez, (8:12)) 0.0g
max (D 2,)
dh
where tD is negative binary cross-entropy loss function on the variational and original node embeddings, defined as:
(8) The min-max adversarial learning strategy involves training the domain discriminator to distinguish whether the node embeddings are synthesized or original while simultaneously enforeing constraint on the model to generate indistinguishable node embeddings from the domain discriminator, This interplay aims to yield synthesized node embeddings that are more comprehensive and maintain integrity. It leverages the strengths of generative methods for increased representational complexity of buffer nodes to address CT Simultaneously, employs adversarial learning and regularization to ensure this expansion does not lead to distortions.
(p( = log D(zi, oa) + log D(á, 0s)).
Consolidating Generalization of Synthesized Embeddings. Furthermore, to adequately capture the node relationships within the variational node embeddings, we use the variational node embeddings to generate a reconstructed graph on the buffer nodes. As the buffer nodes are sampled from disparate regions, and the initial connections between them are sparse, instead employ the ground-truth label to build the reconstructed graph. Specifically, nodes sharing the same labels are linked, while those with different labels are not connected. The reconstructed graph is denoted as Ā E IR Kb Kb and the decoder loss defined as:
LOOSE = E
(2)2) [log pl (A(2)) + KL(gs, (E(=))(p))))))
-E g. 2, A.j log Pig + Aij log(1 ] (E(gol
where p(A(2) is the probability of reconstructing À given the latent variational node embedding matrix 2, following Bernoulli distribution. Pay is the probability of an edge between nodes and j. defined as: P.g sigmoid(3?"" .2,). 3.).10 The second term in Eq. 9 is distribution regularization term, which enforces the variational distribution qo. (&]]²) of each node be close to a prior distribution p(&),, which we assume is a standard Gaussian distribution. KL(-) represents the Kullback- (KL) divergence. The detailed derivation of LEOSE is in the Appendix.
The reconstruction objective incorporates both the inter-class and intra-class relationships between nodes in buffers. This loss facilitates the learning of variational node embeddings with well-defined classification boundaries, further bolstering the model's generalization on the label space. As such, the method can effectively address C2
Replaying on Generated Diversified Memory. Finally, we define the reply objective on the variational embeddings of buffer nodes, rather than the original embeddings, expressed as:
CrP
(22.).))
(10)
j=1 M
Note that the variational operation regenerates synthetic buffer node embeddings with the same size as original embeddings in each training step. i.c., [yyel = |.oal. broadening the diversity of memory while guaranteeing the efficiency of the buffer replay.

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3.3 OVERALL OPTIMIZATION
Combining the new task loss L' Enjeye (f((v; 0),9;) and the above memory replay losses, the overall optimization objective can be written as follows:
min L' + min
AnP + X2 (aXSE)) + AsLoaSE
(11)
0.6b
where Å1, X2 and A is the loss weights.
Synchronized Min-Max Optimization. A gradient reversal layer (GRL) (Ganin et al. 2016) is introduced between the variational embedding and the auxiliary discriminator so as to conveniently perform min-max optimization on 0, é, and da under LMISE in the same training step. GRL acts as an identity transformation during the forward propagation and changes the signs of the gradient from the subsequent networks during the backpropagation.
Scaliability on Large-Scale graphs. In each training step. training DMSG on the entire graph and buffer at once may not be practical, especially for large-scale graphs. Following methods like GraphSAGE (Hamilton et al.] (017)) and GraphSAINT (Zeng et al., 2l19). we adopt a mini-batch optimization strategy. We sample multi-hop neighborhood for each node and set two kinds of batch sizes, B and Bbulller for the new task and replay losses in Eq. [1 respectively. The ratio of these batch sizes corresponds to the ratio between the total training nodes in the new task and the buffer.
EXPERIMENTS
Experiment Setup. In this section, we describe the experiments perform to validate our proposed method. We use the four growing graph datasets, CoraFull, OGB-Arxiv. Reddit, and OGB--rodducts, introduced in Continual Graph Learning Benchmark (CGLB) (Zhang al. 2022a). These graphs contain 35, 20, 20, and 23 sub-graphs, respectively, where each sub-graph corresponds to new tasks with novel classes. For baselines, we establish the upper bound bascline Joint defined in Section 2. The lower bound baseline Fine-tune employs only the newly arrived training nodes for model adaptation without memory replay. Then, we set multiple continual learning models for the graph as baselines, including EWC (Kirkpatrick et al. 2017)). MAS (Aljundi al.) 2018). GEM (Lopez-Paz & Ranzato 2017), LwF (Li & Hoiem 2017). TWP (Liu et al. (021). ER ER-GNN (Zhou & Cao (021]. l). SSM (Zhang et al. 2022c). and SEM (Zhang et al. 2023). For a fair comparison, the backbone is set as two layers and the hidden dimension as 256 for all baselines. For evaluation metric, we first report the accuracy matrix Me RTTT which is lower triangular where MC 2 j) represents the accuracy on the j-th tasks after learning the task i. To derive a single numeric value after learning all tasks, we report the Average Accuracy (AA) T E M4.3 and the Average Forgetting (AF) T-1
T-1 ==1 Ma M for each task after learning the last task. For a more detailed introduction to the experimental setup. please refer to Appendix A.5
Overall Comparison. This experiment aims to answer: How is DMSG's performance the continual learning on graphs? We compare DMSG with various baselines in the class-incremental continual learning task and report the experimental results in Table [ Initially, we observe that DMSG attains significant margin over other baseline methods across all datasets. Certain baseline methods demonstrate exceedingly poor results. This be attributed to the difficulty of the problem, which involves more than 20 timesteps' continual learning. When the model forgets intermediate tasks, errors are cumulatively compounded for subsequent tasks, potentially leading to the model easily collapsing. However, our model addresses this challenge through superior buffer selection and replay training strategies, effectively avoiding catastrophic problems. Among the various baselines. the most comparable method to DMSG is SEM. Our method outperforms SEM mainly because we improve the buffer selection strategy, i.e., instead of random selection, we employ distance measures to choose more representative nodes for each class. Additionally, the variational replay method enables our model to effectively learn the data distribution from previous tasks. When compared to Joint, DMSG achieves comparable results, demonstrating its effectiveness in preserving knowledge from previous tasks, even with limited training samples. Notably, our method outperforms Joint on the Reddit dataset, and also exhibits positive AF. This improvement can be attributed to the proposed buffer selection strategy, which can select representative nodes, in other words, eliminate the noise nodes, and thereby enhance the results.
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Table 1: The model performance comparisons( f: higher is better, Joint is the upper bound).
Methods
CoreFull
OGB-Arxiv
Reddit
OGB-Products
AA/% 1
AF75 1
AA/$ t
AF%%
AA/%
AF/%
AA/S-1
AF/%
Fine-tune
3.5400.5
.9..2400.5
4,9+00.0
89.740.44
5.9-1..2 1.2
397.943.3
3.4+0.8
.82.5-0.8
EWC
52.6+8.2
13.55+12.1
8,5+1.0
-69.5=8.0
10.3=11.6
-33.2++26.1
23,8=3.8
-21.7=7.5
MAS
12.3+3.8
-83.7+4.1
4,9+0.0
-6.8+0.66
13.1+22.6
-35.2433.5
16.744.8
-57.0+31.9
GEM
8,4+111
18
4.9+0.0
08,8
28.44:3.5
-71.944.2
5.5+0.7
-84.3=099
TWP
62.6+-2.2
-30.6+4.3
6.7++155
50..6+13.2
13,5++2.66
89.7++2.7
14.1=44.0
-11.4=2.0
LwF
334++166
-59.6+2.22
9,9-1221
13.6++119
86.6+:1.1
-9.24111
48.2+116
-18.6=1.6
ER GNN
34.5::4.4
-61.61433
3..
15.001..3
88.5+:2.3
-10.8:22.4
5..7=0.3
-3..3
SSM
754400.1
-9.74-0.0
48.3400.5
-10.7+0.3
94.4+00.0
-1.3+0000
63.3+0.1
-964-0,3
SEM
71.710.8
-10.011.2
49.9
-8.41..3
96.31.0.1
-0.:::0.1
65.1=110
9..5...88
Joint 81,2+0.4
-3.3+0.8
51.3+0.5
-6.7+0.5
97.1+0.11
-0.7+-0.1
71.5=001
-5.4-0.3
DMSG
77.820.3
00.5:10.5
50.7=0.4
-19910
98.11:0.0
0.9
66.0=0.4
-0.9-11.6
AA
AA
Tasks
Tasks
Tasks
Tasks
(a) CoraFull
(b) OGB-Arxiv
(c) Reddit
(d) OGB--roddcct
Figure 3: Dynamics of the average accuracy during incremental learning on different growing graphs.
In-Depth Analysis of Continuous Performance. This experiment aims to answer: How does DMSG's 's fine-grained performance evolve after continuously learning each task? To present more fine-graine ine-grained demonstration of the model's s performance in continual learning on graphs, we analyzed the average performance across all previous tasks each time new task was learned. The comparative results of Fine-tune, Joint, DMSG, and the top-performing baseline, SEM, are depicted in Figure 3 The curve represents the model's is performance after in terms of AA on all previous tasks. Also, we visualize the accuracy matrices of DMSG and SEM on the -rriv and OGB- GrG-uut datasets. The results are presented in Figure In these matrices, each row represents the performance across all tasks upon learning new one, while each column captures the evolving performance of a specific task as all tasks are learned sequentially. In the visual representation, lighter shades signify better performance, while darker hues indicate inferior outcomes. From the results, we observed that as the number of tasks increases, the learning objectives grow increasingly complex, resulting a reduction in performance across all examined methods, including Joint. That is because tasks accumulate and the learning objectives become multifaceted, it becomes challenging for models to maintain optimal performance across all classes. Notably, the Fine-Tunine strategy experienced substantial decline, with the model collapsing with the arrival of merely two new tasks, demonstrating that catastrophic forgetting occurs almost immediately when the model fails access previous memories. This reinforces the need for effective continual learning techniques on the growing graphs where new tasks frequently emerge. While the performance drop was observed across all methods, DMSG demonstrated resilience and outperformed the top-performing baseline SEM. Also, DMSG predominantly displays lighter shades across the majority of blocks compared to SEM in Figure 4 Moreover, its competitive performance with Joint in specific datasets signifies its robustness and capability. This could be attributed to diversified memory selection and generation in DMSG that not only help in mitigating forgetting but also in adapting efficiently to new tasks.
Component Analysis of Memory Replay. This experiment aims to answer: Are all the proposed memory replay technologies of DMSG have the claimed contribution to continual learning? To inves- tigate the distinct contributions of the diversified memory generation replay method, we conducted an ablation study it. We design three variant methods for DMSG- w/o LMISE: This variant excludes the adversarial learning loss for maintaining the integrity of synthesized embeddings; w/o LOaSE: This variant excludes the graph reconstruction loss on variational embeddings for consol- idating their generalization to label space; w/o all: both losses were removed, and as a result, the model operates without any variational embeddings and just replays the original nodes in the memory buffers. From the results in Table we can observe when both LMISE and LOASE are removed (w/o all), the performance the lowest across all datasets. Also, a progressive improvement is observed as individual components in the model. This confirms their respective contributions to continual learning. An interesting trend emerges when comparing the individual contributions of the two components.
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Tasks
Tasks
Tadks
Tasks
Tasks
Tasks
Taskks
(a) CoraFull (SEM)
(b) CoraFull (DMSG)
(c) OGB-Arxiv (SEM)
(d) OGB-Arxiv (DMSG)
Figure 4: Accuracy matrices of DMSG and SEM in different datasets.
The w/o LOGSE variant slightly surpasses the performance of w/o CMISE. This suggests that while both components are crucial, adversarial variational embedding learning may have more pronounced ef- feet in capturing essential and diverse pat- terns inherent in the data. The best per- formance occurs with all components, sup- porting that the proposed components are beneficial individually and collectively, ensuring the model can effectively memorize the previous knowledge while continually adapting to new tasks.
Table 2: The ablation study of memory replay,
OGB- Arxiv
OGB-
Methods
CoreFull
Roddit
Products
w/o all
73,910.66
48.2:1.44
89.3
60.1100.8
74.4+008
49.3+-0.3
95.1
60.1
LooSE DMSG
74.8+0077
49.7::.22
60.5:10.77 97.8:1044
07.8+0.3
50.7=0.4
98.1=0000
66.0=00.4
RELATED WORKS
Many graphs in real-world applications, such as social networks and transportation systems, are not static but evolve over time. To accommodate this dynamic nature, various methods have been
developed to manage growing graph data [Wang et al. 2020a Tang & Matteson 2020: Daruna
et al., 2021 Luo et al. 2020). Incremental learning (Parisi al. 2019 Schwarz et al. 2018
Castro et al. 2018) involves models continuously learning and adapting, often facing the catastrophic
forgetting problem. Solutions include regularization techniques (Pomponi al. 2020 Lin et al.
2023), parameter isolation (Wang et al.
2021a Lyu et al. 2021) and memory replay (Wang et al.
2021b Mai et al. 2021). Recent works (Lu al. 2022] Wang al.
2022 Yang a 2022 lan
iet al. 2022) specifies this problem to growing graph data-new nodes introduce unseen classes to the
graph. Methods of Graph Incremental Learning (Rakaraddi al. 2022 Kim et 2022 Sun
et al. 2023) Su & Wu 2023 Feng et al. 2003) Liu et 2023) Niu et al. 2024) strive to retain knowledge of current classes and adapt to new ones, enabling continuous prediction across all classes.
For example, TWP (Liu et al. (02I) employs regularization to ensure the preservation of critical parameters and intricate topological configurations, achieving continuous learning. HPNs ZZhang et al. 2022b) adaptively choose different trainable prototypes for incremental tasks. ER-GNN (Zhou & Cao 2021 proposes multiple memory sampling strategies designed for the replay of experience nodes. SEM (Zhang et al. 2023) leverages sparsified subgraph memory selection strategy for memory replay on growing graphs. However, the trade-off between buffer size and replay effect is still Gordian knot, i.e., aiming for small buffer size usually results in ineffective memory preserving and knowledge replay. To address this gap, this paper introduces an effective memory selection and replay method that explores and preserves the essential and diversified knowledge contained within restricted nodes, thus improving the model in learning previous knowledge.
6 CONCLUSION
To summarize, this paper presents novel approach DMSG the challenge of incremental learning in ever- werr-growng and increasingly complex graph-structured data. Central to memory diversification, the proposed method includes a holistic and efficient buffer selection module and a generative memory replay module to effectively prevent the model from forgetting previous tasks when learning new tasks. The proposed method works in both preserving comprehensive knowledge in limited memory buffers and enhancing previous knowledge memorization when learning new tasks.
One potential limitation of DMSG that it does not improve the graph feature extractor the model, which may result in suboptimal performance when dealing with increasing graph data, the model parameters are insufficient to learn and retain massive amounts of information effectively. Future work may focus integrating more sophisticated parameter incremental learning techniques to dynamically adapt the model to the growing complexity of graph data, ultimately leading to improved performance in incremental learning scenarios.

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7 ACKNOWLEDGMENT
The work is partially supported by the National Natural Science Foundation of China (Grant No. 62406056), the Beijing Natural Science Foundation (Grant No. 4254089), the National Key R&D Program of China (Grant No. 2023YFF0725001), the National Natural Science Foundation of China (Grant No. 92370204), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 00231151512007)) and Brangzhou-HKKSSTCG Joint Funding Program (Grant No. 2023A03J0008), Education Bureau of Guangzhou Municipality, The computational resources are supported by SongShan Lake HPC Center (SSL--HPC) in Great Bay University.
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A APPENDIX
A.1 EXTENDED ANALYSIS OF THEOREM 1
In the context of Theorem 1 and Eq 3 of the diversity within the distributions of p(G²zt and g(Bzt), respectively. According to the Cochran theorem (Soch. 2023), the sampled variance og for an univariate is related to the chi-squared distribution:
The covariance matrices Σp and Eg are key indicators
(n
X
where on is the ture variance and n is the sample number. The mean of the chi-squared distribution is and its right-skewed nature implies that:
P 1i-i-n1ll 101-1)>11 0.5
P( <o))= - (n 1000p00000 d < -1 1 P(x <n 1) > 0.5
This indicates that there is greater than 50% chance that the sample variance underestimates the population variance. In higher dimensions, the sample covariance matrix Mg (related the Wishart distribution) displays properties analogous to the chi-squared distribution used in the unidimen- sional case. This statistical property extends to the sample covariance matrix in higher dimensions, suggesting that the eigenvalues of Σg are likely to be smaller than those of Ep.
Thus, the replay buffer Bet, being a sampled subset of Get, typically exhibits less diversity than the entire graph dataset from previous tasks, meaning Σg is often smaller than Σp. Assuming the sampling strategy is unbiased upon means, as the Bęt more diversified, Σ. + Eep. leading to the Wasserstein distance decreases. Based on Theorem [ the discrepancy between the expected loss
under true distribution and the buffer distribution becomes less, making the optimization on the buffer more closely approximate the optimization on all previous graph data.
A.2 THEORETICAL ANALYSIS OF GREEDY ALGORITHM
In the Heuristic Diversified Memory Selection section, we propose a heuristic buffer selection algorithm and give a proposition of approximation guarantee of the algorithm:
Proposition 2. (Greedy Approximation Guarantee of Algorithm 1). The greedy Algorithm I that sequentially adds elements to an initially empty set based on the largest marginal gain 2xp under a cardinality constraint provides solution Bü that is at least (1 1) times the optimal solution, i.e.,
f(B;) N (1 (1-2)- -(OPT),
(10O)))(OPT),
(12)
where OPT represents the optimal solution of the buffer set B,.
Below we first give a greedy approximation guarantee and then give the proof of Proposition I Theorem 2. (Greedy Approximation Guarantee for Monotonic and Submodular Functions): Let f:20 TR be set function defined a finite ground set U such that:
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f is non-decreasing (monotonic), t...for every A S B CU,,
S(A) S J(B)
J is submodular, i.e., for every A S B C U and for every U B, the marginal increase due to at least as large when added to the smaller set A as when added to the larger set B. Formally,
f(AU(=)) - f(A) 2 f(BU(z)) f(B)
Then, a greedy algorithm that sequentially adds elements to an initially empty set based on the largest marginal gain of f produces a solution S such that:
f(5") 2(5")2 (1- f(OPT)
where OPT is an optimal solution. Below is the proof:
Proof. Let S be the constructed by the greedy algorithm. Begin with $ = and f(S) 0. At the k-th step, the greedy algorithm picks an element 23 that maximizes the marginal gain: Th = arg max A (x|S)
2EU
where (x(s))) = (()
Let OPT be an optimal solution, and without loss of generality, let OPT for 02.... Om J- For each k. consider the gain of the greedy algorithm in the k-th step relative to adding the k-th element of OP to S:
1
m
(o:1s)))
m
This inequality is derived from the submodularity of f. The right-hand side the average marginal gain of adding elements of OPT to S.
The total increase in f over the first & steps of the greedy algorithm is at least:
1 S(S) > (1-))) )
-(OPT) )
By analyzing the expression on the right and considering the limit as k approaches m, we obtain the (1 1--2 -) factor.
After m steps (or fewer, if the greedy algorithm terminates early), the set S constructed by the greedy algorithm satisfies:
f(8*) 1 - f(OPT)
This completes the proof.
Given IDB,)) = EVEB, (A(u, x- Ejnr,te A(v, is the set score function defined on the buffer set B3 of the i-th class, (n(v(B)) is the gain of choosing into B, We have the following
Lemmas of ID::
Lemma 1. The function ID is monotonic with respect to set Bi.
Proof. For the intra-class diversity, when new nodes are added to B;, they positively contribute to D due to their own distances to other nodes within B,. The addition of these nodes can decrease the distances the existing nodes in B, to their closest neighbors. For the inter-class diversity, the addition of new nodes to B; increases the value of D since these nodes have their own distances to nodes in other classes By. The distances from existing nodes in B, to nodes in other classes remain unchanged, there is no loss in inter-class diversity. Given that the gains from inter-class distances generally overshadow the potential losses from intra-class distances, we can infer that as we include more nodes in B, the value of D will increase. Therefore, the function is monotonic.
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Lemma 2. The function DD is submodular with respect set B
Proof. For the function DD, be submodular, it must satisfy the following condition: For any set B; and node and any set V from C, such that v is not element of VT,, the following inequality holds:
(B, Ub) (D(B,) (B UV Uo) (B, UV
For the first term EeEB, A(v, B:), given the definition of the function A, the distance the nearest point B, for any v will be greater than or equal to the distance the nearest point B, UV- Therefore, adding to B, potentially reduce the distance more significantly than adding it to B, UV.. Regarding the subsequent term, which sums the distances from all nodes in the set to other sets of buffers Bj. can be deduced that adding into either B, or B; U yields identical gain in the function's 's value. In light of the above observations, we can validate the aforementioned inequality. Consequently, the function MD submodular with respect to set B,.
Eventually, our optimal solution in Equation 4 can written as:
B, = arg max (B,)) B,C.,
The proposed greedy Algorithm 1 aims to sequentially add elements to B; based on the largest marginal gain of ID, which is monotonic and submodular. Based on Theorem 2 Lemma | and Lemma 2 establish the validity of Proposition
A.3 DERIVATION OF Loss LCASE.
In the Diversified Memory Generation Replay section, aim the variational node embeddings to generate reconstructed graph on the buffer nodes. The optimization problem is described by the likelihood of observing reconstructed adjacency matrix A based on surrogate source node embeddings 7:
Theorem 3. Given the variational posterior gl g(á,|z) via the instantiating of synthesized node em- beddings and a prior distribution p(2,) acting as a regularization for q (().)),, we have the Evidence Lower Bound (ELBO), which is surrogate objective for maximizing the log- log-likelihood:
log ((A) 2 Er.
40. (212) log pl p(112) KL (21=2)l)))))))
where KL(.) represents the Kullback-Leible (KL) divergence. The term p(A(2) denotes the re- construction probability from the surrogate source node embeddings to the reconstructed adjacency matrix.
Proof. The optimization problem we are dealing with is described by the likelihood of observing reconstructed adjacency matrix À based surrogate source node embeddings Z:
logp(A) = log / v(A,2)dō
log p(A)2)p(2)d2
This equation encapsulates the joint probability of observing the graph and the latent variables. To enable tractable optimization, introduce variational distribution, ga. (å(z), approximating the true posterior of the node embeddings. Multiplying and dividing by this term, we can express the likelihood as:
log pg Ā) = log ((AlZ) p(Z) 9o. (2/12) no. (21l2)d2
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This expression can be interpreted expectation with respect to the variational distribution:
p(A]Z) p
log p(pp(() = log Bag
Do (2x(2)
Applying Jensen's inequality allows us to bring the logarithm inside the expectation, leading to lower bound:
logp(A A) Bgg log (())(A p(2)
To (Zilz)
p(7)
[og p( A|2)
Egg
+ Egoo
log
9 (2112)
We recognize the second term in the above inequality as the negative of the KL divergence between the variational distribution and the prior:
Io (2
Eys. [log
p(2,)
The KL divergence acts regularization term, penalizing deviations of variational distribution from the prior. Combining the terms, we have the Evidence Lower Bound (ELBO), which is a surrogate objective for maximizing the log-likelihood:
log p(A) 2 Ens, [logg(AA))))) (A(2)) (=.=))
Thus, we obtain the optimization objective LOOSE. Specifically, the actual calculation formulas of the two components of LOGSE are defined as:
Eyg, [log [log((A(2)] Asg log Pis + Aos log(1 Pig)
K Σ k=1
KL (N Ex)1
K
(tr(E)) + uh h - log [Xx])
where tr(-) denotes the trace of a matrix, is the dimensionality of the source node embedding S and [> is the determinant of Σx.
A.4 SYNCHRONIZED MIN-MAX OPTIMIZATING OF OVERALL Loss LDMSG.
Recall that the overall optimization objective is follows:
min L + min Xr + X2 9.d.
+ AsLOaSE
where λ1 d2 and À the weights to balance different losses. Then, the parameters 0, d.. and da of DMSG can be optimized by Stochastic Gradient Decent (SGD) as follows:
Oc
DCRP
dLMISE
dLOGSE
- 1
+ A
+ +
+ +X3
08
00
08
08
dLRP
ALMISE
ôLOGSE
On t- Q
A
+ X2 Dgv
+ Xa
dLMISE
dd x- 0 -
->x2
00g
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where j is the learning rate.
Camu Sum
35
Tosks
Toslss
Tasks
12.k3
(a) CoraFull
(b) OGB-Arxiv
(c) Reddit
(d)
Figure Cumulative number of nodes within different growing graphs.
Table The statistics of four datasets.
Dataset
#Nodes
#Edges
#Classes
#Tasks
CoreFull
19,793
130,622
70
35
OGB-Arxiv
169,343
1,166,243
40
20
Reddit
232,965
114,615,892
20
OGB-Products
2,449.029
61,859,140
A.5 EXPERIMENT SETUP
A.5.1 DATASETS
We use the four graph datasets, CoraFull, OGB-Arxiv, Reddit, and OGB-Products, introduced in Continual Graph Learning Benchmark (CGLB) Zhang et al. 2022a). CoraFull (McCallum al. 2000) and OGB-Arxiv (Wang et al.) 2020b) are citation networks with papers as nodes and citation relationships as edges and labeled based on paper topics. Reddit (Hamilton al. (017) a social network with posts as nodes and posts are connected if the same user comments. The node labels are the community the posts belong to. DGB-Products (Hu et al., 2020) is a product co-purchasing network with nodes representing products and edges indicating that the connected products are purchased together. The node labels are the class the products belong to. Each graph is considered a volume-increasing graph over time, where its size expands with the arrival of new nodes with several novel classes at each time, leading to a more complex node classification task. To elaborate, given an original graph comprised of C class nodes, these classes are partitioned into original class order. This ensures that each group contains k: classes of nodes. The graph is divided into m sub-graphs accordingly. where each sub-graph represents the newly added data with novel classes at particular time, resulting in a new learning task. In the context of continual learning, we commence by training a model on the first graph. Subsequently, at each time, we integrate the succeeding sub-graph into the prevailing graph, prompting the model to continuously learn and adapt new tasks. To accentuate the forgetting problems in continual learning, we set ie for each graph, which basically maximizes the number of tasks on growing graph, challenging the capabilities of baselines. The detailed statistics the datasets are shown Table Figure 5 the curves of the cumulative number of nodes within different growing graphs..
groups with the
A.5.2 BASELINES
First, we establish the upper bound and lower bound baselines of our problem. The upper bound baseline Joint is defined Section [ which involves continuously training the model each time with all accumulated training nodes from previous and new tasks, thus without the forgetting problem. The lower bound baseline Fine-tune employs only the newly arrived training nodes
model adaptation,
yielding fine-tuning mode that easily forgets the previous tasks. Then, we set multiple continual learning models for graph as baselines, including EWC (Kirkpatrick et al.) 2017). MAS (Aljundi) et al. 2018). GEM (Lopez-Paz & Ranzato, 2017). LWF (Li & Hoiem 2017). TWP (Liu et al. 2021), GR- (Zhou Cao 2021). SSM (Zhang et al. 2022c), and SEM (hang et al. 2023). A not originally designed for graph data, we utilize a Graph Neural Network (GNN) as the backbone of all baselines for extracting graph information. The specific GNN model of baselines is selected from
detailed introduction to these methods be found in the Appendix. As some of the methods
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GCN WWeling & Kipi 2016). SGC (Wu et al. 2019). GAT (Casanova et al. 2018), and GIN (X et al. 2018), based on which yields the best performance. For a fair comparison, the backbone is set as two layers and the hidden dimension 256 for all basclines. Here, we give detailed introduction
to the baseline models.
EWC imposes a constraint, based on the Fisher Information Matrix and weight adjustments, to preserve knowledge from prior tasks during new task learning.
LwF learns new tasks without necessitating the retention of old task samples by training neural networks minimize discrepancies between predictions on new and preceding tasks.
GEM facilitates effective continual learning by storing knowledge from previous tasks and archiving prior tasks while permitting updates solely if they don't amplify the loss these tasks.
MAS mitigates catastrophic forgetting by imposing penalties modifications to critical synapses, determined by the influence of weight changes on output, and preserves old knowledge without requiring the storage of previous tasks.
TWP preserves both the minimized loss and the topological structure of the graph, and harmonizes past and new task knowledge, thus enabling more robust model performance and circumventing catastrophic forgetting.
SSM uses a strategy that sparsifies computational graphs into fixed size before storing them in memory, which not only minimizes memory consumption but also enhances the learning of tasks from diverse classes.
SEM develops the subgraph episodic memory to store the explicit topological information in the form of computation subgraphs and perform memory replay-based continual graph representation learning.
A.5.3 EXPERIMENTAL SETTING
We use a 2-layer GCN as our backbone. For the baselines, we report their experimental results from SEM (Zhang et al. 2022c), and we set the same experimental setting with the bucket size of DMSG as 60 for CoraFul and 400 for other datasets. For the diversified memory replay, we set the number of generated diversified node embeddings in the memory buffers the same as the original counts. Following (Zhang et al.] 2022a c). the training rate for each task is set as 60%, the validation rate 20%, and the rate as 20%. The training epoch for each task is set as 200 epochs. The training nodes of previous tasks exclusively come from the buffer. The learning rate is set as 0.001 and the weight decay as 3e-3, The weights for the four losses are set as [1, 20, 1, 1], respectively, For evaluation metric. we utilize the Average Accuracy (AA) meaning the mean accuracy of the model on all tasks after learning the final task, and Average Forgetting (AF) meaning the average reduction in accuracy for each task from when it was first learned to after the model has learned all tasks. we first report the accuracy matrix Mace T which is lower triangular where M 2 j) represents the accuracy the j-th tasks after learning the task i. To derive a single numeric value after learning all tasks, we report the Average Accuracy (AA) Σ Mq.. and the Average Forgetting (AF)
T-1 Mase Mare for each task after learning the last task. 11
A.6 EXTENTAL EXPERIMENTS
A. VISUALIZATION OF ACCURACY MATRIX
To further understand the dynamics of our methods under the incremental learning task, we visualize the accuracy matrices of DMSG and SEM on the CoraFull and OGB-Arxiv datasets. The results are presented in Figure 4 and 6 In these matrices, each row represents the performance across all tasks upon learning new one, while each column captures the evolving performance of a specific task as all tasks are learned sequentially. In the visual representation, lighter shades signify better performance, while darker hues indicate inferior outcomes. Upon comparison, DMSG predominantly displays lighter shades across the majority of blocks compared to SEM, showing that DMSG can consistently achieve better performance.
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Tasks
Tasks
Tasks (a) Reddit (SEM)
Tasks
Tasks
Tasks
(b) Reddit (DMSG)
(c) OGB-Product (SEM) (d) OGB-Produce (DMSG)
Figure 6: Accuracy matrices of DMSG and SEM in different datasets..
A.6.2 ANALYSIS OF BUFFER SELECTION.
This experiment aims answer: Is the proposed buffer selection strategy more effective than other selection strategies in selecting representative nodes? The choice of buffer sampling strategies is critical in graph's 's continual learning, as it determines which knowledge will be stored and later replayed to the model. We choose different buffer sampling strategies, including our proposed Diversified Memory Selection (DMS) method, K-center sampling (Nguyen et al.) 2018), Coverage Maximization (CM), and Mean of Feature (MF) (Zhou & Cao 2021). We perform these sampling methods in our continual learning framework. The results are demonstrated in Table [ We can observe that our sampling method consistently excels in performance. This consistency can be attributed to exploring both the intra-class and inter-class diversity of nodes within our method that efficiently captures the required diversity among nodes, ensuring holistic representation of the dataset. The K-center approach, although it shows commendable results, lags behind our method. This can be attributed buffers. However, the K-center approach does not fully consider intra- and inter-class diversity, leading to comparatively lower performance. It's worth highlighting that both CM and MF, when implemented within our framework, demonstrate marked improvement in performance compared to their native ER ER-GNN framework. This outcome underscores the flexibility of our proposed diversified memory generation replay model, suggesting that it not only complements various sampling strategies but can potentially improve their effectiveness.
sharing similar assumption with our method-capturing diverse sample
Table 4: Comparison of buffer selection methods.
OGB- Arxiv
OGB- Products
Methods
CoreFull
Reddit
Kcenter
74.41007
43.7110.
85.242.7
49.7=0.8
CM
74.5=006
40.6+1.0
7..4=:1.4
43.5=0.8
MF
74.5+0.8
42.3+00.9
87.2+0.77
49.3=1.1
DMS
778.10.3
50.710.4
98.110.0
0.4
A.6.3 ANALYSIS OF BUFFER SIZES.
This experiment aims to answer: How do different buffer size affect the performance of DMSG? To comprehensively understand the influence of buffer size the performance of DMSG, evaluate DMSG across different buffer sizes, specifically 40, 50, 60, 70, and 80 for the CoraFull dataset, and 200, 300, 400, 500, and 600 for other datasets. The results illustrated in Figure 7 There's clear trend that, generally, as the buffer size increases, the performance also sees an enhancement. This can be intuitively understood: more extensive buffer can store more data from past tasks, acting as a richer source of knowledge when learning new tasks and thereby mitigating the effects of catastrophic forgetting. An equally important observation is the consistency in the standard deviation of results across different buffer sizes. The compact standard deviation, even for smaller buffers, is indicative of the robustness of DMSG. On both the Reddit and OGB-Product datasets, the performance at a buffer size of 600 exhibited marginal decline. While it might appear counterintuitive given the general trend, this could be due to the larger buffer size introducing more noise nodes. These nodes, which might not be representative result, they consequently reduce the model's generalization ability- a consideration that aligns with discussion in the overall comparison.
essential others, can dilute the quality of information stored. As
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AA
54
AA
AA
50-
48-
64
96
40
50
60
70
200
300
400
500
600
200
300
400
500
600
200
300
400
500
600
Buffer Size
Buffer Size
Buffer Size
Buffer Size
(a) CoraFull
(b) OGB-Arxiv
(c) Reddit
(d) OGB-Product
Figure 7: The model performance with different buffer sizes.
A.7 DETAILED RELATED WORKS
A.7.1 LEARNING ON GROWING GRAPHS.
Graph-based learning often operates under the assumption that the entire graph structure is available upfront. For example, Graph Neural Networks (GNNs) (Ju et al. 2024 Qiao al. 2020) have rapidly become one of the most prominent tools for learning graph- graph-structured data, bridging the gap between deep learning and graph theory. Representative methods includes GCN (Welling & Kipf 2016), GraphSAGE (Hamilton et al., 2017). and GAT (Veličković et al., 2018), etc. However, these methods predominantly operate on static graphs. Many graphs real-world applications, such as social networks and transportation systems, are not static but evolve over time. To accommodate this dynamic nature, various methods have been developed to manage growing graph data (Wang et al.) 2020a] Tang & Matteson| 2020: Daruna et al. 2021| Luo et al. (020). For instance, Evolving Graph Convolutional Networks (EvolveGCN) (Pareja al. 2020) emphasizes temporal adaptability in graph evolution. Temporal Graph Networks (TGNs) (Rossi al. 2020) operates continuous-ting time dynamic graphs represented as sequence of events. Temporae Graph Networks (STGN) et al. 2018) integrates spatial and temporal information enhance prediction accuracy. However, these methods primarily concentrate on singular task in evolving graphs and often encounter difficulties when more complicated tasks emerge the graph expands.
A.7.2 INCREMENTAL LEARNING.
Incremental learning PParisi et al. 2019) refers to evolving paradigm within machine learning where the model continues to learn and adapt after initial training. The continuous integration of new tasks often leads to the catastrophic forgetting problem. There are usually two types of continual learning settings-clas waagggs-clls-inne ittass-iccrementll learning about expanding the class space within the same task domain, while mask-incremental learning involves handling entirely
tasks, which may may not be related to previous ones (Schwarz et al., 2018 Castro et al., 2018). Typically, three different categories of methods have emerged address the continual learning problem. The first category revolves around regularization techniques (Pomponi et al. 2020 Lin et al. 2023). By imposing constraints, these methods prevent significant modifications to model parameters that are critical to previous tasks, ensuring a degree of stability and retention. The second category encompasses parameter-isolation based approaches (Wang al., [2021]] Lyu et al., (202T) These strategies dynamically allocate new parameters exclusively for upcoming tasks, ensuring that crucial parameters intrinsic to previous tasks remain unscathed. Lastly, memory replay-basee methods (Wang et al.) 2021b) Mai al. 2021 present solution by selectively replaying representative data from previous tasks mitigate the extent of catastrophic forgetting, while are more preferred due to their reduced memory storage requirements and flexibility in parameter training. This paper delve deeper and present an effective strategy for selecting and replaying memory on graphs.
A.7.3 GRAPH CLASS-INCREMENTAN LEARNING.
Graph incremental learning, also known as graph continual learning, aims to continually train a graph model on growing graphs perform more complex tasks. This problem includes two settings, task- incremental learning and class- incremental learning. Graph task incremental learning methods treat the learning different tasks and assume the task affectations of newly added nodes known when inference. Many works (Su Wu 2023] Su et al., 2203)) Niu et al., 2023) Su et al.) (004)) have been introduced recently under this setting. Class- Class-incrementa Learning (Belouadah et al. 2021 means
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the specific scenario where the number of classes increases along with the samples introduced, which does not presuppose knowledge of node class assignments in different tasks, presenting more
complex challenge. Graph class-incremental learning (Lu et al. 2022 Wang et al.
2022 Yang et al.)
2022 Tan et al. 2022) specifies this problem to growing graph Lata-new nodes introduce unseen
classes the graph. Methods of graph class-incremental learning (Rakaraddi et al.
2022 Kim et al.)
2022] Sun et al. [023] Feng et al. [0233] Liu et al. 2023 Niu et al. (2024) strive to retain knowledge of current classes and adapt to new ones, enabling continuous prediction across all classes. In the
past years, various strategies have been proposed to tackle this intricate problem. For example, TWP (Liu et al. (20I)) employs regularization ensure the preservation of critical parameters and intricate topological configurations, achieving continuous learning. HPNs (Zhang et al., 2022b) adaptively choose different trainable prototypes for incremental tasks. ER-GNN (Zhou & Cao. [ao]]02]]] (021) proposes multiple memory sampling strategies designed for the replay of experience nodes. SSM (Zhang et al., 2022ch and SEM (Zhang et al., 2022c) leverage a sparsified subgraph memory selection strategy for memory replay growing graphs. PDGNN (Niu et al. 2023) proposes parameter decoupled graph neural networks with sopology-awand embedding memory for the graph incremental learning problem. PUMA (Liu et al. 2024) and DeLoMe (Zhang al. (024) both use different graph condensation technology to preserve memory graphs. However, the trade-off between buffer size and replay effect still a Gordian knot, i.e., aiming for small buffer size usually results in ineffective knowledge replay. To address this gap. this paper introduces an effective memory selection and replay method that explores and preserves the essential and diversified knowledge contained within restricted nodes, thus improving the model in learning previous knowledge.
22


Reviews:
[{"review_id": "dF2Yd7vDhe", "reviewer": "Reviewer_NW1X", "summary": "This paper addresses the problem of incremental learning in growing graphs with new-coming node classes. It introduces a novel holistic Diversified Memory Selection and Generation (DMSG) framework containing two modules: (1) a buffer selection strategy that considers both intra-class and inter-class diversities, with a greedy algorithm; and (2) a diversified memory generation replay method with variational generation, with integrity loss and reconstructed loss under adversarial learning. Experiments over evolving graphs on node classification tasks could verify its effectiveness, along with ablation study over memory generation replay module.", "questions": "See Weakness.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "S1. [Clear Motivation & Descriptions] The paper provides a well-defined motivation for addressing continual learning on growing graphs, focusing on memory selection and memory reply effectiveness. The reason for developing the proposed method can be compelling, along with clear and detailed descriptions of the problem background and definition, making it accessible and understandable.\n\nS2: [Rationale Methodology] The rationale for the DMSG approach is well-grounded, combining heuristic buffer selection and generative memory reply to broaden the replay capability. The methodology introduces two strategies: first, a buffer selection algorithm that maximizes intra-class and inter-class diversity; second, a variational generation layer that synthesizes embeddings for effective replay, which sounds rational and novel to me.\n\nS3. [Theoretical and Empirical Experiments] The paper validates its approach with both theoretical and empirical support, for instance, theoretical analysis to demonstrate the importance of effective buffer selection. Experimentally, the DMSG framework is tested on multiple evolving graph datasets, a good improvement over the AF/% metric.", "weaknesses": "Here are still some questions mainly regarding the buffer selection part and the variational part:\n\nW1: For the buffer node selection part, are the buffer nodes only node-set or graph-structural data, if graph data, how to connect these nodes? and if node-set, how to directly feed it into GNN in Figure 2?  Further clarification on this would be appreciated.\n\nW2: How many nodes are typically selected in the buffer for each class? How experimental results would change along with the varying number of nodes in buffers?\n\nW3: In the ablation study, the effectiveness of the buffer node selection is not verified. For instance, how to illustrate the effectiveness of the proposed heuristic greedy method? \n\nW4: Why the variational layer in the memory replays could broaden knowledge from the buffer? Does that mean, it generates something new $\\hat{Z}$ from the original Z? Additionally, the minimization term in equation (7) is difficult to interpret—could you provide a more detailed explanation or expanded expressions for this term?\n\nW5: With the introduction of complex mechanisms for memory selection and replay, how do the time and computational costs of the proposed method compare to other baseline approaches in the experiments?\n\nW6: Why have a direct assumption that \"Let the loss function L(θ, x) be β-Lipschitz continuous in respect to the input x\" in Theorem 1. ? And how can we evaluate whether the selected nodes in buffers are with diversity?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Q6ik1Tj0sW", "reviewer": "Reviewer_8sJn", "summary": "This paper presents a novel approach called Diversified Memory Selection and Generation (DMSG) for incremental learning in growing graphs. The authors address the challenge of continually training graph models to handle new tasks while retaining knowledge from previous tasks.", "questions": "see above.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The developed model is supported by a theoretical foundation. The authors provide a theoretical analysis to support the importance of buffer diversity in incremental learning scenarios.\n\nThe studied problem is important. The authors try to tackle the issues of limited buffer size and potential overfitting through their diversified memory generation approach.\n\nclear visualization and presentation. The authors use well-structured figures to convey the incremental learning process, memory selection, and generative replay methods in a relatively straightforward approach.", "weaknesses": "Lack of novelty. This paper largely builds on existing concepts of memory replay and buffer selection strategies that are already well-established in incremental learning and continual learning literature. While the paper proposes a diversified memory selection and generative replay approach, the techniques, such as adversarial learning and variational embedding, have been previously applied in other contexts. The paper simply combines different losses to facilitate learning.\n\nLack of baselines. The following papers should be discussed and compared for experiments:\nTowards robust graph incremental learning on evolving graphs. ICML 2023\nReplay-and-Forget-Free Graph Class-Incremental Learning: A Task Profiling and Prompting Approach. NeurIPS 2024\nOn the Limitation and Experience Replay for GNNs in Continual Learning. CoLLAs 2024\nTopology-aware Embedding Memory for Continual Learning on Expanding Networks. KDD 2024\nPUMA: Efficient Continual Graph Learning for Node Classification With Graph Condensation. TKDE 2024\nGraph Continual Learning with Debiased Lossless Memory Replay. ECAI 2024\nAccordingly, it is encouraged that the authors discuss the difference between their proposed model and these baselines.\n\nLack of comprehensive datasets. What about the performance of the proposed model on Citeseer, Pubmed, and PPI? How about Collab, IMDB, Proteins, and NCI1?\n\nLack of hyperparameter sensitivity study. The method introduces several hyperparameters such as λ1, λ2, and λ3 for balancing the loss. A discussion on their impact and guidelines for tuning these hyperparameters would be valuable. More in-depth analyses about balancing these losses to understand the contribution and reasons for developing them are encouraged.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "z3ZGrlDjYm", "reviewer": "Reviewer_Mh5c", "summary": "This paper studies incremental learning on growing graphs, aiming to continually train a model on new tasks without loosing the inference ability on previous tasks. The method proposed in this work, namely holistic diversified memory selection and generation (DMSG), is a memory based technique, with a focus on improving the data diversity in the memory, which is neglected by the existing works. The unique design of DMSG comes from two perspectives. First, it proposes a novel method to sample the data, second, instead of directly using the buffered data, DMSG train a generator to generate the data to replay.\n\nOverall, this method proposes a novel memory based technique, and the experimental results justify the effectiveness of the method. However, there are also some major problems regarding the theoretical analysis, as listed below in the weakness part.", "questions": "1. Please explain more on the probability distance used in Section 3.1, e.g. the specific formulation.\n\n2. Is the replay data generator trained from scratch each time when a new task comes in? Or is the generator train each time when a new task comes in, but is initialized from the generator from the previous task?\n\n3. If the generator is trained every time when a new task comes in, will this induce significant extra computational burden?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper is overall well written, and the main idea is clearly conveyed.\n\n2. Experiments are comprehensively conducted on multiple benchmark datasets against multiple baselines.\n\n3. According to the results, the proposed method consistently outperform the baselines, although the improvement on some datasets are negligible.", "weaknesses": "1. The theoretical analysis is not rigorous enough. Theorem 1 reveals that smaller distance between the memory data distribution and the full data distribution indicates that the loss computed based on memory can more closely mirrors the expected over the full previous data. This is a straightforward and reasonable conclusion. But what follows is not convincing enough. First, it is assumed that the distributions of the memory data and full data is Gaussian. I guess this is acceptable, although a little bit arbitrary. Next, it is stated that the buffered data is typically less diverse, therefore increasing its diversity could make it closer to the full data distribution. This is not convincing, since the 'diversity' here refers to the covariance. Why is the buffered data has a smaller variance than the real (full) distribution? This should depends on the sampling strategy instead of the size of the set. Moreover, although the diversity here refers to the covariance, in the following of the paper, the diversity is measured by the average distance among the data, which is inconsistent.\n\n2. The implemented diversity maximization strategy is inconsistent with the theoretical motivation, as mentioned in the first weakness point.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mzbtk7wdrH", "reviewer": "Reviewer_T2ad", "summary": "This paper presents a memory replay approach to address the challenges of graph incremental learning. Specifically, the proposed method includes a diversified buffer selection module and a generative memory replay module to prevent the model from forgetting previous tasks when learning new tasks. The experimental results demonstrate the effectiveness of the proposed method.", "questions": "Please see the weaknesses.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The studied problem is practical and interesting.\n\nThe paper is well-written and easy to understand.\n\nThe proposed method introduces novel approaches for buffer selection and memory utilization.", "weaknesses": "1. The title presented on the website is not the same as the one in the paper\n2. The citation style is not used appropriately. Most of the citations should be in parenthesis using \\citep{}.\n3. The authors are encouraged to include the time consumption of different memory selection strategies.\n4. The statements in lines 178-181 are not clear. Please revise it to make it clearer.\n5. The definition of L_{adv} is not clear in line 334. Moreover, there is no Eq.A.3.\n6. The analysis of parameter sensitivity is missing.\n7. The comparisons to more recent baselines are encouraged.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)