Towards Continuous Reuse of Graph Models via Holistic Memory Diversification

## Abstract

Abstract This paper addresses the challenge of incremental learning in growing graphs with increasingly complex tasks. The goal is to continually train a graph model to handle new tasks while retaining its inference ability on previous tasks.
Existing methods usually neglect the importance of memory diversity, limiting in effectively 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, we propose a diversified memory generation replay method. This method first 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.
Finally, we evaluate our model on node classification tasks involving increasing class numbers. Extensive experimental results on publicly accessible datasets demonstrate the superiority of DMSG over state-of-the-art methods.

## 1 Introduction

Graphs, owing to their flexible relational data structures, are widely employed for many applications in various domains, including social networks [, ], recommendation systems [, ], and bioinformatics []. 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 on growing graph data [, , ].
However, as the growing graph in Figure 1 shows, when new nodes are added, the associated learning tasks can become increasingly complex.
For 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 to a specific task [, , ] 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 is introduced.
In recent years, model reuse via incremental learning [, ], also known as 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.

Figure: Figure 1: An example of incremental learning in 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.
Refer to caption: x1.png

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 to store the knowledge gained from previous tasks. When learning a 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.
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 [, ] 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 [, ] concentrate on memory selection, neglecting to broaden the boundaries of memory within the buffer, resulting in a discount in replay.
Finding an effective way to replay knowledge from these limited nodes is critical to incremental learning in graphs.

In this paper, we propose a 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 Retention: 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 algorithm, 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 Enhanced Knowledge Memorization: we introduce a 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 embedding learning technique and a reconstruction-based decoder. These are designed to preserve the integrity of the information and strengthen the generalization of the synthesized node embeddings on the label space, ensuring the essential knowledge is carried over accurately and effectively.

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 representative 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. (3) Extensive experiments on various incremental learning benchmark graphs demonstrate the superiority of the proposed DMSG over state-of-the-art methods.

## 2 Problem Formulation

In this section, we present the formulation for the incremental learning problem in growing graphs.
Generally, a growing graph is represented by a sequential of $m$ snapshots: $G=\{G^{1},G^{2},...,G^{m}\}$, and each snapshot corresponds to the inception of a new task, represented as $\mathcal{T}=\{\mathcal{T}^{1},\mathcal{T}^{2},...,\mathcal{T}^{m}\}$. Each graph $G^{i}$ is evolved from the previous graph $G^{i-1}$, i.e., $G^{i-1}\subset G^{i},\forall i\in 2,...,m.$, and each learning task $\mathcal{T}^{i}$ is more complex than the previous task $\mathcal{T}_{i-1}$.
This paper specifies the learning tasks to classification tasks, i.e., the number of classes increases alongside graph growth, increasing the task complexity.
In this scenario, we aim to continually learn a model $f(\theta)$ on $\mathcal{T}$.
For the $t$-th step, the task $\mathcal{T}^{t}$ incorporates a training node set $\mathcal{V}^{t}$ with previously unseen labels (i.e., novel classes), where each vertex $v_{i}\in\mathcal{V}^{t}$ has the label $y_{i}\in\mathcal{Y}^{t}$, and $\mathcal{Y}^{t}=\{y^{t}_{1},y^{t}_{2},...,y^{t}_{n}\}$ is the set of $n$ novel classes.
The task $\mathcal{T}^{t}$ is to train the $f(\theta):v_{i}\rightarrow\bigcup_{j=1}^{t}\mathcal{Y}^{j}$ to ensure it can infer well on the current novel classes while preventing catastrophic forgetting of the inference ability on previous classes.

Jointly Incremental Learning. This is a straightforward solution for the problem, which collects training nodes of all classes of previous tasks to train $f(\theta)$ in each step. This treats the accumulated tasks $\{\mathcal{T}^{1},\mathcal{T}^{2},...,\mathcal{T}^{t}\}$ as a whole new task and retrains the model from scratch.
However, this solution is inefficient because it leads to redundant training of labeled nodes and creates computational challenges due to the growing graph size. Conversely, the buffer memory replay model offers a more practical solution.

Memory Replay for Incremental Learning. This method, instead of gathering all previous training nodes, maintains buffers $\mathcal{B}$ that store a small yet representative subset of training nodes for each class of previous tasks.
The objectives can be formulated as follows:

$$ $\mathcal{L}=\underbrace{\sum_{v_{i}\in\mathcal{V}^{t}}\ell^{t}(f(v_{i};\theta) ,y_{i})}_{\text{Loss on new tasks}}+\underbrace{\lambda\sum_{j=1}^{K}\sum_{v_{ k}\in\mathcal{B}_{j}}\ell^{t}(f(v_{k};\theta),y_{k})}_{\text{Memory replay on previous tasks}},$ (1) $$

where $\ell^{t}$ is the loss function on the accumulated all class set, $K=|\bigcup_{i=1}^{t-1}\mathcal{Y}^{i}|$ is the number of previous classes, the $\lambda$ is a balance hyper-parameter, and $\mathcal{B}_{j}$ is the buffer for the $j$-th class.
The second term ensures the representative training nodes from previous classes are included in the current training phase, efficiently mitigating the risk of catastrophic forgetting of previous classes.
Also, the size of $\mathcal{B}_{j}$ 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 a substantial increase in efficiency.

Figure: Figure 2: The framework of DMSG. In this instance, the graph model underwent training on a 2-class node classification task on $G^{1}$. Two new classes of nodes are added to form $G^{2}$. Certain nodes of the previous two classes are first selected into buffers. Then, the model is further trained on the two new classes of nodes and buffers to perform incremental learning.
Refer to caption: x2.png

## 3 Methodology

Without loss of generality, we choose the plain GCN model followed by a classifier head as the backbone of $f(\theta)$, which can encode each node $v_{i}$ into an embedding $z_{i}$ and a probability $p_{i}$.
As shown in Figure 2,
initially, this model is trained on the graph $G_{1}$. When the $t$-th task introducing new classes arrives, we first extend new parameters (highlighted as 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 $f(\theta)$, we leverage the memory replay framework, which incorporates both the Heuristic Diversified Memory Selection (Section 3.1) and the Diversified Memory Generation Replay (Section 3.2).

Motivation. Consider $p(G_{<t})$ as the true data distribution of graphs from prior $t-1$ tasks, and $q(\mathcal{B}_{<t})$ as the data distribution encapsulated within the memory replay buffers $\mathcal{B}$ sampled from $G_{<t}$. To understand the efficacy of the buffer diversity in incremental learning scenarios, we engage in a theoretical examination to indicate that a high diversity within $\mathcal{B}$ ensures that the empirical loss $\mathcal{L}(\theta)$ over $\mathcal{B}$ closely mirrors the total expected loss $\mathcal{L}(\theta)$ over $p(G_{<t})$.

###### Theorem 1 .

Let the loss function $\mathcal{L}(\theta,x)$ be $\beta$-Lipschitz continuous in respect to the input $x$. Under this condition, the discrepancy between the expected loss under the true data distribution $p(G_{<t})$ and that under the replay buffer distribution $q(\mathcal{B}_{<t})$ is bounded as follows:

$$ $\left|\mathbb{E}_{v\sim p(G_{<t})}[\mathcal{L}(\theta,v)]-\mathbb{E}_{v\sim q( \mathcal{B}_{<t})}[\mathcal{L}(\theta,v)]\right|\leq\beta\cdot W(p(G_{<t}),q( \mathcal{B}_{<t})),$ (2) $$

where $W(p,q)$ denotes the Wasserstein distance between distributions $p$ and $q$, defined by:
$W(p,q)=\inf_{\gamma\in\Gamma(p,q)}\mathbb{E}_{(v,v^{\prime})\sim\gamma}[d(v,v^
{\prime})],$
and $\Gamma(p,q)$ represents the set of all possible joint distributions (couplings) that can be formed between $p$ and $q$.

Assume that both $p(G_{<t})$ and $q(\mathcal{B}_{<t})$ follow Gaussian distributions with means $\mu_{p},\mu_{q}$ and covariance matrices $\Sigma_{p},\Sigma_{q}$ respectively. Thus, the squared 2-Wasserstein distance between two Gaussian distributions is given by:

$$ $W_{2}^{2}(\mathcal{N}(\mu_{p},\Sigma_{p}),\mathcal{N}(\mu_{q},\Sigma_{q}))=\| \mu_{p}-\mu_{q}\|^{2}+\operatorname{Tr}(\Sigma_{p}+\Sigma_{q}-2(\Sigma_{p}^{1/ 2}\Sigma_{q}\Sigma_{p}^{1/2})^{1/2}).$ (3) $$

Since the $\Sigma$ measure the distribution diversity and $\mathcal{B}_{<t}$ is the subset of $\mathcal{G}_{<t}$ and is typically less diverse.
Assuming the sampling strategy is unbiased upon means.
As the $\mathcal{B}_{<t}$ more diversified, $\Sigma_{q}\rightarrow\Sigma_{p}$, leading to the Wasserstein distance decreases. Based on Theorem 1, 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.

###### Theorem 1 .

### 3.1 Heuristic 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, we 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 intra-diversity and inter-diversity for the buffers. Our goal is to select the buffer $\mathcal{B}_{i}$ corresponding to the $i$-th class of training nodes based on the following criteria:

$$ $\mathcal{B}_{i}=\arg\max\limits_{\mathcal{B}_{i}\subset\mathcal{C}_{i}}\sum \limits_{v\in\mathcal{B}_{i}}[\underbrace{\mathcal{A}(v,\mathcal{B}_{i})}_{ \text{intra-diversity}}+\underbrace{\frac{1}{K-1}\sum_{\begin{subarray}{c}j=1, j\neq i,\mathcal{B}_{j}\subset\mathcal{C}_{j}\end{subarray}}^{K}\mathcal{A}(v, \mathcal{B}_{j})}_{\text{inter-diversity}}],$ (4) $$

where $\mathcal{C}_{i}$ is set of $i$-th class of training nodes,
$\mathcal{A}(v,\mathcal{B}_{i},G^{t})$ denotes the distance measure between node $v$ and $\mathcal{B}_{i}$ in the current graph $G^{t}$, which we define as the L2-norm distance on probabilities between node $v$ and its closest node in $\mathcal{B}_{i}$.
While the measure can be defined as any topological distance, such as the shortest path, we use probability distance because it offers finer resolution, reduced noise towards tasks, and computational efficiency.
The first term quantifies the intra-diversity within the buffer $\mathcal{B}_{i}$, reflecting the variations among its own nodes, while the second term quantifies the inter-diversity between $\mathcal{B}_{i}$ and other buffers, illustrating the differences between the nodes of $\mathcal{B}_{i}$ 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 methods [].
Thus, we introduce a greedy algorithm to sample representative training nodes when new tasks are introduced. Specifically, suppose $\mathcal{V}^{t}=\bigcup_{i=K+1}^{K+n}\mathcal{C}^{t}_{i}$ is the training nodes of $t$-th task and $\mathcal{C}^{t}_{i}$ is the training set corresponding to the $i$-th novel class. We have previously selected buffers $\{\mathcal{B}_{i}\}_{i=1}^{K}$ in previous $t-1$ tasks, where $K$ and $n$ are the numbers of previous classes and novel classes, respectively. Then, the greedy selection strategy is defined in the Algorithm 1,
where $\mathbb{D}(\mathcal{B}_{i})=\sum_{v\in\mathcal{B}_{i}}(\mathcal{A}(v,\mathcal{
B}_{i})+\frac{1}{K-1}\sum_{j=1,j\neq i,\mathcal{B}_{j}\subset\mathcal{C}_{j}}^
{K}\mathcal{A}(v,\mathcal{B}_{j}))$ is the set score function defined on the buffer set $\mathcal{B}_{i}$ of the $i$-th class, $\triangle_{\mathbb{D}}(v|\mathcal{B}_{i})$ is the gain of $f$ choosing $v$ into $\mathcal{B}_{i}$, and $v*$ is the chosen node using the greedy strategy.
In greedy Algorithm 1, the core idea is to make the currently best choice of buffer nodes at every step, hoping to obtain the global optimal solution for the objective Eq.4 through this local optimal choice.

Figure: Algorithm 1 Heuristic Buffer Selection

Below, we give a Proposition of approximation guarantee of our greedy algorithm.

###### Proposition 1 .

(Greedy Approximation Guarantee of Algorithm 1).
The greedy Algorithm 1 that sequentially adds elements to an initially empty set based on the largest marginal gain $\triangle_{\mathbb{D}}$ under a cardinality constraint provides a solution $\mathcal{B}^{*}_{i}$ that is at least $(1-\frac{1}{e})$ times the optimal solution, i.e.,

$$ $f(\mathcal{B}^{*}_{i})\geq\left(1-\frac{1}{e}\right)\cdot f(OPT),$ (5) $$

where $OPT$ represents the optimal solution of the buffer set $\mathcal{B}_{i}$.

###### Proof.

The above Proposition can be derived from the Greedy Approximation Guarantee for Monotonic and Submodular Functions [] (proof can be found in Theorem 1 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 a solution that is at least $(1-\frac{1}{e})$ times the optimal solution.
∎

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 $O((K+n)*|\mathcal{C}^{t}_{i}|)$, by determining distances and making comparisons. Thus, the overall complexity of selecting each buffer is $O(b(K+n)*|\mathcal{C}^{t}_{i}|)$. Note that $b$ (the buffer size) and $K+n$ (the total number of classes up to $t$-th task) are typically much smaller than $|\mathcal{C}^{t}_{i}|$, ensuring the efficiency of the algorithm.

###### Proposition 1 .

###### Proof.

### 3.2 Diversified Memory Generative Replay

During training for the $t$-th task $\mathcal{T}^{t}$, the stored representative nodes in the buffers $\{\mathcal{B}_{i}\}_{i=1}^{K}$ from previous $t-1$ 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 be constrained and might not encompass the full complexity of previous tasks, leading to a potential bias in replaying, and C2: the training process can become difficult as the model may easily overfit to the limited nodes in the buffers, undermining its ability to generalize across different tasks.
Thus, we proposed the Diversified Memory Generation Replay to address the above problems.

Broadening Diversity of Buffer Node Embeddings. Specifically, the embeddings of the buffer nodes are first subjected to a variational layer, which aims to create more nuanced representations that encapsulate the inherent probabilistic characteristics of nodes. Let $z_{i}\in\mathbb{R}^{h}$ denote the embedding of node $v_{i}\in\mathcal{B}_{j},1\leq j\leq K$, where $h$ is the hidden dimension.
Specifically, we treat the nodes in the buffers as the observed samples $\mathcal{V}_{ob}$ drawn from the ground-truth distribution of the previous nodes:

$$ $Z=\bigcup_{j=1}^{K}\bigcup_{v_{i}\in\mathcal{B}_{j}}\{z_{i}\}\in\mathbb{R}^{(K \times b)\times h}\xlongequal{\text{def}}\mathcal{V}_{ob}.$ (6) $$

The node variable $\widehat{Z}$ is drawn from the variational network layer $q_{\phi_{v}}(\widehat{Z}|Z)$ with parameters $\phi_{v}$. Specifically, $q_{\phi_{v}}$ outputs the mean and variance of the node embeddings distributions respectively, expressed as $Z^{\mu}=q_{\phi_{v}}^{\mu}(Z)$ and $Z^{\sigma}=q_{\phi_{v}}^{\sigma}(Z)$, where $q_{\phi_{v}}^{\mu}(\cdot)$ is the identity function and $q_{\phi_{v}}^{\sigma}(\cdot)$ is a Liner layer followed with a Relu activation layer. Then we use the reparameterization technique to sample from $\mathcal{N}(Z^{\mu},Z^{\sigma})$, expressed as $\widehat{Z}=Z^{\mu}+Z^{\sigma}\odot\epsilon$, where $\widehat{Z}\in\mathbb{R}^{h}$ and $\epsilon$ is drawn from standard normal distributions.
Thus, we define the generated samples as $\mathcal{V}_{ge}$.
The variational operation augments the diversity of observed buffer nodes $\mathcal{V}_{ob}$, empowering the model to explore more expansive distribution spaces.

Maintaining Integrity of Synthesized Embeddings.
Then, we further propose to maintain the integrity of these variational node embeddings to prevent them from deviating too far, which implies that while the generated embeddings should exhibit diversity, they must remain similar to the ground-truth ones.
Specifically, we adopt an adversarial learning strategy [].
We introduce an auxiliary discriminator, $\mathcal{D}:\mathbb{R}^{h}\rightarrow\mathbb{R}^{1}$ with parameters $\phi_{d}$, 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:

$$ $\displaystyle\mathcal{L}_{MISE}=\min_{\theta,\phi_{v}}\mathbb{E}_{z_{i}\sim Z} \mathbb{E}_{q_{\phi_{v}}(\hat{z}_{i}|z)}$ $\displaystyle\left[\max_{\phi_{d}}\text{ }\ell_{\mathcal{D}}(z_{i},\hat{z}_{i} )\vphantom{\max_{\phi_{d}}}\right],$ (7) $$

where $\ell_{\mathcal{D}}$ is a negative binary cross-entropy loss function on the variational and original node embeddings, defined as:

$$ $\ell_{\mathcal{D}}(z_{i},\hat{z}_{i})=\log\mathcal{D}(z_{i},\phi_{d})+\log \left(1-\mathcal{D}(\hat{z}_{i},\phi_{d})\right).$ (8) $$

The min-max adversarial learning strategy involves training the domain discriminator to distinguish whether the node embeddings are synthesized or original while simultaneously enforcing a 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 C1. Simultaneously, it employs adversarial learning and regularization to ensure this expansion does not lead to distortions.

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, we 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 $\widehat{A}\in\mathbb{R}^{Kb\times Kb}$ and the decoder loss is defined as:

$$ $\displaystyle\mathcal{L}_{CGSE}$ $\displaystyle=-\mathbb{E}_{q_{\phi_{v}}(\widehat{Z}|Z)}[\log p(\widehat{A}| \widehat{Z})]+\text{KL}(q_{\phi_{v}}(\hat{z}_{i}|z)||p(\hat{z}_{i}))$ (9) $\displaystyle=-\mathbb{E}_{\hat{z}_{i},\hat{z}_{j}\sim\widehat{Z}}\left[ \widehat{A}_{ij}\log\widehat{p}_{ij}+\widehat{A}_{ij}\log(1-\widehat{p}_{ij}) \right]+\text{KL}(q_{\phi_{v}}(\hat{z}_{i}|z)||p(\hat{z}_{i})),$ $$

where $p(\widehat{A}|\widehat{Z})$ is the probability of reconstructing $\widehat{A}$ given the latent variational node embedding matrix $\widehat{Z}$, following a Bernoulli distribution. $\widehat{p}_{ij}$ is the probability of an edge between nodes $i$ and $j$, defined as: $\widehat{p}_{ij}=\text{sigmoid}(\widehat{z}_{i}^{T}\cdot\widehat{z}_{j})$. The second term in Eq. 7 is a distribution regularization term, which enforces the variational distribution $q_{\phi_{v}}(\hat{z}_{i}|z)$ of each node to be close to a prior distribution $p(\hat{z}_{i})$, which we assume is a standard Gaussian distribution. $\text{KL}(\cdot)$ represents the Kullback-Leibler (KL) divergence. The detailed derivation of $\mathcal{L}_{CGSE}$ 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:

$$ $\mathcal{L}_{RP}=\sum_{j=1}^{K}\sum_{v_{i}\in\mathcal{B}_{j}}\ell^{t}(\hat{z_{ i}},y_{i}).$ (10) $$

Note that the variational operation regenerates synthetic buffer node embeddings with the same size as original embeddings in each training step, i.e., $|\mathcal{V}_{ge}|\equiv|\mathcal{V}_{ob}|$, broadening the diversity of memory while guaranteeing the efficiency of the buffer replay.

### 3.3 Overall Optimization

Combining the new task loss $\mathcal{L}^{t}=\sum_{v_{i}\in\mathcal{V}^{t}}\ell^{t}(f(v_{i};\theta),y_{i})$ and the above memory replay losses, the overall optimization objective can be written as follows:

$$ $\min_{\theta}\mathcal{L}^{t}+\min_{\theta,\phi_{v}}\left\{\lambda_{1}\mathcal{ L}_{RP}+\lambda_{2}\max_{\phi_{d}}\{\mathcal{L}_{MISE}\}+\lambda_{3}\mathcal{L }_{CGSE}\right\},$ (11) $$

where $\lambda_{1}$, $\lambda_{2}$ and $\lambda_{3}$ is the loss weights.

Synchronized Min-Max Optimizating.
A gradient reversal layer (GRL) [] is introduced between the variational embedding and the auxiliary discriminator so as to conveniently perform min-max optimization on $\theta,\phi_{v}$ and $\phi_{d}$ under $\mathcal{L}_{adv}$ 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 practice, in each training step, training the proposed method on the entire graph and buffer at once may not be practical, especially for large-scale graphs.
Following methods like GraphSAGE [] and GraphSAINT [], we adopt a mini-batch optimization strategy. We sample a multi-hop neighborhood for each node and set two kinds of batch sizes, $B^{\text{new}}$ and $B^{\text{buffer}}$, for the new task and replay losses in Eq. 11, respectively. The ratio of these batch sizes corresponds to the ratio between the total training nodes in the new task and the buffer.

## 4 Experiments

Experiment Setup. In this section, we describe the experiments we perform to validate our proposed method.
We use the four growing graph datasets, CoraFull, OGB-Arxiv, Reddit, and OGB-Products, introduced in Continual Graph Learning Benchmark (CGLB) [].
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 baseline Joint defined in Section 2. The lower bound baseline Fine-tune employs only the newly arrived training nodes for model adaptation withour memory replay.
Then, we set multiple continual learning models for graph as baselines, including EWC [], MAS [], GEM [], LwF [], TWP [], ER-GNN [], and SEM [].
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 $M^{acc}\in\mathbb{R}^{T\times T}$, which is lower triangular where $M^{acc}_{i,j}(i\geq j)$ 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) $\frac{1}{T}\sum_{i=1}^{T}M^{acc}_{T,i}$ and the Average Forgetting (AF) $\frac{1}{T-1}\sum_{i=1}^{T-1}M^{acc}_{T,i}-M^{acc}_{i,i}$ for each task after learning the last task. For detailed introduction to dataset description, compared methods, evaluation metrics, and hyperparameter setting, please refer to Appendix.

Overall Comparison.
This experiment aims to answer: How is DMSG’s performance on 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 1.
Initially, we observe that DMSG attains a significant margin over other baseline methods across all datasets.
Certain baseline methods demonstrate exceedingly poor results. This can 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 a 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 enhancing the results.

**Table 1: The model performance comparisons( $\uparrow$: higher is better, Joint is the upper bound).**
| Methods | CoreFull | OGB-Arxiv | Reddit | OGB-Products |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| AA/% $\uparrow$ | AF/% $\uparrow$ | AA/% $\uparrow$ | AF/% $\uparrow$ | AA/% $\uparrow$ | AF/% $\uparrow$ | AA/% $\uparrow$ | AF/% $\uparrow$ |  |
| Fine-tune | 3.5$\pm$0.5 | -95.2$\pm$0.5 | 4.9$\pm$0.0 | -89.7$\pm$0.4 | 5.9$\pm$1.2 | -97.9$\pm$3.3 | 3.4$\pm$0.8 | -82.5$\pm$0.8 |
| EWC | 52.6$\pm$8.2 | -38.5$\pm$12.1 | 8.5$\pm$1.0 | -69.5$\pm$8.0 | 10.3$\pm$11.6 | -33.2$\pm$26.1 | 23.8$\pm$3.8 | -21.7$\pm$7.5 |
| MAS | 12.3$\pm$3.8 | -83.7$\pm$4.1 | 4.9$\pm$0.0 | -86.8$\pm$0.6 | 13.1$\pm$2.6 | -35.2$\pm$3.5 | 16.7$\pm$4.8 | -57.0$\pm$31.9 |
| GEM | 8.4$\pm$1.1 | -88.4$\pm$1.4 | 4.9$\pm$0.0 | -89.8$\pm$0.3 | 28.4$\pm$3.5 | -71.9$\pm$4.2 | 5.5$\pm$0.7 | -84.3$\pm$0.9 |
| TWP | 62.6$\pm$2.2 | -30.6$\pm$4.3 | 6.7$\pm$1.5 | -50.6$\pm$13.2 | 13.5$\pm$2.6 | -89.7$\pm$2.7 | 14.1$\pm$4.0 | -11.4$\pm$2.0 |
| LwF | 33.4$\pm$1.6 | -59.6$\pm$2.2 | 9.9$\pm$12.1 | -43.6$\pm$11.9 | 86.6$\pm$1.1 | -9.2$\pm$1.1 | 48.2$\pm$1.6 | -18.6$\pm$1.6 |
| ER-GNN | 34.5$\pm$4.4 | -61.6$\pm$4.3 | 30.3$\pm$1.5 | -54.0$\pm$1.3 | 88.5$\pm$2.3 | -10.8$\pm$2.4 | 56.7$\pm$0.3 | -33.3$\pm$0.5 |
| Joint | 81.2$\pm$0.4 | -3.3$\pm$0.8 | 51.3$\pm$0.5 | -6.7$\pm$0.5 | 97.1$\pm$0.1 | -0.7$\pm$0.1 | 71.5$\pm$0.1 | -5.8$\pm$0.3 |
| DMSG | 77.8$\pm$0.3 | -0.5$\pm$0.5 | 50.7$\pm$0.4 | -1.9$\pm$1.0 | 98.1$\pm$0.0 | 0.9$\pm$0.1 | 66.0$\pm$0.4 | -0.9$\pm$1.6 |

Figure: (a) CoraFull
Refer to caption: x3.png

In-Depth Analysis of Continuous Performance.

This experiment aims to answer: How does DMSG’s fine-grained performance evolve after continuously learning each task?
To present a more fine-grained demonstration of the model’s performance in continual learning on graphs, we analyzed the average performance across all previous tasks each time a 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 performance after $t$ in terms of AA on all previous $t$ tasks.
Also, we visualize the accuracy matrices of DMSG and SEM on the OGB-Arxiv and OGB-Product datasets.
The results are presented in Figure 4.
In these matrices, each row represents the performance across all tasks upon learning a 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 in a reduction in performance across all examined methods, including Joint. That is because as tasks accumulate and the learning objectives become multifaceted, it becomes challenging for models to maintain optimal performance across all classes.
Notably, the Fine-Tuning strategy experienced a 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 to 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.

Figure: (a) CoraFull (SEM)
Refer to caption: x7.png

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 investigate the distinct contributions of the diversified memory generation replay method, we conducted an ablation study on it.
We design three variant methods for DMSG to verify the effectiveness of adversarial synthesized embedding learning and the graph reconstruction optimization objective.
w/o $\mathcal{L}_{MISE}$: This variant excludes the adversarial learning loss for maintaining the integrity of synthesized embeddings.
; w/o $\mathcal{L}_{CGSE}$: This variant excludes the graph reconstruction loss on variational embeddings for consolidating 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 2, we can observe when both $\mathcal{L}_{MISE}$ and $\mathcal{L}_{CGSE}$ are removed (w/o all), the performance is the lowest across all datasets. Also, a progressive improvement is observed as individual components in the model.

**Table 2: The ablation study of memory replay.**
| Methods | CoreFull | OGB-<br>Arxiv | Reddit | OGB-<br>Products |
| --- | --- | --- | --- | --- |
| w/o all | 73.9$\pm$0.6 | 48.2$\pm$0.4 | 89.3$\pm$3.6 | 60.1$\pm$0.8 |
| w/o $\mathcal{L}_{MISE}$ | 74.4$\pm$0.8 | 49.3$\pm$0.3 | 95.1$\pm$2.9 | 60.1$\pm$0.9 |
| w/o $\mathcal{L}_{CGSE}$ | 74.8$\pm$0.7 | 49.7$\pm$0.2 | 97.8$\pm$0.4 | 60.5$\pm$0.7 |
| DMSG | 77.8$\pm$0.3 | 50.7$\pm$0.4 | 98.1$\pm$0.0 | 66.0$\pm$0.4 |

This confirms their respective contributions to continual learning.
An interesting trend emerges when comparing the individual contributions of the two components. The w/o $\mathcal{L}_{CGSE}$ variant slightly surpasses the performance of w/o $\mathcal{L}_{MISE}$. This suggests that while both components are crucial, adversarial variational embedding learning may have a more pronounced effect in capturing essential and diverse patterns inherent in the data.
The best performance occurs with all components, supporting that the proposed components are beneficial individually and collectively, ensuring the model can effectively memorize the previous knowledge while continually adapting to new tasks.

### 4.1 Related Works

#### 4.1.1 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) have rapidly become one of the most prominent tools for learning graph-structured data, bridging the gap between deep learning and graph theory.
Representative methods includes GCN [], GraphSAGE [], and GAT [], etc.
However, these methods predominantly operate on static graphs.
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 [, , , ].
For instance, Evolving Graph Convolutional Networks (EvolveGCN) [] emphasizes temporal adaptability in graph evolution. Temporal Graph Networks (TGNs) [] operates on continuous-time dynamic graphs represented as a sequence of events. Spatio-Temporal Graph Networks (STGN)[] integrates spatial and temporal information to enhance prediction accuracy.
However, these methods primarily concentrate on a singular task in evolving graphs and often encounter difficulties when more complicated tasks emerge as the graph expands.

#### 4.1.2 Incremental Learning.

Incremental learning [] refers to a 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–class-incremental learning is about expanding the class space within the same task domain, while task-incremental learning involves handling entirely new tasks, which may or may not be related to previous ones [, ].
Typically, three different categories of methods have emerged to address the continual learning problem.
The first category revolves around regularization techniques [, ]. 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 [, ]. These strategies dynamically allocate new parameters exclusively for upcoming tasks, ensuring that crucial parameters intrinsic to previous tasks remain unscathed. Lastly, memory replay-based methods [, ] present a solution by selectively replaying representative data from previous tasks to 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.

#### 4.1.3 Graph Class-incremental Learning.

Class-incremental Learning [] means the specific scenario where the number of classes increases along with the new samples introduced. Graph class-incremental learning [, , , ] specifies this problem to growing graph data–new nodes introduce unseen classes to the graph.
Methods of graph class-incremental learning [, , , , ] 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  [] employs regularization to ensure the preservation of critical parameters and intricate topological configurations, achieving continuous learning. HPNs [] adaptively choose different trainable prototypes for incremental tasks.
ER-GNN [] proposes multiple memory sampling strategies designed for the replay of experience nodes.
SEM [] leverages a sparsified subgraph memory selection strategy for memory replay on growing graphs.
However, the trade-off between buffer size and replay effect is still a Gordian knot, i.e., aiming for a 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 preserve the essential and diversified knowledge contained within restricted nodes, thus improving the model in learning previous knowledge.

## 5 Conclusion

To summarize, this paper presents a novel approach DMSG to the challenge of incremental learning in ever-growing 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 is that it does not improve the graph feature extractor of the model, which may result in suboptimal performance when dealing with increasing graph data, as the model parameters are insufficient to learn and retain massive amounts of information effectively. Future work may focus on 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.

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 6
presentation: 2
questions: See Weakness.
soundness: 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.

S2: [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.

S3. [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.
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.
weaknesses: Here are still some questions mainly regarding the buffer selection part and the variational part:

W1: 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.

W2: 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?

W3: 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? 

W4: 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?

W5: 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?

W6: 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?

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 3
questions: see above.
soundness: 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.

The studied problem is important. The authors try to tackle the issues of limited buffer size and potential overfitting through their diversified memory generation approach.

clear 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.
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.
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.

Lack of baselines. The following papers should be discussed and compared for experiments:
Towards robust graph incremental learning on evolving graphs. ICML 2023
Replay-and-Forget-Free Graph Class-Incremental Learning: A Task Profiling and Prompting Approach. NeurIPS 2024
On the Limitation and Experience Replay for GNNs in Continual Learning. CoLLAs 2024
Topology-aware Embedding Memory for Continual Learning on Expanding Networks. KDD 2024
PUMA: Efficient Continual Graph Learning for Node Classification With Graph Condensation. TKDE 2024
Graph Continual Learning with Debiased Lossless Memory Replay. ECAI 2024
Accordingly, it is encouraged that the authors discuss the difference between their proposed model and these baselines.

Lack of comprehensive datasets. What about the performance of the proposed model on Citeseer, Pubmed, and PPI? How about Collab, IMDB, Proteins, and NCI1?

Lack 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.

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: 1. Please explain more on the probability distance used in Section 3.1, e.g. the specific formulation.

2. 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?

3. If the generator is trained every time when a new task comes in, will this induce significant extra computational burden?
soundness: 2
strengths: 1. The paper is overall well written, and the main idea is clearly conveyed.

2. Experiments are comprehensively conducted on multiple benchmark datasets against multiple baselines.

3. According to the results, the proposed method consistently outperform the baselines, although the improvement on some datasets are negligible.
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.

Overall, 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.
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.

2. The implemented diversity maximization strategy is inconsistent with the theoretical motivation, as mentioned in the first weakness point.

---

confidence: 5
contribution: 2
initial_rating: 6
presentation: 3
questions: Please see the weaknesses.
soundness: 2
strengths: The studied problem is practical and interesting.

The paper is well-written and easy to understand.

The proposed method introduces novel approaches for buffer selection and memory utilization.
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.
weaknesses: 1. The title presented on the website is not the same as the one in the paper
2. The citation style is not used appropriately. Most of the citations should be in parenthesis using \citep{}.
3. The authors are encouraged to include the time consumption of different memory selection strategies.
4. The statements in lines 178-181 are not clear. Please revise it to make it clearer.
5. The definition of L_{adv} is not clear in line 334. Moreover, there is no Eq.A.3.
6. The analysis of parameter sensitivity is missing.
7. The comparisons to more recent baselines are encouraged.

Meta-review: The paper addresses the challenge of incremental learning in growing graphs, aiming to retain inference ability on previous tasks while learning new ones. 

The reviewers highlighted several strengths of the paper, including its clear motivation, innovative methodology, and detailed theoretical analysis. The experimental results were praised for their robustness and clarity. However, some concerns were raised regarding the buffer node selection process, the role of the variational layer, and the time complexity of the proposed methods. The authors addressed these concerns effectively, providing additional justifications and detailed analyses. 

Given the overall positive reception, I recommend its acceptance.

Decision: Accept (Poster)