Edge Prompt Tuning for Graph Neural Networks

• W3: The datasets included in the experimental section do not contain initial edge features, which raises doubts about the effectiveness of EdgePrompt on graphs that inherently have edge features. If the original graph already contains edge features, how should EdgePrompt be integrated with these edge features? What would its performance be like in that case?

• R3: Thanks for bringing this up. When handling graph data with edge features, we can still use the current strategy in EdgePrompt and EdgePrompt+ to learn prompts vectors. The only difference is that edge features/embeddings will be aggregated along with prompt vectors. To evaluate the performance of our method over graph data with edge features, we conduct experiments over BACE and BBBP from the MoleculeNet dataset [1]. The following two tables report the accuracy of our method and other baselines. We have added the discussion in our paper (see Appendix D.2 in our revised PDF).

   
  [1] MoleculeNet: a benchmark for molecular machine learning. Chemical science 2018.

  Pre-training: SimGRACE	BACE	BBBP
  Classifier Only	57.62$\pm$1.92	63.56$\pm$1.03
  GraphPrompt	59.37$\pm$0.53	63.39$\pm$1.75
  All-in-one	56.73$\pm$1.33	65.72$\pm$3.48
  GPF	57.36$\pm$1.52	63.89$\pm$1.66
  GPF-plus	57.16$\pm$2.21	64.17$\pm$1.29
  EdgePrompt	58.12$\pm$1.04	63.89$\pm$1.26
  EdgePrompt+	60.46$\pm$2.63	70.50$\pm$1.92

  Pre-training: EP-GraphPrompt	BACE	BBBP
  Classifier Only	60.40$\pm$1.03	66.17$\pm$1.15
  GraphPrompt	61.69$\pm$1.36	66.86$\pm$0.70
  All-in-one	56.17$\pm$1.54	61.72$\pm$6.97
  GPF	60.89$\pm$0.71	66.72$\pm$0.84
  GPF-plus	61.39$\pm$0.22	67.58$\pm$0.67
  EdgePrompt	61.09$\pm$1.22	66.94$\pm$0.97
  EdgePrompt+	64.66$\pm$2.20	72.75$\pm$2.12

• W4: The downstream tasks involved in the experiments are limited to node classification and graph classification, with other graph tasks such as link prediction and node regression not being included.

• R4: Thanks for bringing this up. We would like to clarify that we provide results for node classification and graph classification as downstream tasks, as these tasks are commonly used in previous studies on graph pre-training and graph prompt tuning. For example, in graph pre-training studies, GraphCL, SimGRACE, and InfoGraph use graph classification, while DGI uses node classification. As for graph prompt tuning studies, GPPT focuses on node classification, GPF focuses on graph classification, and GraphPrompt focuses both. Therefore, we follow these studies to conduct experiments in our study. In addtion, we would like to argue that link prediction as the downstream task may be incompatible with the "pre-training, adaptation" scheme. During pre-training, GNN models should be trained via self-supervised learning. If the downstream task is link prediction, however, we will directly have label information (i.e., whether an edge exists between a node pair) in graph data. In this case, we can simply follow an end-to-end manner by using link prediction to train GNN models and then making inferences (we guess it is the reason why the above studies choose not to include the results of link prediction as the downstream task). Considering this, we believe node classification and graph classification are proper and sufficient for performance evaluation in our experiments.

We deeply appreciate your insightful comments to make our paper better. We hope that we can address all your concerns in our point-by-point responses.

• W1: The motivation for constructing EdgePrompt is insufficient. Why is it necessary to design EdgePrompt under graph prompt tuning? What core problem does EdgePrompt address compared to existing graph prompt tuning methods? What are its advantages?

• R1: As indicated in Introduction, the existing graph prompt tuning methods mainly focus on learning graph prompts at the node level and overlook the crucial role of edges in graph prompt design. As a result, they cannot effectively enhance pre-trained GNN models in capturing complex graph structural information for downstream tasks. In fact, graph structures are the essence of graph data that differentiates graph data from image or text data. Motivated by this, we propose EdgePrompt and its advanced version EdgePrompt+ in this study. Our method innovatively learns graph prompts at the edge level and explicitly captures graph structural information to enhance pre-trained GNN models for downstream tasks.

• W2: Compared to ALL-in-one and GPF, EdgePrompt and EdgePrompt+ set different prompt vectors $p^{(l)}$ for each layer. What are the benefits of this design? Both All-in-one and GPF only add prompt vectors in the first layer to reduce dependency on the specific structure of the model. EdgePrompt lacks such advantages, and the paper does not explore the reasoning behind this design. Furthermore, the experimental section does not include relevant comparisons to demonstrate the necessity of setting different prompt vectors for each layer.

• R2: Thanks for pointing it out. The intuition of edge prompts for each layer can be illustrated in Figure 1. Node $v_3$ may receive adverse information from node $v_1$ when node $v_3$ and node $v_1$ are from different classes. If we learn edge prompts only in the first layer, node $v_3$ will still receive adverse information from node $v_1$ in the following layers. In contrast, our method instead learns layer-wise edge prompts, which can consistently avoid the above issue in each layer. We provide the results of EdgePrompt and EdgePrompt+ with edge prompts only in the first layer in the following tables. We can observe performance degradation in some cases compared with their original versions with edge prompts in each layer, especially for EdgePrompt+. In addition, we would like to note that learning layer-wise prompts has been adopted by recent studies [1, 2] from other areas. If layer-wise prompts are not allowed, learning prompts in the first layer can be an alternative approach. We have added the discussion in our paper (See Appendix D.3 in our revised PDF).

    [1] Visual Prompt Tuning. ECCV 2022.
    [2] MaPLe: Multi-Modal Prompt Learning. CVPR 2023.

  Pre-training: GraphCL	Cora	CiteSeer	PubMed
  EdgePrompt (first layer)	57.74$\pm$4.42	42.41$\pm$3.21	67.33$\pm$3.57
  EdgePrompt	58.60$\pm$4.46	43.31$\pm$3.23	67.76$\pm$3.01
  EdgePrompt+ (first layer)	61.66$\pm$6.81	44.96$\pm$2.63	67.54$\pm$3.95
  EdgePrompt+	62.88$\pm$6.43	46.20$\pm$0.99	67.41$\pm$5.25

  Pre-training: EP-GPPT	Cora	CiteSeer	PubMed
  EdgePrompt (first layer)	36.74$\pm$4.79	29.47$\pm$3.16	47.98$\pm$6.42
  EdgePrompt	37.26$\pm$4.53	29.83$\pm$1.01	47.20$\pm$7.06
  EdgePrompt+ (first layer)	56.10$\pm$6.39	42.10$\pm$1.41	60.61$\pm$7.57
  EdgePrompt+	56.41$\pm$3.62	43.49$\pm$2.62	61.51$\pm$4.91

  Pre-training: SimGRACE	ENZYMES	NCI1	NCI109
  EdgePrompt (first layer)	28.83$\pm$1.74	61.58$\pm$2.71	61.82$\pm$1.15
  EdgePrompt	29.33$\pm$2.30	62.02$\pm$3.02	62.02$\pm$1.03
  EdgePrompt+ (first layer)	28.58$\pm$2.45	61.81$\pm$3.03	62.36$\pm$0.98
  EdgePrompt+	32.67$\pm$2.53	67.07$\pm$1.96	66.53$\pm$1.30

  Pre-training: EP-GraphPrompt	ENZYMES	NCI1	NCI109
  EdgePrompt (first layer)	30.75$\pm$1.03	61.81$\pm$2.57	62.07$\pm$1.42
  EdgePrompt	30.80$\pm$2.09	61.75$\pm$2.49	62.33$\pm$1.65
  EdgePrompt+ (first layer)	31.92$\pm$1.41	62.07$\pm$2.64	61.66$\pm$1.64
  EdgePrompt+	33.27$\pm$2.71	65.06$\pm$1.84	64.64$\pm$1.57

Thank you for the author's patient responses. I have thoroughly read all the author's replies as well as the feedback from other reviewers. The additional experiments have made the paper more convincing. I will maintain the score I have given.

We deeply appreciate your insightful comments to make our paper better. We hope that we can address all your concerns in our point-by-point responses.

• W1: Inaccurate statement: GraphPrompt [1] is not based on a specific pre-training strategy. As shown in GraphPrompt+ [2], all contrastive learning pre-training methods can be unified as subgraph similarity calculations. The link prediction used in [1] can be replaced by other methods.

• R1: Thanks for pointing it out. In fact, we indeed had a tough time identifying the compatibility of GraphPrompt with different pre-training strategies. While we notice that the authors of GraphPrompt use link prediction for pre-training as a component of GraphPrompt, the adaptation phase in GraphPrompt does not explicitly require any specific information from the pre-training phase. We conjecture that the authors may think using link prediction is the most suitable pre-training task regarding the loss function for prompt tuning in GraphPrompt. We thank the reviewer for bringing up its variant GraphPrompt+, a great complement to the compatibility of GraphPrompt with different pre-training strategies. We have modified Table 1 to correct the inaccurate statement about GraphPrompt in our revised PDF.

• W2: Missing related work: GraphPrompt+ [1] also adds prompt vectors to each layer of the pre-trained graph encoder, which should be discussed and compared.

• R2: Thanks for bringing this up. We have added GraphPrompt+ in Table 1 of our revised PDF.

• W3: Unclear explanation of anchor prompts in EdgePrompt+: It is unclear what the anchor prompts in EdgePrompt+ represent. In my opinion, anchor prompts are introduced to address the overfitting problem caused by directly learning edge-specific prompts for different edges, but there lacks a explanation for the meaning of the anchor prompts. A more reasonable and effective solution could be conditional prompting [3,4], which I highly recommend the authors explore in future work.

• R3: Thanks for bringing this up. We agree that anchor prompts can address the overfitting problem caused by learning an independent prompt for each edge. However, we also want to emphasize that learning independent edge-specific prompts encounters critical supervision starvation for node classification, especially in the few-shot setting. As explained in Section 4.2, if one edge is not involved in computing the representations of any labeled nodes, its edge prompt will not be updated at all. In this case, we cannot learn anything on this edge prompt. To overcome this issue, we propose to learn the prompt vectors as a weighted average of multiple anchor prompts. We may regard these anchors prompts as a set of basis prompts shared by all edges. Therefore, an edge prompt is a combination of these basis prompts in the prompt space. In this case, each edge just needs to learn the weight scores by Equation (5) and (6). We appreciate your suggestion using conditional prompting. We have mentioned it as our future work in our paper (see Appendix E in our revised PDF).

Dear Reviewer 7GLy,

Thank you again for reviewing our paper. Your evaluation is very important to our paper. According to your valuable comments, we have modified Table 1 (about GraphPrompt and GraphPrompt+) and Future Works (about conditional prompting) in our PDF. We believe that these modifications and our clarifications have addressed all your concerns — in light of this, we hope you could consider raising your rating score. If you have any further questions, we are willing to provide more explanations.

Thanks,
Authors of Submission 4905

We sincerely appreciate your efforts to review our paper and provide insightful suggestions. We hope our following point-by-point clarifications can address your concerns.

• W1: EdgePrompt uses shared prompt vectors, which may not capture the different relationships between edges well. This can limit the model’s ability to use all the information in the graph.

• R1: Yes. That is why we propose an advanced version of EdgePrompt, e.g., EdgePrompt+, in this study to overcome this issue.

• W2: EdgePrompt+ adds multiple anchor prompts and score calculations, which can make the model more complex. This can lead to higher computational costs, making it harder to use in larger graphs.

• R2: Thanks for bringing this up. We would like to argue that our method does not introduce significant computational cost. Our method only needs $L$-hop local graphs to compute edge prompts, which is scalable in larger graphs like ogbn-arxiv. Here, we provide the results of running time (seconds per epoch) for each method in the following two tables. We have added the discussion in our paper (See Appendix D.1 in our revised PDF).

  Tuning Methods	Cora	CiteSeer	Pubmed	ogbn-arxiv	Flickr
  Classifier Only	0.116	0.136	0.663	1.186	5.156
  GPPT	0.141	0.151	0.713	1.381	5.828
  GraphPrompt	0.126	0.136	0.673	1.377	4.362
  All-in-one	0.477	0.578	3.090	6.085	7.357
  GPF	0.121	0.131	0.678	1.070	3.482
  GPF-plus	0.116	0.131	0.668	1.075	3.427
  EdgePrompt	0.121	0.136	0.693	1.106	3.824
  EdgePrompt+	0.146	0.156	0.804	1.377	5.894

  Tuning Methods	ENZYMES	DD	NCI1	NCI109	Mutagenicity
  Classifier Only	0.216	0.176	0.291	0.332	0.302
  GraphPrompt	0.276	0.211	0.347	0.357	0.322
  All-in-one	0.457	0.643	1.337	1.397	1.206
  GPF	0.221	0.191	0.342	0.322	0.307
  GPF-plus	0.231	0.191	0.347	0.296	0.312
  EdgePrompt	0.226	0.196	0.347	0.296	0.317
  EdgePrompt+	0.332	0.302	0.442	0.382	0.402

• W3: The method struggles with few-shot learning because most edges lack supervision. This can reduce the model’s performance in real-world tasks where labeled data is limited.

• R3: We would like to clarify that our method aims to deal with the few-shot setting. Therefore, our method does not struggle with few-shot learning and does not encounter performance degradation when labeled data is limited. The lack of supervision is exactly the motivation of our design in EdgePrompt+ to handle the few-shot learning. In addition, our experiments are based on the few-shot setting. Experimental results demonstrate that our method outperforms other baselines under the few-shot setting.

• Q1: How can the performance of EdgePrompt be improved in scenarios with limited labeled data to enhance its effectiveness in node classification tasks?

• A1: EdgePrompt can be enhanced by its advanced version - EdgePrompt+. Our theoretical analysis and empirical results validate the superiority of EdgePrompt+.

Thanks for your feedback. We would like to clarify that the novelty of our work lies in the following two aspects.

• A novel graph prompting method from a fundamentally different perspective of edges. As illustrated in Table 1, GPF and GPF-plus design graph prompts on node features $X$. However, such a desgin does not capture the uniqueness of graph data, as they do not integrate any structure information in graph prompts. In other words, their design can be seamlessly used on Euclidean data, such as images. In contrast, our method finds a new direction by designing graph prompts from the perspective of edges $\mathcal{E}$, which has never been investigated by previous studies. As we know, it is graph structures that differentiate graph data from image data. As indicated in line 271, GPF-plus can be regarded as a special case of our method. Therefore, we believe that only our study handles the key issue of graph data on edges when designing graph prompts.

• Theoretical analysis on node-level tasks. In our study, we provide theoretical analysis on the effectiveness of our study for node-level tasks. Our analysis indicates that our design can effectively enhance the pre-trained GNN model for node classification, while GPF and GPF-plus fail to achieve this. To the best of our knowledge, our paper is the first work to provide theoretical analysis of graph prompt tuning methods on node-level tasks. The theoretical analysis is also taken as an important contribution by other reviewers (Reviewer 7GLy, t54u).

Considering this, we would like to argue that our study is novel and make a great contribution to the community in terms of prompt design and theoretical analysis. We believe this study will attract and inspire following studies in graph prompt tuning to explore how to design graph prompts at the edge level in the future.

We hope the above clarification solves your new concern. We are willing to provide more explanations if you have any further questions.

Dear Reviewer WRHJ,

Thank you again for reviewing our paper. As the discussion period is ending in two days, we are eager to know whether our following clarifications have adressed your concerns. We hope these clarifications can still be considered for your evaluation, which is very important to us. We are willing to provide more explanations if you have any further questions.

Thanks,
Authors of Submission 4905

Dear Reviewer WRHJ,

Thank you again for reviewing our paper. As the discussion period is ending in less than 24 hours, we are eager to know whether our following clarifications have adressed your concerns. We hope these clarifications can still be considered for your evaluation, which is very important to us. We are willing to provide more explanations if you have any further questions.

Thanks,
Authors of Submission 4905

We sincerely appreciate your efforts to review our paper and provide valuable suggestions.

• Before our point-by-point clarifications, we first would like to provide an overall summary of this study in plain words to avoid misunderstanding. Graph prompt tuning methods aim to learn "something" extra (i.e., prompt vectors) to adapt pre-trained GNN models for downstream tasks while keeping the pre-trained GNN models frozen. For example, GPF learns "something" extra on node features, and GraphPrompt learns "something" extra on node representations. Under the same setting, we hope to answer the question: can we adapt pre-trained GNN models by learning "something" extra on edges? As we know, it is graph structures that differentiate graph data from image data or text data. In this study, we propose EdgePrompt and its advanced version EdgePrompt+ that learn prompt vectors on edges. EdgePrompt learns shared prompt vectors for all the edges, while EdgePrompt+ learns customized, unique prompt vectors for each edge. In a nutshell, this study targets the same goal under the same settings as previous studies (like GPF and GraphPrompt) but designs a different strategy from a novel perspective of edges.

• C1. As a study focused on edge-level prompt tuning, the assumption that there is only one type of edge could significantly undermine the contributions and claims of this paper. In line 154, the modeling of the adjacency matrix, $\mathbf{A} \in \{0, 1\}^{N \times N}$, implies that the paper does not target multi-relational graphs. However, compared to other node-level graph prompting systems, the proposed edge-level graph prompting method could be more suitable for graphs with multiple edge types. The authors may need to clarify this in the submission.

• R1: Thanks for bringing this up. We would like to emphasize that our study shares the same assumption with previous graph prompt tuning studies, such as GPF, GraphPrompt, and All-in-one. In addition, our graph prompt tuning method on edge prompts is irrelevant with edge types. Instead, we aim to adapt the pre-trained GNN models by learning customized prompt vectors for each edge. As indicated in Section 4.2, the prompt vectors are edge-specific, which means every edge will have its unique prompt vectors. Therefore, we will have $|\mathcal{E}|$ different $e^{(l)}$ for a graph with $|\mathcal{E}|$ edges. We believe it is completely different from multi-relational graphs where we may hope to model edge types.

• C4. More classic and promising pre-trained GNNs, such as Infomax, EdgePred, AttrMasking, MGSSL, GraphMAE, and Mole-BERT, could be included in the experimental section. At the very least, the authors should discuss these models and explain why they are excluded from comparison.

• R4: Thanks for bringing this up. We would to clarify that our framework is compatible with various pre-training methods. As summarized in Related Work, the existing numerous pre-training methods can be roughly categorized into two genres: contrastive methods and generative methods. For example, EdgePred, AttrMasking, and GraphMAE are generative methods while Infomax is a contrastive one. In our experiments, we select two contrastive methods (GraphCL and SimGRACE) and two generative methods (EP-GPPT and EP-GraphPrompt). We adopt them because they are representative pre-training methods in the two genres and are also used by other graph prompt tuning studies. For example, All-in-one uses GraphCL and SimGRACE. In addition, EP-GPPT and EP-GraphPrompt are edge prediction-based pre-training methods proposed by GPPT and GraphPrompt, respectively. Therefore, we believe the adopted four pre-training methods are inclusive and fair for performance comparison of different graph prompt tuning methods. We will explore the performance of our framework under other pre-training methods in the future (see Appendix E in our revised PDF).

• C5. Figure 2 presents convergence speeds in terms of the number of epochs. The authors should also analyze the efficiency of the proposed method using learning curves or running time comparisons.

• R5: Thanks for bringing this up. We would like to emphasize that most deep learning papers (e.g., GPPT and GPF in our baselines) report performance per epoch since the evaluation is conducted after each epoch. Therefore, we follow the common evaluation scheme in our experiment. In addition, we provide the results of running time (seconds per epoch) for each method in the following two tables. From the tables, we can observe that our method does not introduce significant computational cost. We have added the discussion in our paper (see Appendix D.1 in our revised PDF).

  Tuning Methods	Cora	CiteSeer	Pubmed	ogbn-arxiv	Flickr
  Classifier Only	0.116	0.136	0.663	1.186	5.156
  GPPT	0.141	0.151	0.713	1.381	5.828
  GraphPrompt	0.126	0.136	0.673	1.377	4.362
  All-in-one	0.477	0.578	3.090	6.085	7.357
  GPF	0.121	0.131	0.678	1.070	3.482
  GPF-plus	0.116	0.131	0.668	1.075	3.427
  EdgePrompt	0.121	0.136	0.693	1.106	3.824
  EdgePrompt+	0.146	0.156	0.804	1.377	5.894

  Tuning Methods	ENZYMES	DD	NCI1	NCI109	Mutagenicity
  Classifier Only	0.216	0.176	0.291	0.332	0.302
  GraphPrompt	0.276	0.211	0.347	0.357	0.322
  All-in-one	0.457	0.643	1.337	1.397	1.206
  GPF	0.221	0.191	0.342	0.322	0.307
  GPF-plus	0.231	0.191	0.347	0.296	0.312
  EdgePrompt	0.226	0.196	0.347	0.296	0.317
  EdgePrompt+	0.332	0.302	0.442	0.382	0.402

• C2. Since this work emphasizes edge-level prompt tuning, it would be beneficial for the authors to explore edge-related tasks, such as edge classification and link prediction, to further expand the scope of the paper.

• R2: Thanks for bringing this up. We would like to clarify that designing edge-level graph prompts does not mean we particularly focus on edge-level tasks. Instead, our design aims to enhance pre-trained GNN models in capturing graph structural information for diverse downstream tasks. We provide results for node classification and graph classification as downstream tasks, as we are following previous studies on graph pre-training and graph prompt tuning. For example, in graph pre-training studies, GraphCL, SimGRACE, and InfoGraph use graph classification, while DGI uses node classification. As for graph prompt tuning studies, GPPT focuses on node classification, GPF focuses on graph classification, and GraphPrompt focuses both. We follow these studies to conduct experiments in our study.

• C2-1. In many real-world scenarios, studying edge-level tasks is highly relevant because the space of edge types can evolve over time. For example, in a social network, a newly introduced user interaction feature might require predicting new edge types using a trained GNN.

• R2-1: Thanks for bringing this up. We would like to clarify again that this study is irrelevant with edge types.

• C2-2. If the research on edge-level tasks is beyond the scope of current pre-trained GNNs (i.e., no existing pre-trained GNNs focus on edge-level tasks), the authors should clarify this limitation in the submission.

• R2-2: Thanks for bringing this up. Current pre-trained GNNs mainly focus on node classification and graph classification. Even if we regard it as a limitation, it is about graph pre-training studies but not about the graph prompt tuning stage. In addtion, we would like to argue that link prediction as the downstream task may be incompatible with the "pre-training, adaptation" scheme. During pre-training, GNN models should be trained via self-supervised learning. If the downstream task is link prediction, however, we will directly have label information (i.e., whether an edge exists between a node pair) in graph data. In this case, we can simply follow an end-to-end manner by using link prediction to train GNN models and then making inferences (we guess it is the reason why previous studies choose not to include the results of link prediction as the downstream task). Considering this, we believe node classification and graph classification are proper and sufficient for performance evaluation in our experiments.

• C3. The core Equation (4) in EdgePrompt+ appears overly similar to existing work, which may diminish the paper’s technical contribution. In CompGCN [1], the operation of weighting relation embeddings based on relation base embeddings has already been shown to be simple and parameter-efficient. Therefore, the authors should elaborate on the unique technical contributions of their method.

• R3: Thanks for bringing this up. We would like to clarify that they are different in two aspects. First, they basically have different targets. Equation (4) in EdgePrompt+ computes edge-specific prompt vectors, while CompGCN aims to compute relation-specific embeddings. Second, they obtain weights in different ways. The score vector in Equation (4) is obtained through a score function, while CompGCN takes weights as independent variables.

Dear Reviewer D2XH,

Thank you again for reviewing our paper. Your evaluation is very important to our paper. We believe that our point-by-point clarifications have addressed all your concerns — in light of this, we hope you could consider raising your rating score. If you have any further questions, we are willing to provide more explanations.

Thanks,
Authors of Submission 4905

In addition, we conduct experiments on edge classification for each method. Edge labels are constructed following All-in-one. The following tables report the accuracy of these methods under GraphCL and EP-GraphPrompt. According to the tables, we can observe that our method can still outperform other baselines for edge classification in most cases.

We hope the new results can still be considered for your evaluation. We will add them in our revised version.

Dear Reviewer D2XH,

Thank you again for reviewing our paper. As the discussion phase is ending in three days, we are eager to learn whether our answers have addressed your concerns. We are looking forward to your feedback and happy to answer any extra questions.

Best,
Authors of Submission 4905

Dear Reviewer D2XH,

Thanks for your reply.

Our study follows the same assumptions and focuses on the same downstream tasks (i.e., node classification and graph classification) in previous studies. The only difference is how we design graph prompts (i.e., edge-based prompts in our study vs node-based prompts in previous studies).

We would like to argue that the importance of graph prompts on edges has been discussed in our theoretical analysis Section 4.3 and 4.4. We believe that graph prompts on edges are significant for node-level and graph-level tasks and should not be underestimated. We use Figure 1 to illustrate why edge-based approach is better than node-based approaches. Our edge-based method enables neighboring nodes to receive different finer learned prompt vectors from one node, which cannot be achieved by node-based method.

As for time cost, we provide the results of time cost per epoch. Since we run each experiment 200 epochs, the overall running time is 200$\times$(seconds per epoch) for every method.

We hope the above clarification can better address your concerns. We will be happy to answer any further questions you may have.