Graph Few-Shot Learning via Adaptive Spectrum Experts and Cross-Set Distribution Calibration

We sincerely thank the reviewer for dedicating significant time and effort to evaluate our paper. Below, we provide detailed responses to your comments, and we hope that these clarifications can address your concerns.

W1 & Q1: Why handling nodes with diverse connectivity patterns is emphasized? Include a baseline that combines graph few-shot learning with a method designed for heterophilic graphs.

A1: We kindly clarify that in graph few-shot learning, the first step is typically to learn expressive node embeddings [1][2], followed by a meta-learning algorithm that can rapidly adapt to new tasks with only a few labeled nodes. Modeling diverse connectivity patterns can help learn more discriminative node representations.

Moreover, most existing methods for heterophilic graphs rely on global high-pass filtering to capture inter-node differences and achieve high-quality representations [3]. In contrast, our method employs an adaptive spectrum expert mechanism to perform node-specific filtering, thereby capturing diverse local connectivity patterns. We further incorporate a cross-set distribution correction strategy to align the distributions of the support and query sets, which enables more accurate decision boundaries.

To further address the reviewer’s concerns, we also replace the encoder in TENT with H2GCN [4], a model specifically designed for heterophilic graphs. The results are presented as follows.

From the results, we can observe that even when equipped with convolutional networks specifically designed for heterophilic graphs, the competitive graph few-shot learning model TENT not only fails to outperform our method on certain datasets but in fact exhibits a significant performance drop.

[1] Graph prototypical networks for few-shot learning on attributed networks. In CIKM. 2020.
[2] Few-shot learning on graphs. In IJCAI. 2022.
[3] Heterophily and graph neural networks: Past, present and future. In IEEE Data Engineering Bulletin. 2023
[4] Beyond homophily in graph neural networks: Current limitations and effective designs. In NeurIPS. 2020.

W2 & Q2: It would strengthen the analysis to include the final accuracy values for Figure 5. Include experiments comparing the accuracy with and without prototype calibration under varying levels of distributional shift.

A2: We thank the reviewer for this valuable suggestion. Following your feedback, we have included the final accuracy results with respect to different levels of node homophily. We use the node homophily ratio metric proposed in [1], which is defined as $\frac{1}{|V|}\sum_{v \in V}\frac{|\{(u, v): u\in N(v) \wedge y_v=y_u\}|}{|N(v)|}$, where $N(v)$ denotes the neighborhood of node $v$ and $y_v$ is the label of node $v$. Next, we partition all nodes into intervals based on their homophily values and evaluate the model’s performance within each interval. The results are presented below.

Table: Results of our model under different levels of node homophily.

From the results in the table above, it is evident that our model demonstrates superior recognition capability across nodes with varying levels of homophily.

[1] Geom-GCN: Geometric Graph Convolutional Networks. In ICLR. 2020.

Moreover, we have conducted further experiments comparing the model’s performance with and without prototype calibration under varying levels of distribution shift across multiple datasets. Specifically, we compute the maximum mean discrepancy (MMD) between the support set and the query set in each meta-test task to quantify the degree of distribution shift. Based on this metric, we evenly divided the tasks into three groups according to their shift levels. The corresponding results are presented below.

From the above results, we observe that incorporating the proposed prototype calibration technique consistently improves model performance across different settings, and the improvement becomes more pronounced as the degree of distribution shift increases.

Q3: Could you clarify the specific scenarios in the graph domain where this meta-learning framework is needed?

A3: We kindly clarify that a representative application scenario lies in cell type annotation in bioinformatics. Specifically, we first construct a graph from spatial transcriptomics data and then employ a graph few-shot learning algorithm to acquire transferable knowledge from common cell types (e.g., epithelial and stromal cells). This enables rapid adaptation to rare cell types (e.g., macrophages) with very limited annotations.

We conduct relevant experiments on the human breast dataset released in [1]. This dataset contains 17 cell types, where 12 cell types are used for meta-training and the remaining 5 cell types are reserved for meta-testing. The comparison results with competitive baseline models are presented in the table below.

Table: Results of different models on the cell type annotation.

[1] High resolution mapping of the tumor microenvironment using integrated single-cell, spatial and in situ analysis. In Nature Communications. 2024.

Q1: More experiments with various GNN models.

Q2: Further statistical validation.

Q3: More explain about the cell type annotation.

Dear Reviewer ZVRV,

Thank you again for your constructive feedback!

As the rebuttal period is approaching its end, we would greatly appreciate it if you could kindly review our response to ensure it adequately addresses your concerns.

Thank you for your time and consideration.

Sincerely,
Authors.

We sincerely thank the reviewer for recognizing the quality and contributions of our work, and we also greatly appreciate the valuable time and effort you dedicated to reviewing our paper. Below, we provide point-by-point responses to the concerns you raised.

W1: It is a nice contribution, but leaves the reader thinking if there are things that can be done beyond this structure.

A1: We thank the reviewer for raising this point. Since our work focuses on graph few-shot learning, we adopted the widely used episodic training paradigm to ensure fair comparison with mainstream methods in this field. We also agree that exploring a departure from this paradigm by incorporating a pretraining–fine-tuning framework could be a promising direction for future work to further enhance model performance.

W2: It is not clear to me whether the same datasets would be easy or difficult for say a simple prompted LLM.

A2: We thank the reviewer for raising this important question. In the era of LLMs, we argue that it is non-trivial for directly applying LLMs to the graph dataset. As mentioned in [1], current LLMs cannot explicitly construct graph structures and thus fail to fully exploit topological information when performing graph tasks, which limits their effectiveness.

To support our argument, we utilize the Cora and CiteSeer datasets with original textual descriptions provided in [2] and fed the test nodes into LLama3-8B for evaluation. The prompt used is: “Given the title and abstract, predict the category of this paper”. We evaluate the model on the same test data, and the resulting performance is reported below.

Table: Results of the LLM across different datasets.

From the results, we can observe that our model outperforms the LLM on this task.

[1] A survey of large language models for graphs. In KDD. 2024.
[2] Exploring the potential of large language models (llms) in learning on graphs. In SIGKDD Explorations Newsletter. 2024.

Q1: Why CiteSeer seems to show a different pattern for the ablation in Table 5?

A3: We thank the reviewer for carefully identifying this phenomenon. We kindly clarify that this behavior may arise from two factors: first, the CiteSeer dataset is relatively small in scale; and second, it has the lowest average node degree among all the evaluated datasets. These two factors combined likely make the prototype calibration strategy play a more critical role on this dataset compared to other components of the model.

We sincerely thank the reviewer for dedicating significant time and effort to evaluate our work and for providing valuable feedback. We believe these comments will help further improve the quality of our paper. In the following, we address each of your concerns point by point and hope that our clarifications will adequately resolve them.

W1: Prototype Calibration Novelty.

A1: We kindly clarify that the core of our proposed prototype calibration technique lies in the calibration mechanism. Inspired by the concept of Kernel Density Estimation (KDE), our method calibrates class prototypes by leveraging samples located in high-density regions of the query distribution, thereby enabling more accurate boundary modeling. Specifically, we compute the feature differences between nodes and apply a correction vector to dynamically adjust the prototypes. In contrast, conventional prototypical networks directly infer labels based on the nearest prototype in Euclidean space, which can easily lead to erroneous class boundaries, particularly in scenarios with complex distributions or closely related classes.

W2: The design of attention mechanism in Eq. (3).

A2: In Eq. (3), we introduce a Transformer-like attention mechanism on the generated difference features to assign higher weights to neighboring nodes that are significantly different from the target node, thereby enhancing the model’s sensitivity to heterophilic connections, as described in lines 149–151 of the main text. To highlight the advantage of this attention mechanism, we conduct an extra ablation study by removing this component (denoted as model w/o attention) and evaluate its performance across multiple datasets, with the results presented below.

From the results in the table above, we observe a significant performance drop when the attention mechanism is removed, highlighting the crucial role of this component in the overall model.

W3: The dimension of the node degree matrix.

A3: We would like to kindly clarify that in Eq.(4), we combine the node degree information D with the other three types of information because all four share the same number of nodes $n$.

W4: Why use |AX-X|?

A4: We kindly clarify that the purpose of using |AX−X| in our method is to capture the structural pattern of a node by computing the absolute difference between the node’s features and those of its one-hop neighbors. This design is motivated by the absence of explicit ground truth indicating which structural pattern each node belongs to, making absolute differences a natural and unsupervised measure for characterizing such patterns.

W5: Why $\hat{\beta}$ is a trainable parameter?

A5: We apologize for the misunderstanding this may have caused. In practice, we set $\beta$ as a learnable parameter, and therefore $\hat{\beta}$ is also learnable. In the revised version, we will clarify this statement to avoid potential confusion for readers.

Q1: Can additional experiments on heterophilic datasets be provided?

A6: Following the node homophily ratio metric proposed in [1], defined as $\frac{1}{|V|}\sum_{v \in V}\frac{|\{(u, v): u\in N(v) \wedge y_v=y_u\}|}{|N(v)|}$, where $N(v)$ denotes the neighborhood of node $v$ and $y_v$ is the label of node $v$, we compute the homophily values for all datasets, as shown in the table.

Table: The homophily values of different datasets.

The CoraFull, ogbn-arxiv, and DBLP datasets exhibit heterophilic property. This demonstrates that our model achieves superior performance even on heterophilic datasets.

[1] Geom-GCN: Geometric Graph Convolutional Networks. In ICLR. 2020.

Q2: Why removing the low-pass expert (w/o low) yields better performance than removing the high-pass expert (w/o high) on 5 homophilic datasets?

A7: We kindly clarify that, based on the homophily metrics calculated earlier, the DBLP, CoraFull, and ogbn-arxiv datasets exhibit strong heterophilic properties. Thus, achieving better performance with a high-pass filter on these datasets is reasonable. As for the remaining two datasets, their superior performance with high-pass filtering may stem from the fact that their original node features rely more heavily on high-frequency information to obtain discriminative representations, while low-pass filters may blur such critical features.

Q3: The parameter $\lambda$ in Eq. (2) lacks comprehensive analysis.
A8: We thank the reviewer for highlighting this point. Since we treat $\lambda$ as a learnable parameter in practice, we conduct an extra ablation study on this parameter, and the corresponding results are presented below.

From the results in the table above, we can see that our method exhibits no significant performance fluctuation across different $\lambda$ values, indicating its robustness to this hyperparameter.

We sincerely appreciate the reviewer for dedicating significant time and effort to evaluate our work and for providing constructive feedback. In the following, we address each of your comments point by point, and we hope that our clarifications effectively resolve your concerns.

W1.1: Figure 3 lacks a legend.

A1.1: We thank you for pointing out this issue. Following your suggestion, we have added a comprehensive legend in the revised version to clarify the meaning of all visual elements.

W1.2: The related work section is missing in the main text, which is quite important and should be included.

A1.2: We thank the reviewer for pointing out this issue. In the initial submission, the related work section is placed in Appendix A.7 due to space constraints. In the revised version, we will follow your suggestion and incorporate this section into the main text to provide readers with a more comprehensive understanding of the research background.

W2: There is a lack of discussion on the limitations of the research work in the main text.

A2: We appreciate the reviewer for highlighting this point. In the initial submission, the discussion of research limitations was placed in Appendix A.8 due to space constraints. Following your suggestion, we will integrate this section into the main text in the revised version to provide readers with a more comprehensive understanding of the model’s applicability and potential directions for improvement.

W3: The ablation studies are relatively comprehensive, with experiments conducted under various settings on all datasets. Could more experimental settings be considered, such as simultaneously testing the model's performance under 3-shot and 5-shot settings on the DBLP dataset?

A3: We appreciate the reviewer’s valuable suggestion. We would like to kindly note that additional experimental settings across all evaluation datasets have been included in Appendix A.6 “More Ablation Study,” with the corresponding results presented in Tables 6–9.