Title: What Matters in Graph Class Incremental Learning? An Information Preservation Perspective
Venue: NeurIPS 2024
Accepted: yes
Keywords: Graph neural network

Class incremental learning
Abstract: Graph class incremental learning (GCIL) requires the model to classify emerging nodes of new classes while remembering old classes. Existing methods are designed to preserve effective information of old models or graph data to alleviate forgetting, but there is no clear theoretical understanding of what matters in information preservation. In this paper, we consider that present practice suffers from high semantic and structural shifts assessed by two devised shift metrics. We provide insights into information preservation in GCIL and find that maintaining graph information can preserve information of old models in theory to calibrate node semantic and graph structure shifts. We correspond graph information into low-frequency local-global information and high-frequency information in spatial domain. Based on the analysis, we propose a framework, Graph Spatial Information Preservation (GSIP). Specifically, for low-frequency information preservation, the old node representations obtained by inputting replayed nodes into the old model are aligned with the outputs of the node and its neighbors in the new model, and then old and new outputs are globally matched after pooling. For high-frequency information preservation, the new node representations are encouraged to imitate the near-neighbor pair similarity of old node representations. GSIP achieves a 10\% increase in terms of the forgetting metric compared to prior methods on large-scale datasets. Our framework can also seamlessly integrate existing replay designs. The code is available through https://github.com/Jillian555/GSIP.

What Matters in Graph Class Incremental Learning? An Information Preservation Perspective

Abstract

Graph class incremental learning (GCIL) requires the model to classify emerging nodes of new classes while remembering old classes. Existing methods are designed to preserve effective information of old models or graph data to alleviate forgetting, but there is no clear theoretical understanding of what matters in information preservation. In this paper, we consider that present practice suffers from high semantic and structural shifts assessed by two devised shift metrics. We provide insights into information preservation in GCIL and find that maintaining graph information can preserve information of old models in theory to calibrate node semantic and graph structure shifts. We correspond graph information into low-frequency local-global information and high-frequency information in spatial domain. Based on the analysis, we propose a framework, Graph Spatial Information Preservation (GSIP). Specifically, for low-frequency information preservation, the old node representations obtained by inputting replayed nodes into the old model are aligned with the outputs of the node and its neighbors in the new model, and then old and new outputs are globally matched after pooling. For high-frequency information preservation, the new node representations are encouraged to imitate the near-neighbor pair similarity of old node representations. GSIP achieves a 10% increase in terms of the forgetting metric compared to prior methods on large-scale datasets. Our framework can also seamlessly integrate existing replay designs. The code is available through https://github.com/Jillian555/GSIP .

1 Introduction

In real-world applications, graph data is continuously generated. For instance, in citation networks, new types of papers and their citations may constantly emerge, an ideal literature classifier needs to continuously distinguish literature in emerging research areas [1, 2]. Therefore, it is critical for a graph model to incrementally integrate new classes on an extended graph, which is referred to as Graph class incremental learning (GCIL). However, this poses a major challenge known as catastrophic forgetting, where the model needs to preserve previous information while continuously acquiring new information [3, 4].

Many approaches attempt to preserve information from previous models or graph data to prevent catastrophic forgetting in GCIL, which can be divided into four groups. The parameter isolation methods entirely or partially preserve parameters of different tasks to protect model performance, such as dynamically incrementing feature extractors and prototypes [2]. Regularization methods, on the one hand, preserve important parameters, such as assessing parameter importance by considering loss and topology [1], and maintaining orthogonality with parameters from previous tasks [5], on the other hand, preserve the absolute position of nodes in feature space or output space, such as aligning the outputs of samples on old and new models [6]. The replay methods preserve a few nodes or subgraphs to retrain the model to prevent forgetting, such as saving representative nodes [7], selecting subgraphs according to node degree [8], and compressing training graphs [9]. The hybrid methods combine different learning paradigms ( i.e. the combination of replay and regularization methods), such as feature distillation after identifying critical nodes [10] and minimizing distribution disparity of selected nodes across new and prior models [11]. These hybrid methods have demonstrated considerable potential and achieved state-of-the-art results. Despite their effectiveness, the information preservation mechanism by existing methods remains unclear, making it challenging to develop effective solutions for GCIL. This motivates us to explore a fresh perspective: What matters in information preservation when learning from the old model to the new model for GCIL?

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We investigate the unique characteristics of catastrophic forgetting on graphs and find node semantic and graph structure shifts in GCIL. The visualization of node embeddings for new model of baseline (ERGNN [7]) and our method on old classes of CoraFull dataset are exhibited in Figure 1. The structure learned by old model is selected as target instead of original topology due to noisy real structure [12]. Five nodes belonging to two old classes are randomly selected and connected (darker edges indicate more similar features). We detect distortion in the features of baseline (Figure 1(a)) relative to those of the target (Figure 1(c)), especially nodes located within the black dotted box. The two categories can be well separated in the feature distribution of target but not in the baseline model and lead to false predictions (grey nodes in Figure 1(a)). The topological correlation is also significantly changed, node #2 is in proximity to node #1 but is distant from node #3. Surprisingly, within the representation space of baseline, node #2 appears to be moving closer to node #3 while simultaneously becoming more distant from node #1, which exacerbates catastrophic forgetting. Our method (Figure 1(b)) designs graph information preservation modules to mitigate shifts successfully.

In this paper, we inspect GCIL from the perspective of information preservation and theoretically find a key factor in reducing catastrophic forgetting risk with hybrid methods is preserving old graph information. We correspond graph information into low-frequency local-global information and highfrequency information in spatial domain. Subsequently, a Graph Spatial Information Preservation (GSIP) framework is proposed for calibrating semantic and structural shifts. In detail, the old and new representations of nodes are obtained after replay graph data is input to old and new models. The old representations of a node are locally aligned with new representations of a node and its neighbors. Further, old and new representations are globally matched after mean pooling. Finally, new representations of nodes are encouraged to mimic neighbor distance similarities that appear in old representations.

The proposed GSIP can outperform existing replay designs by up to 10% in terms of the forgetting metric on large-scale datasets. It is easy to implement and can be easily adapted to informationpreserving approaches to boost their performance. Experiments show that GSIP greatly improves

over current information-preserving methods under different experimental settings and calibrates node semantic and graph structure shifts. Our main contributions can be summarized as follows:

We provide theoretical insights into GCIL and find that preserving old graph information corresponding to low-frequency local-global and high-frequency information in spatial domain can calibrate semantic and structural shifts and reduce catastrophic forgetting risk.

We propose a simple yet effective method that utilizes node representations on old and new models to preserve node features, graph representations, and neighbor distances.

By combining with graph replay-based methods, our framework consistently achieves performance improvements across several benchmark datasets and shows the effectiveness of all the proposed components.

2 Related Work

2.1 Incremental Learning

Incremental learning requires the model to retain the capability of predicting old tasks while acquiring information about new ones [3, 13, 14, 15, 16, 17, 18]. Class incremental learning is not assigned a task ID and has greater training difficulty than task incremental learning [19, 20]. Existing methods can be categorized into three groups. Parameter isolation methods dynamically adapt the model without restricting its structure and capacity, providing distinct parameters for each task [21, 22, 23, 24, 25]. Replay-based methods replay a subset of examples stored in previous tasks or generated using generative models to mitigate forgetting [26, 27, 28, 29]. Regularization-based methods introduce an additional regularization term in the loss function to prevent modifications to crucial parameters related to previous tasks [6, 30, 31, 32, 33].

Traditional incremental learning methods for images or text lack topology learning, making it challenging to achieve effective topology mining and information preservation. By contrast, we analyze the basics of preventing catastrophic forgetting in GCIL from information preservation and solve them in the spatial domain.

2.2 Graph Incremental Learning

Graph incremental learning focuses on handling streaming graph data, and numerous methods have been developed explicitly for graph data [34, 35, 36, 37, 38, 39, 40, 41]. Topology-aware Weight Preserving (TWP) preserves key parameters and topology of previous tasks through regularization terms [1]. Experience Replay Graph Neural Network (ERGNN) framework incorporates memory replay by storing representative nodes [7]. Sparsified Subgraph Memory (SSM) stores sampled sparse subgraphs in a memory repository to preserve structural information [8]. Su et al. introduced regularization terms to mitigate catastrophic forgetting from structural drift [11]. Zhang et al. redesigned the architecture into a three-layer prototype that adaptively selects different parameter combinations for different tasks [2]. The Condense and Train (CaT) [9] framework compresses the graph into a small but informative synthetic replay graph. Furthermore, two graph incremental learning benchmarks have recently been developed [42, 43].

In comparison, GSIP combines graph information preservation to avoid catastrophic forgetting through low-frequency local-global and high-frequency information preservation.

3 Problem Analysis

Graph Class Incremental Learning (GCIL). GCIL addresses the problem of supervised node classification within the context of an expanding graph. Specifically, each G t denotes a newly emerging subgraph within the overarching graph. A G t consists of a node set V t and an edge set E t with its connectivity captured by adjacency matrix A t ∈ R n × n , where n is the number of nodes. Each vertex v is associated with node features X v and a target label Y v ∈ { 0 , 1 } c , where c represents the total number of classes. At time t , the GCIL problem denoted as /a80 GCIL is provided with a subgraph G t = { X t , A t } . The GCIL problem is formally defined with the following signature:

where f is graph neural networks and M signifies an external memory capable of storing a subset of training nodes or other useful graph data.

In the scenario of graph incremental learning, disparate tasks are mapped into distinct partitions of the graph. Once the learning for a specific task is completed, access to the corresponding data is restricted. Our objective is to learn a shared graph neural network model that distinguishes all classes from existing ones. Formally, we aim to minimize the loss caused by previously seen nodes at time step τ in /a80 GCIL , the statistical risk of catastrophic forgetting is defined as:

where θ indicates parameters of the model, H represents cross-entropy loss, and σ denotes softmax activation function.

Replay-Based GCIL. Replay-based methods store replayed nodes or subgraphs in memory M by sampling. Catastrophic forgetting is solved by maintaining the historical distribution. These methods train a new model by minimizing loss of old task nodes on new model concerning the true labels. Given node representations on new model Z new ( Z = f ( M ; θ )) , the replay loss is calculated as:

Semantic Shift and Structural Shift. Due to memory and privacy limitations, a large amount of old graph data cannot be accessed in graph incremental learning, which leads to material information of old models being gradually forgotten and seriously damages new model performance on old classes. We design two novel shift metrics measuring semantic and structural forgetting degrees when trained on novel classes to show that model divergence manifests in node-level semantics and graph-level structure aspects. On CoraFull dataset, we conduct shift tests using model representations Z old and Z new generated by classical replay method ERGNN [7]. Specifically,

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central kernel alignment [44] scheme is leveraged to compute Semantic Shift Score ( SSS X ):

where C is centering matrix C n = I n -1 /n 11 ⊤ . In particular, Structural Shift Score ( SSS A ) is derived by performing structure ̂ A inference using feature cosine similarity, then computing differences between graph representations obtained by Anonymous Walk Embedding (AWE) [45]:

SSS A ( Z old , Z new ) = 1 -COS ( AWE ( ̂ A old ) , AWE ( ̂ A new )) , ̂ A ij = ✶ [ COS ( Z i , Z j ) > δ ] , (5) where cosine similarity function COS ( a, b ) = a ⊤ b/ ( ∥ a ∥ ∥ b ∥ ) is used to calculate feature similarity degree, and δ is similarity threshold. Each task is trained for 200 epochs, and shift scores range from 0 (no shift) to 1 (completely different). We observe that SSS X and SSS A in Figure 2 gradually rise with the increase of epochs. Serious shifts are found in both node semantic and graph structure between old and new models as new classes are trained.

4 Graph Spatial Information Preservation

4.1 Graph Information Preservation

Model information preservation for GCIL can be defined as the mutual information of graph information across old and new models when considering the corresponding model parameters:

here, Z old and Z new are graph information on old and new models. We directly maximize mutual information between Z old and Z new , which inherits powerful encoding capability of θ old to θ new .

Proposition 1. The upper bound on graph information preservation can be estimated as:

we expect to maximize mutual information I ( Z old ; Z new ) , thus minimizing -I ( Z old ; Z new ) in estimation is needed.

Proposition 1 is proved in Appendix A.1, which suggests that graph information preservation is bounded with the square of Euclidean norm between old graph information Z old and new graph information Z new .

4.2 Spatial Property

Based on the spatial properties of graphs, we analyze the maintenance of graph information in spatial domain to capture complex spatial relationships between nodes and edges in graphs.

Lemma1. (Graph spatial information factorization [46]) The graph convolution between convolution kernel F and the signal x to obtain graph information is formulated as follows:

where F l ∗ x and F h ∗ x are low-/high- frequency graph information, F l = I n + ˜ D -1 2 ˜ A ˜ D -1 2 , F h = I n -˜ D -1 2 ˜ A ˜ D -1 2 , ˜ D is diagonal degree matrix with ˜ D i,i = ∑ j ˜ A i,j , and ˜ A = A + I n represents adjacency matrix with self-loop. Two pieces of information in spatial domain can be derived as follows:

where N represents node neighbors.

According to Lemma 1, there is an identity map that filters out graph information Z with graph convolution, which provides effective solutions to correspond Z old and Z new to spatial domain. For each component i , low-frequency information preserving ∥ ∥ ∆ Z l i ∥ ∥ 2 2 is defined as:

where Z old and Z new denote obtained representations on old and new models. This implies that the low-frequency information preserving is a semantic gap between the sum of node features and their neighbor features of replay data on old and new models.

Sustained global connectivity is crucial to avert the erasure of global semantic information inherited from the preceding model. As displayed in Figure 3, global semantic shift does exist. We extend the concept of first-hop neighbor nodes in the previous equation to include the entire replay graph ( i.e. multi-hop neighbors), which is denoted as:

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Similarly, the generalized low-frequency information preserving is the gap between the sum of node features and all replay data features on old and new models. It is worth noting that Eq. (10) provides a semantic comparison from a local perspective, whereas Eq. (11) compares from a global perspective.

For each component i , high-frequency information preserving ∥ ∥ ∆ Z h i ∥ ∥ 2 2 is defined as:

High-frequency information preserving captures the gap between the difference in node features and neighbor features on old and new models from topological space.

Motivated by the above concepts, we introduce the following definition:

Definition 1. (Graph spatial information preservation) A graph spatial information preservation model mainly consists of three kinds of information preservation ∥ ∆ Z ∥ 2 2 ≈ ∥ ∥ ∆ Z l ∥ ∥ 2 2 ∪ ∥ ∥ ∥ ∆ Z ̂ l ∥ ∥ ∥ 2 2 ∪ ∥ ∥ ∆ Z h ∥ ∥ 2 (defined in Eq. (10) , (11) , and (12) ).

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4.3 Instantiations for Graph Spatial Information Preservation

The above analysis yields two crucial insights: (1) old model information preservation can be solved by preserving the learned graph information; (2) graph information preserving can correspond to lowfrequency local-global information and high-frequency information from spatial domain to calibrate node semantic and graph structure shifts. Inspired by these two insights, we propose low-/highfrequency information preservation to adequately capture the old model's information. A high-level overview of GSIP framework is shown in Figure 4. The pseudo-code can be found in Appendix A.4.

Low-Frequency Information Preservation. The node representations within the previous model are derived via iterative feature integration and neighborhood communication, so it contains lowfrequency graph information. The information of old model is aligned into the neighborhood of new model to better utilize low-frequency information, which can be represented as:

where Z is the output given by model. Low-frequency local information preserving loss uses Mean Squared Error (MSE) loss to locally match representations of nodes on old model Z old with representations of nodes and their neighbors on new model Z new . For replay methods that do not explicitly save neighbors, neighbor selection can be found in Appendix A.2. It is worth noting that since inputs become sparse when converted to probabilities, the softmax followed by Kullback Leibler (KL) divergence loss is not applied [47].

Preserving global information about low-frequency components aligns old model information as a whole and prevents catastrophic forgetting. Low-frequency global information preserving loss is introduced to minimize difference between global representations of old and new models, which is defined as:

where R represents pooling method, which is computed by mean pooling R ( Z ) = 1 / |M| ∑ i ∈M Z i . Similarly, MSE loss is used to calculate global representation gaps.

High-Frequency Information Preservation. The high-frequency part of spatial domain represents the difference between the features of nodes and neighbors. The updated model preserves old topology by incorporating prior local contextual information and then mitigates heterogeneous information propagation blockage caused by smoothness assumption. Specifically, for node v i , N i denotes neighborhood node set and defines S old ( v i , N i ) as the similarity of selected node vector with adjacent nodes computed by old model:

where K ( · , · ) represents kernel function that measures pairwise distances between each node and its neighbors in the latent feature space, and element-wise absolute values K ( Z i , Z j ) = | Z i -Z j | is used. Then, we measure similarity distribution from new model S new ( v i , N i ) , which is formed by:

High-frequency information preserving is proposed to map neighborhood pairwise differences between old and new models in topological space, information loss from old structure to new structure is more easily recognized with the help of KL divergence, which is denoted as follows:

Model Learning. To combine different preserving losses, the final graph information preservation loss function is defined as:

where β and γ are loss weights.

Node classification loss is obtained by L nc = 1 / | G | ∑ i ∈ G H ( Y i , σ ( f ( G ; θ new )))) . Therefore, the overall model learning objective is the weighted sum of current node classification loss, replay loss, and graph information preserving loss:

where α replay and α gip are loss weights, and the value of α replay is relevant to the design of replayed method. More analysis about the preservation of other graph frequency information ( i.e. mid-frequency information and high-frequency global information) is given in Appendix A.3.

5 Experiments

5.1 Datasets and Setups

Datasets and Settings. We utilize five public datasets to evaluate the effectiveness of the proposed method in GCIL, the statistics of datasets are reported in Appendix B.1. Three ways of dividing classes are used: one is divided unequally, and the other two are divided equally, with equal classes per task. The first dataset is CoraFull [48], which has 70 classes, 30 classes are used as base classes for dividing unequally, then 20 classes are used as an increment, and we divide classes equally into 10 or 2 classes per task. Arxiv [49] and Reddit [50], both containing 40 classes, dividing unequally using 10 classes as base classes, then in increments of 5 classes, and dividing equally with 10 or 2 classes per task. Each dataset has 3 tasks with 2 classes per task on Cora [51] and Citeseer [51]. The latest benchmark [42] is employed to implement ERGNN, along with CaT [9] is used to implement SSM and CaT, we follow their settings in graph class incremental learning. Our implementation and detailed settings are available in Appendix B.4 and B.5.

Baselines and Metrics. Wecompare our method with the following baselines, including Finetuning, Joint, EWC [30], GEM [31], MAS [32], LwF [6], TWP [1], SSRM [11], and three replay-based methods ( i.e. ERGNN [7], SSM [8], and CaT [9]), where three graph replay methods apply our framework. Finetuning is the lower bound baseline updating the model only with newly emerging graph data. Joint is the ideal upper bound and inputs contain all previous graph data. We choose two widely used metrics to evaluate the performance of the compared methods, including Average Performance (AP) and Average Forgetting (AF) [31].

5.2 Performance Comparison

GSIP can improve the performance of existing replay-based information preservation methods.

The effect of GCIL on five datasets is presented in Table 1 and Table 2, and the results with standard deviation are presented in Appendix C.1. Joint does not provide AF due to its non-compliance with the incremental learning setting. The existing regularization term relies on the correlation between old and new classes leading to catastrophic forgetting, and some of them do not take topology into account. The hybrid method SSRM absorbs partial old information, resulting in extremely limited performance gains. GSIP consistently demonstrates significant improvements in AP and AF when combined with existing replay methods. For example, ERGNN-GSIP improves both AP and AF by about 10% on Reddit. On CoraFull, SSM-GSIP under unequal partitioning situation improves AP and AF by 4.81% and 8.06%, respectively. CaT-GSIP performs remarkably well on Arxiv, even surpassing the performance of Joint, which has a 16.22% increase in AF on a setting with an increment of 2. CaT experiences a slight decrease in AP in some settings after using GSIP. This can be

attributed to GSIP enabling better preservation of graph spatial information from old model, resulting in a lower forgetting rate. In addition, for ERGNN-GSIP, the AP and AF increase by 5.81% and 9.14% on Cora and by 13.64% and 21.74% on Citeseer. On Cora and Citeseer datasets, the AF of SSM-GSIP improves by more than 5%, and CaT-GSIP achieves the highest performance in most cases, with the AP approaching the value of Joint.

GSIP can consistently achieve excellent performance on old classes in different task IDs. The performance matrices of ERGNN on CoraFull before and after incorporating GSIP are shown in Figure 5(a) and Figure 5(b). It is difficult to remember the information of old classes before employing graph spatial information preservation. After implementing the GSIP scheme, the performance matrix demonstrates a deceleration in the forgetting process ( i.e. , the color of each column does not change much and the color deepens), which indicates that the catastrophic forgetting problem is mitigated due to the preserving of old graph information.

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GSIP can offer information preservation capability to calibrate semantic shift and structural shift. Figure 5(c) exhibits the curves of shift scores during the incremental process for ERGNN on CoraFull. It can be noted that shift scores start at a relatively high value, gradually decrease, and smooth out after graph spatial information is maintained, demonstrating that the low-frequency local-global information and high-frequency information of old model are well captured, and semantic and structural shifts are nicely calibrated.

5.3 Ablation Study

We investigate the effectiveness of low-frequency local modules (LL), low-frequency global modules (LG), and high-frequency modules (H), the experimental results use ERGNN as baseline (B). The results of ERGNN, SSM, and CaT with standard deviation are summarized in Appendix C.2. The above components are added one by one to baseline for performance comparison. From Table 3 we observe that: (1) When LL is utilized, the model can easily learn the aggregation rules of nodes and neighbors from old model locally. AP (AF) improves by about 2% (6%) to 45% (55%) over the baseline demonstrating the superiority of LL. (2) Combining LG significantly improves performance, especially on Reddit. The reason may be that larger datasets have greater overall shifts during increments. (3) H also brings significant improvements, with AP (AF) improving by about 1.6% (0.9%) to 2.4% (7.4%) over B+LL+LG on Reddit. This indicates that the H module can extract more topology information for better performance.

5.4 Further Analysis

Hyper-Parameter Analysis. We analyze the impact of the number of storage nodes for each task # M on performance. As depicted in Figure 5(d), it can be observed that the proposed method consistently outperforms the original method in terms of the -AF metric (the lower, the better), regardless of the value of # M . Interestingly, even with less memory, the proposed method still achieves better performance. CaT cannot be trained on 400 nodes due to Cuda memory constraints. We analyze the impact of loss weight α gip on ERGNN, SSM, and CaT across CoraFull, Arxiv, and Reddit datasets with increments of 2 in Figure 6. For ERGNN, SSM, and CaT, α gip, 1 is set to [1 , 1 , 0 . 1] , [0 . 01 , 0 . 01 , 0 . 01] , and [0 . 1 , 0 . 01 , 0 . 01] for three datasets. It can be observed that the performance change is not as significant with the variation of α gip on SSM and CaT. However, different α gip has a greater impact on performance with ERGNN-GSIP. The possible reason is that ERGNN selects representative nodes for replay, which may cause class imbalance and topology discarding. For ERGNN, SSM, and CaT, the optimal hyper-parameters α gip on three datasets are [50 , 10 , 1] , [0 . 1 , 0 . 1 , 0 . 1] , and [1 , 0 . 5 , 0 . 5] . Because of space limitation, we provide more curves about # M in Appendix C.3 and hyper-parameter analysis of loss weights β and γ in Appendix C.4.

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Visulization. To qualitatively demonstrate the effectiveness of our representations, we adopt tSNE [52] to visualize the learned node embeddings. After learning the last task, Figure 7(a) and Figure 7(b) show the results of the learned node embeddings in Task 1 on CoraFull, while Figure 7(c) and Figure 7(d) demonstrate the results of the last task. We can clearly observe that GSIP possesses better representation ability by considering representations and classifying old and new classes well.

6 Conclusion

We contribute to the literature of GCIL by addressing the issue of information preservation from old model when adapting to new classes. The key insight is that preserving graph information from spatial domain plays a vital role in preserving information about old model, and subsequently calibrates semantic and structural shifts and reduces catastrophic forgetting risk. To accomplish this objective, we introduce a framework, GSIP, which utilizes the outputs of nodes in old model to diffuse the outputs of new model and its neighbors, then aligns the outputs of new model with old model after pooling. Finally, GSIP maintains kernel distance of neighbor pairs on both old and new models. The graph information is remembered by low-frequency local-global information preserving and high-frequency information preserving in feature and topological space. Evaluations over benchmark datasets show the superiority of GSIP in handling different dataset splitting cases. In the future, we will investigate comprehensive analysis for the preservation of complicated graph signals.

References

Huihui Liu, Yiding Yang, and Xinchao Wang. Overcoming catastrophic forgetting in graph neural networks. In Thirty-Fifth AAAI Conference on Artificial Intelligence , pages 8653-8661, 2021.

Xikun Zhang, Dongjin Song, and Dacheng Tao. Hierarchical prototype networks for continual graph representation learning. IEEE Trans. Pattern Anal. Mach. Intell. , 45(4):4622-4636, 2023.

Matthias De Lange, Rahaf Aljundi, Marc Masana, Sarah Parisot, Xu Jia, Ales Leonardis, Gregory G. Slabaugh, and Tinne Tuytelaars. A continual learning survey: Defying forgetting in classification tasks. IEEE Trans. Pattern Anal. Mach. Intell. , 44(7):3366-3385, 2022.

Xinting Hu, Kaihua Tang, Chunyan Miao, Xian-Sheng Hua, and Hanwang Zhang. Distilling causal effect of data in class-incremental learning. In IEEE Conference on Computer Vision and Pattern Recognition , pages 3957-3966, 2021.

Jie Cai, Xin Wang, Chaoyu Guan, Yateng Tang, Jin Xu, Bin Zhong, and Wenwu Zhu. Multimodal continual graph learning with neural architecture search. In The ACM Web Conference , pages 1292-1300, 2022.

Zhizhong Li and Derek Hoiem. Learning without forgetting. IEEE Trans. Pattern Anal. Mach. Intell. , 40(12):2935-2947, 2018.

Fan Zhou and Chengtai Cao. Overcoming catastrophic forgetting in graph neural networks with experience replay. In Thirty-Fifth AAAI Conference on Artificial Intelligence , pages 4714-4722, 2021.

Xikun Zhang, Dongjin Song, and Dacheng Tao. Sparsified subgraph memory for continual graph representation learning. In IEEE International Conference on Data Mining , pages 1335-1340, 2022.

Yilun Liu, Ruihong Qiu, and Zi Huang. Cat: Balanced continual graph learning with graph condensation. In IEEE International Conference on Data Mining , pages 1157-1162, 2023.

Seoyoon Kim, Seongjun Yun, and Jaewoo Kang. Dygrain: An incremental learning framework for dynamic graphs. In Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence , pages 3157-3163, 2022.

Junwei Su, Difan Zou, Zijun Zhang, and Chuan Wu. Towards robust graph incremental learning on evolving graphs. In International Conference on Machine Learning , volume 202, pages 32728-32748, 2023.

Seungyoon Choi, Wonjoong Kim, Sungwon Kim, Yeonjun In, Sein Kim, and Chanyoung Park. DSLR: diversity enhancement and structure learning for rehearsal-based graph continual learning. In The ACM Web Conference , pages 733-744, 2024.

Dipam Goswami, Yuyang Liu, Bartlomiej Twardowski, and Joost van de Weijer. Fecam: Exploiting the heterogeneity of class distributions in exemplar-free continual learning. In Advances in Neural Information Processing Systems , pages 1-14, 2023.

Yaoyao Liu, Bernt Schiele, and Qianru Sun. RMM: reinforced memory management for classincremental learning. In Advances in Neural Information Processing Systems , pages 3478-3490, 2021.

Qi-Wei Wang, Da-Wei Zhou, Yi-Kai Zhang, De-Chuan Zhan, and Han-Jia Ye. Few-shot classincremental learning via training-free prototype calibration. In Advances in Neural Information Processing Systems , pages 1-17, 2023.

Depeng Li, Tianqi Wang, Junwei Chen, Qining Ren, Kenji Kawaguchi, and Zhigang Zeng. Towards continual learning desiderata via hsic-bottleneck orthogonalization and equiangular embedding. In Thirty-Eighth AAAI Conference on Artificial Intelligence , pages 13464-13473, 2024.

Liyuan Wang, Jingyi Xie, Xingxing Zhang, Mingyi Huang, Hang Su, and Jun Zhu. Hierarchical decomposition of prompt-based continual learning: Rethinking obscured sub-optimality. In Advances in Neural Information Processing Systems , pages 1-23, 2023.

Qi Chen, Changjian Shui, Ligong Han, and Mario Marchand. On the stability-plasticity dilemma in continual meta-learning: Theory and algorithm. In Advances in Neural Information Processing Systems , pages 1-15, 2023.

Marc Masana, Xialei Liu, Bartlomiej Twardowski, Mikel Menta, Andrew D. Bagdanov, and Joost van de Weijer. Class-incremental learning: Survey and performance evaluation on image classification. IEEE Trans. Pattern Anal. Mach. Intell. , 45(5):5513-5533, 2023.

Songsong Tian, Lusi Li, Weijun Li, Hang Ran, Xin Ning, and Prayag Tiwari. A survey on few-shot class-incremental learning. Neural Networks , 169:307-324, 2024.

Andrei A. Rusu, Neil C. Rabinowitz, Guillaume Desjardins, Hubert Soyer, James Kirkpatrick, Koray Kavukcuoglu, Razvan Pascanu, and Raia Hadsell. Progressive neural networks. CoRR , abs/1606.04671, 2016.

Jaehong Yoon, Eunho Yang, Jeongtae Lee, and Sung Ju Hwang. Lifelong learning with dynamically expandable networks. In Sixth International Conference on Learning Representations , pages 1-11, 2018.

Yue Wu, Yinpeng Chen, Lijuan Wang, Yuancheng Ye, Zicheng Liu, Yandong Guo, and Yun Fu. Large scale incremental learning. In IEEE Conference on Computer Vision and Pattern Recognition , pages 374-382, 2019.

Mitchell Wortsman, Vivek Ramanujan, Rosanne Liu, Aniruddha Kembhavi, Mohammad Rastegari, Jason Yosinski, and Ali Farhadi. Supermasks in superposition. In Advances in Neural Information Processing Systems , pages 15173-15184, 2020.

Johannes von Oswald, Christian Henning, João Sacramento, and Benjamin F. Grewe. Continual learning with hypernetworks. In Eighth International Conference on Learning Representations , pages 1-12, 2020.

Hanul Shin, Jung Kwon Lee, Jaehong Kim, and Jiwon Kim. Continual learning with deep generative replay. In Advances in Neural Information Processing Systems , pages 2990-2999, 2017.

Jeremias Knoblauch, Hisham Husain, and Tom Diethe. Optimal continual learning has perfect memory and is np-hard. In Proceedings of the Thirty-Seventh International Conference on Machine Learning , volume 119, pages 5327-5337, 2020.

Lucas Caccia, Eugene Belilovsky, Massimo Caccia, and Joelle Pineau. Online learned continual compression with adaptive quantization modules. In Proceedings of the Thirty-Seventh International Conference on Machine Learning , volume 119, pages 1240-1250, 2020.

Liyuan Wang, Xingxing Zhang, Kuo Yang, Longhui Yu, Chongxuan Li, Lanqing Hong, Shifeng Zhang, Zhenguo Li, Yi Zhong, and Jun Zhu. Memory replay with data compression for continual learning. In The Tenth International Conference on Learning Representations , pages 1-13, 2022.

James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaume Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Grabska-Barwinska, et al. Overcoming catastrophic forgetting in neural networks. Proceedings of the national academy of sciences , 114(13):3521-3526, 2017.

David Lopez-Paz and Marc'Aurelio Ranzato. Gradient episodic memory for continual learning. In Advances in Neural Information Processing Systems , pages 6467-6476, 2017.

Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In European Conference on Computer Vision , volume 11207, pages 144-161, 2018.

Yilin Lyu, Liyuan Wang, Xingxing Zhang, Zicheng Sun, Hang Su, Jun Zhu, and Liping Jing. Overcoming recency bias of normalization statistics in continual learning: Balance and adaptation. In Advances in Neural Information Processing Systems , pages 1-12, 2023.

Qiao Yuan, Sheng-Uei Guan, Pin Ni, Tianlun Luo, Ka Lok Man, Prudence W. H. Wong, and Victor Chang. Continual graph learning: A survey. CoRR , abs/2301.12230, 2023.

Falih Gozi Febrinanto, Feng Xia, Kristen Moore, Chandra Thapa, and Charu Aggarwal. Graph lifelong learning: A survey. IEEE Comput. Intell. Mag. , 18(1):32-51, 2023.

Zonggui Tian, Du Zhang, and Hong-Ning Dai. Continual learning on graphs: A survey. CoRR , abs/2402.06330, 2024.

Dongjie Wang, Zhengzhang Chen, Yanjie Fu, Yanchi Liu, and Haifeng Chen. Incremental causal graph learning for online root cause analysis. In Proceedings of the Twenty-Ninth ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages 2269-2278, 2023.

Chen Wang, Yuheng Qiu, Dasong Gao, and Sebastian A. Scherer. Lifelong graph learning. In IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 13709-13718, 2022.

Bin Lu, Xiaoying Gan, Lina Yang, Weinan Zhang, Luoyi Fu, and Xinbing Wang. Geometer: Graph few-shot class-incremental learning via prototype representation. In The Twenty-Eighth ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages 1152-1161, 2022.

Thanh Duc Hoang, Do Viet Tung, Duy-Hung Nguyen, Bao-Sinh Nguyen, Huy Hoang Nguyen, and Hung Le. Universal graph continual learning. Trans. Mach. Learn. Res. , 1(1):1-15, 2023.

Jiajun Liu, Wenjun Ke, Peng Wang, Ziyu Shang, Jinhua Gao, Guozheng Li, Ke Ji, and Yanhe Liu. Towards continual knowledge graph embedding via incremental distillation. In Thirty-Eighth AAAI Conference on Artificial Intelligence , pages 8759-8768, 2024.

Xikun Zhang, Dongjin Song, and Dacheng Tao. CGLB: benchmark tasks for continual graph learning. In Advances in Neural Information Processing Systems , pages 13006-13021, 2022.

Jihoon Ko, Shinhwan Kang, and Kijung Shin. Begin: Extensive benchmark scenarios and an easy-to-use framework for graph continual learning. CoRR , abs/2211.14568, 2022.

Simon Kornblith, Mohammad Norouzi, Honglak Lee, and Geoffrey E. Hinton. Similarity of neural network representations revisited. In Proceedings of the Thirty-Sixth International Conference on Machine Learning , volume 97, pages 3519-3529, 2019.

Eunjeong Jeong, Seungeun Oh, Hyesung Kim, Jihong Park, Mehdi Bennis, and Seong-Lyun Kim. Communication-efficient on-device machine learning: Federated distillation and augmentation under non-iid private data. CoRR , abs/1811.11479, 2018.

Lirong Wu, Haitao Lin, Yufei Huang, Tianyu Fan, and Stan Z. Li. Extracting low-/highfrequency knowledge from graph neural networks and injecting it into mlps: An effective gnn-to-mlp distillation framework. In Thirty-Seventh AAAI Conference on Artificial Intelligence , pages 10351-10360, 2023.

Chaitanya K. Joshi, Fayao Liu, Xu Xun, Jie Lin, and Chuan Sheng Foo. On representation knowledge distillation for graph neural networks. IEEE Trans. Neural Networks Learn. Syst. , 35(4):4656-4667, 2024.

Aleksandar Bojchevski and Stephan Günnemann. Deep gaussian embedding of graphs: Unsupervised inductive learning via ranking. In Sixth International Conference on Learning Representations , pages 1-11, 2018.

Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. In Advances in Neural Information Processing Systems , pages 22118-22133, 2020.

William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Advances in Neural Information Processing Systems , pages 1024-1034, 2017.

Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Gallagher, and Tina EliassiRad. Collective classification in network data. AI Mag. , 29(3):93-106, 2008.

Laurens van der Maaten. Accelerating t-sne using tree-based algorithms. J. Mach. Learn. Res. , 15(1):3221-3245, 2014.

Sungsoo Ahn, Shell Xu Hu, Andreas C. Damianou, Neil D. Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In IEEE Conference on Computer Vision and Pattern Recognition , pages 9163-9171, 2019.

Jincheng Huang, Lun Du, Xu Chen, Qiang Fu, Shi Han, and Dongmei Zhang. Robust mid-pass filtering graph convolutional networks. In the ACM Web Conference , pages 328-338, 2023.

Haitong Luo, Xuying Meng, Suhang Wang, Hanyun Cao, Weiyao Zhang, Yequan Wang, and Yujun Zhang. Spectral-based graph neural networks for complementary item recommendation. In Thirty-Eighth AAAI Conference on Artificial Intelligence , pages 8868-8876, 2024.

A Method

A.1 The Proof of Proposition 1

Proposition 1. The upper bound on graph information preservation can be estimated as:

we expect to maximize mutual information I ( Z old ; Z new ) , thus minimizing -I ( Z old ; Z new ) in estimation is needed.

Proof. The mutual information of graph information on old model and new model [53] can be equivalent to:

where expectations are over distribution p ( Z old , Z new ) , H ( Z old ) has been removed since it is constant with respect to optimized parameters. The reason for the inequality is the non-negativity of entropy H and Kullback-Leiber divergence D KL .

We expect to maximize mutual information I ( Z old ; Z new ) , so we need to minimize -I ( Z old ; Z new ) in the loss function, hence we can obtain:

The conditional likelihood is maximized to fit the information of old model, and the new model receives compressed information needed to recover old model. A Gaussian distribution with mean µ and variance σ is employed to estimate variational distribution q ( Z old | Z new ) , which is expressed as follows:

where C is constant. Mean squared error matching can be seen as a specific instance of the above formula when µ ( Z new ) = Z new and σ = 1 , thus -I ( Z old ; Z new ) ≤ ∥ Z old -Z new ∥ 2 2 .

A.2 Neighbor Selection

Some replay-based methods do not explicitly save topology, so we treat nodes with high representation similarity and label correlation on old model as neighbors for each node when computing lowfrequency local information preserving loss. Nodes whose feature similarity is greater than the given threshold and whose labels are the same can be neighbors, formulated as follows:

where the cosine similarity function COS ( Z i , Z j ) = Z ⊤ i Z j / ( ∥ Z i ∥ ∥ Z j ∥ ) is used to calculate the degree of feature similarity, and ̂ δ is similarity threshold.

We only use node feature similarity when calculating the loss of high-frequency information preservation for neighbor selection. The absence of label correlation captures the distance between nodes on different classes, which is conducive to the model to distinguish different classes. The neighborhood selection process is expressed as follows:

where δ is the similarity threshold.

A.3 The Analysis of Other Graph Frequency Information Preservation

We perform analyses and experiments to assess the preservation of various aspects of graph frequency information, including mid-frequency information and high-frequency global information.

Mid-Frequency Information Preservation. According to the definition of mid-frequency filtering graph convolutional networks [54, 55], the mid-frequency convolution can be expressed as:

Through a similar analysis as mentioned above, mid-frequency information preservation is defined as:

where N 2 is the second-hop neighbors of nodes. The distinction between mid-/high- frequency information preservation lies in that mid-frequency signals calculate the differences between the node and its second-hop neighbors.

High-Frequency Global Information Preservation. The general formula for high-frequency global information preservation is represented as follows:

It implies that every node in replayed graph needs to calculate disparity with other nodes. Since graph neural network assumes that neighboring nodes have similar representations, the penalizing distance between nodes and their neighbors at multiple hops away is redundant and does not contribute to structural preservation. Moreover, the inclusion of this term imposes an optimization burden and exhibits high time complexity ( O ( |M| 2 · ) , where denotes the dimensions of the hidden spaces).

❦ ❦ We add mid-frequency information preservation ( M ) and high-frequency global information preservation ( HG ) to GSIP in Table 4, which can yield a slight performance improvement in some cases. However, it does not lead to better performance enhancements or outstanding results. The possible reason is that the preservation of first-hop neighbors is sufficient to calibrate structural shift.

A.4 Algorithm

The proposed method is summarized in Algorithm 1.

Algorithm 1 Framework of GSIP

Input: At time step t > 1 : New input G , Memory M , Graph neural networks f , Labels Y , Learned parameter θ old , Max epochs U , Loss weights α replay , α gip

Output: Parameter θ new which can mitigate catastrophic forgetting of preceding classes

1: Initialize θ new at random

2: for u = 1 to U do

3: L nc = ℓ ce ( Y G , f ( G ; θ new ))

4: L replay = ℓ ce ( Y M , f ( M ; θ new ))

5: L gip = ℓ reg ( f ( M ; θ old ) , f ( M ; θ new ))

6: θ new ← arg min L = L nc + α replay L replay + α gip L gip

7: end for

8: Add selected nodes to memory M

9: return Parameter θ new

B Implementation Details

B.1 Datasets

As illustrated in Table 5, we utilize five public datasets to evaluate the effectiveness of our proposed method in graph class incremental learning. Three different ways for partitioning datasets are employed: one involves an unequal division, where more classes are designated as base classes to enhance model robustness, while the remaining classes are treated as novel classes; the other two ways involve an equal division, with an equal number of classes allocated per task. The first dataset is CoraFull [48], which encompasses 70 classes. For the unequal division, 30 classes are used as base classes, and an additional 20 classes are selected as increments. Additionally, the classes are divided equally into either 10 or 2 classes per task. Arxiv [49] and Reddit [50], both of which consist of 40 classes. In the unequal division, 10 classes are designated as base classes, with increments of 5 classes. Similarly, the classes are evenly divided into either 10 or 2 classes per task. Each dataset has 3 tasks with 2 classes per task on Cora [51] and Citeseer [51].

B.2 Baselines

In this subsection, we introduce the baselines in the main paper. These baselines are as follows:

Finetuning is the lower bound baseline updating the model only with newly emerging graph data.

Joint is the ideal upper bound and inputs contain all previous graph data.

Elastic Weight Consolidation (EWC) [30] quadratically penalizes model weights according to their importance to previous tasks.

Gradient Episodic Memory (GEM) [31] modifies gradients of the current task using gradients computed from stored graph data.

Memory Aware Synapses (MAS) [32] utilizes analysis of parameter prediction as the importance of parameters when adding regularization terms.

Learning without Forgetting (LwF) [6] utilizes information distillation to reduce the discrepancy between old and new models.

Topology-aware Weight Preserving (TWP) [1] preserves the key parameters and topology of the previous task through regularization terms.

Structural Shift Risk Mitigation (SSRM) [11] introduces regularization terms to mitigate catastrophic forgetting from structural drift.

Experience Replay Graph Neural Network (ERGNN) [7] framework incorporates memory replay by storing representative nodes.

Sparsified Subgraph Memory (SSM) [8] stores sampled sparse subgraphs in memory repository to preserve structural information.

The Condense and Train (CaT) [9] framework compresses the graph into a small but informative synthetic replay graph.

B.3 Metrics

We choose two widely used metrics to evaluate the performance of the compared methods, including Average Performance (AP) and Average Forgetting (AF) [31]. When the model learns the latest task, all previous tasks are evaluated and a lower triangular performance matrix W = { w tt ′ } ∈ w τ × τ is formed, where w tt ′ is node classification accuracy on task t after learning task t ′ ( t ≤ t ′ ) and τ is the total number of tasks. Average performance AP = 1 /τ ∑ τ t =1 w τ,t evaluates the average performance of model on previous task after learning from new task τ . Average Forgetting AF = 1 / ( τ -1) ∑ τ -1 t =1 ( w τ,t -w t,t ) represents the average performance degradation on previous tasks after learning from task τ .

B.4 Reproducibility

Our method is trained using a fixed random seed to ensure the consistency and verifiability of results. We are committed to open-sourcing and sharing our code to promote academic collaboration and knowledge sharing, enabling other researchers to reproduce and validate our experimental results.

B.5 Detailed Settings

Our model is deployed in PyTorch with an NVIDIA RTX 3090 GPU and trained with 200 epochs for every task. We use Adam with weight decay for optimization, and the learning rate is set to 0.005. We use a two-layer GCN with a hidden dimension 256 as the backbone. All results are reported in means and standard deviations over 3 trials. The train-validation-test splitting ratios are 60%, 20%, and 20% for all datasets. The train-validation-test split is achieved through random sampling, resulting in variations in performance across different rounds of random sampling. ̂ δ is set to 0.99 and the search space of δ is { 0 . 5 , 0 . 6 , 0 . 7 , 0 . 8 , 0 . 9 } . Table 6 is the hyper-parameters we adopt from [42] and [9].

C Experimental Results

C.1 Performance Comparison

The effect of GCIL on five datasets with standard deviation is presented in Table 7 and 8. GSIP improves existing information preservation methods under different dataset splitting scenarios. The performance matrices of SSM and CaT on CoraFull before and after incorporating GSIP are shown in Figure 8 and Figure 9. Remembering information from previous classes becomes challenging without the implementation of the proposed GSIP. The performance matrix illustrates a deceleration in the forgetting process after adopting the GSIP scheme. This is evident by the minimal changes and deepening in color of each column, indicating mitigation of the catastrophic forgetting problem. This is achieved through the preservation of information from previous model.

C.2 Ablation Study

Efficiency. As shown in Table 9, Table 10, and Table 11, the consequences of ablation experiments with standard deviation for ERGNN, SSM, and CaT as baselines (B) are presented. We investigate the effectiveness of low-frequency local modules (LL), low-frequency global modules (LG), and high-frequency modules (H). The above components are added one by one to baselines for performance comparison. B is the baseline. B+LL indicates that it only uses low-

frequency local preservation. B+LL+LG represents that it uses low-frequency local-global preservation. B+LL+LG+H is the full model, which uses low-frequency and high-frequency preservation. All the components are effective and can bring great benefits to the model in performance improvement.

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C.3 Hyper-Parameter Analysis of Memory Size

We analyze the impact of the number of storage nodes for each task # M on performance of each task that has 2 classes. As depicted in Figure 11-Figure 15, it can be observed that the proposed method consistently outperforms the original method in terms of the AP (the higher, the better) and -AF metric (the lower, the better), regardless of the value of # M . CaT cannot be trained with 400 nodes on CoraFull due to Cuda memory constraints. Interestingly, despite having less memory, the proposed method demonstrates superior performance across three datasets. Furthermore, the performance remains relatively consistent when storing 200 or 400 nodes, indicating that our method does not incur higher storage costs. Notably, storing only 10 nodes per task yields performance comparable to storing 400 nodes on Reddit, highlighting the superiority of our approach.

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As shown in Figure 16, Figure 17, and Figure 18, the analysis for two hyper-parameters, loss weights β and γ on ERGNN, SSM, and CaT in terms of AF is conducted, and the results are in an experimental setting of increment 2. For ERGNN, β 1 is set to [ 2 e -5 , 1 e -1 , 1 e -5 ] and γ 1 is set to [ 2 e -2 , 1 e -8 , 1 e -4 ] for different datasets. For SSM, β 1 is set to [ 1 , 1 , 10 ] and γ 1 is set to [ 1 e -7 , 1 e -8 , 1 e -3 ] for three datasets. For CaT, β 1 is set to [ 1 e -1 , 2 , 2 e -4 ] and γ 1 is set to [ 1 e -1 , 1 e -6 , 2 e -1 ] for three datasets. We notice that the model performance remains unaffected by changes in β when γ is set to 0 and by changes in γ when β reaches its optimal value.

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C.5 Visualization

To qualitatively demonstrate the effectiveness of representations, we utilize t-SNE [52] to visualize the node embeddings of ERGNN and ERGNN-GSIP. After learning the last task, Figure 19(a) and Figure 19(b) display the results of the learned node embeddings in Task 1 on Reddit, while Figure 19(c) and Figure 19(d) illustrate the results of the last task. GSIP exhibits superior representation ability, effectively considering representations and accurately classifying old and new classes.

(a) ERGNN, Task 1

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(c) ERGNN, Task 7

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C.6 Time Complexity Analysis

The time complexity of framework mainly comes from three aspects: (1) node classification O ( | V | ❦ G ❦ + |E| ❦ + | V | ❦ ) , (2) replay scheme O ( |M| ❦ G ❦ + |E M | ❦ + |M| ❦ ) , and (3) graph spatial information preservation O ( |E M | ❦ + ❦ ) . The total time complexity is O ( | V | ❦ G ❦ + |M| ❦ G ❦ + | V | ❦ + |M| ❦ + |E| ❦ + |E M | ❦ + ❦ ) , where V and M are subgraph vertices and memory, E and E M are edge sets of subgraph vertices and memory, then ❦ G and ❦ denote the dimensions of inputs and hidden spaces. The time complexity increases linearly compared with baselines. The running time on CoraFull is presented in Table 12. For ERGNN, | V | ≫|M| leads to phenomenon that the higher the number of tasks, the shorter training time. On the contrary, more tasks result in longer training time due to the properties of compressed graphs in SSM and CaT.

D Discussion

D.1 Limitation

The primary limitation of GSIP lies in its focus on replayed designs and the lack of connection to other methods. Also, the paper does not examine other GCIL settings on the graph, such as the lack of a clear task boundary, which would be an interesting direction to explore in the future.

D.2 Broader Impact

Considering the broader implications of our work, we posit that the proposed framework for information preservation of the old graph model will support the development of systems in an open environment based on machine learning. However, accessing old data may raise privacy concerns, and the dynamic updating of systems could inadvertently marginalize under-represented groups, potentially have a negative impact on outcomes and interfere with fair decision-making.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies graph class incremental learning (GCIL), which requires the model to classify emerging nodes of new classes while remembering old classes. The paper provides a theoretical analysis of GCIL and finds that preserving old graph information that corresponds to local-global low-frequency and high-frequency components in the spatial domain can calibrate semantic and structural shifts to reduce catastrophic forgetting risk. Then, the paper proposes a method to utilise node representations on old and new models to preserve node features, graphs, and neighbor distances.\n\nSTRENGTHS:\n1. The paper studies graph class incremental learning (GCIL), addressing the problem of supervised node classification within the context of an expanding graph. The motivation is interesting, and the challenge really exists in the real-world graph tasks.\n2. The paper gives a theoretical analysis of GCIL and divides the framework into low and high-frequency modules to preserve old information.\n3. The paper evaluates the proposed method on three public datasets and the better results compared with baselines show the effectiveness of the proposed method.\n\nWEAKNESSES:\n1. The motivation for preserving global low-frequency information about the graph is uncleared. Why only separate local and global components for low-frequency and not separate local and global components for high-frequency? More theoretical analysis and studies are needed.\n2. Why is the experimental setting for each dataset's tasks configured as described in the paper? Is it following previous research works? It is highly recommended to provide results for different task settings.\n3. It is highly recommended to add the implementation details, especially the hyper-parameter for each dataset in the paper.\n4. More hyper-parameter experiments about the method are needed. For example, the parameter sensitivity analysis about the \\alpha.\n\nQUESTIONS:\nPlease see the above weakness.\n\nLIMITATIONS:\nThe paper presents several limitations: The primary limitation of GSIP lies in its focus on replayed designs and the lack of connection to other methods. Also, the paper does not examine other GCIL settings on the graph, such as the lack of a clear task boundary, which would be an interesting direction to explore in the future.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies the graph class incremental learning problem, and specially focuses on theoretically investigating what matters in preserving the information from the old classes. \n\nThe authors theoretically demonstrate that maintaining the graph information can preserve information of the old model, such that the node semantic and graph structure shift can be overcome. Based on this finding, the authors split the graph information into low- and high frequency parts, and designed alignment based techniques to preserve these two types of information.\n\nThe proposed GSIP can be integrated with different baseline methods, and the empirical results on three datasets demonstrated the effectiveness of GSIP.\n\nSTRENGTHS:\n1. The proposed work includes both theoretical foundations and empirical improvements.\n\n2. The semantic shift and structural shift are quantified and demonstrated on CoraFull dataset, which makes the mechanism of the forgetting more tangible.\n\nWEAKNESSES:\n1. The writing requires improvements. The abstract and introduction do not provide a clear overview of the work, since there are multiple unclear terms like graph information and local-global parts. I would recommend the authors to revise this part. At least these terms should be briefly introduced in Introduction before being used.\n\n2. The notations are not consistent. In 4.1, the bold Z-old and Z-new seem to be same as the Z-old and Z-new above in Section 3, but are in different fonts.\n\nQUESTIONS:\n1. What is the rationale behind the definition of the structural shift score? Does this implies the difference between each node and its neighbors?\n\n2. The forgetting is demonstrated through the node semantic shift and the structural shift, why is the following analysis conducted from the low- and high-frequency perspectives?\n\nLIMITATIONS:\nThe authors have discussed limitations regarding the method design, positioning of the work against other baselines, and empirical settings.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-11"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes an innovative framework named graph spatial information preservation (GSIP), which alleviates catastrophic forgetting in graph class incremental learning (GCIL), by preserving low-frequency local-global information and high-frequency information in both the feature space and the topological space.\n\nSTRENGTHS:\nStrength 1: This paper has good originality to identify a unique challenge in GCIL task, which is the lack of theoretical understanding of information preservation.  \n\n \n\nStrength 2: This paper provides detailed mathematical derivations to explain how catastrophic forgetting can be alleviated by preserving graph information in the spatial domain.  \n\n \n\nStrength 3: This paper conducts comprehensive experiments, along with ablation studies, hyper-parameter tuning analyses, and case studies, to demonstrate the effectiveness of the proposed framework.\n\nWEAKNESSES:\nWeakness 1: The generalizability regarding Figure 1 could be further improved.  \n\nWeakness 2: The writing in terms of clarity and conciseness could be further improved.  \n\nWeakness 3: It is a bit confusing to take another average (MSE) immediately after an average (mean pooling). The reasoning for Equation 14 could be better clarified with more details.\n\nQUESTIONS:\nQuestion 1: From line 50 to line 52, how to quantitatively understand “a larger distortion”? According to Figure 1, does “a larger distortion” indicate that the black dotted ellipse in Figure 1 (a) has a longer major axis than that in Figure 1 (c)? If so, since the five nodes are randomly selected and connected, then what about other red nodes having the same class but not included within the black dotted ellipse?  \n\n\n \n\nQuestion 2: Do the parameter isolation methods, the replay methods, and the regulation methods mentioned in the Introduction section (from line 28 to line 37), have the same meaning as those mentioned in the Related Work section (from line 83 to line 89)?  \n\n\n \n\nQuestion 3: From line 216 to line 217, based on Equation 14, since the mean pooling has been applied, what is the motivation and reasoning to introduce the mean squared error (MSE) loss to evaluate global representation gaps?\n\nLIMITATIONS:\nThe authors have not adequately addressed the limitations and the potential negative societal impact of their work.  \n\nSuggestion for improvement: Data privacy should be discussed.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper focuses on the challenge of graph class incremental learning (GCIL), where a model must classify new nodes of emerging classes while retaining knowledge of previously learned classes. The primary issue of GCIL is identified as catastrophic forgetting, where new learning overwrites old knowledge. To address this, the author introduce the concept of information preservation, suggesting that preserving graph information can help mitigate semantic and structural shifts that cause forgetting. The paper proposes the Graph Spatial Information Preservation (GSIP) framework, which preserves both low-frequency (local-global) and high-frequency information in the graph's spatial domain. GSIP aligns old and new node representations, ensuring old graph information is retained. Experimental results show that GSIP significantly reduces forgetting by up to 10% on large datasets compared to existing methods.The framework is shown to be effective across various benchmark datasets.\n\nSTRENGTHS:\n- The proposed method GSIP preserves both low-frequency and high frequency information of a graph, which can alleivate the catastrophic forgetting issue of GCIL.\n- The proposed method is proved to be effective across various benchmark datasets.\n\nWEAKNESSES:\n- The design of the method, which only capture low and high frequency information is not comprehensive. There are more complicated signals to capture, e.g., many spectral GNNs are designed for that.\n- The method is only evaluated on 3 datasets, corafull, arxiv and reddit. It would be great to be evaluated on more datasets.\n\nQUESTIONS:\n- Why the method only consider the low and high frequency information in the graph’s spatial domain? Except for these two frequency, there are still other frequency information worth to be captured, e.g., medium, and more to capture complicated signals.\n- Why for the loss function (Equation 19), there is only one scaling factor \\alpha for the second loss term?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-13"}