Graph Few-Shot Learning via Adaptive Spectrum Experts and Cross-Set Distribution Calibration
Authors: Yonghao Liu
Yajun Wang
Chunli Guo
Wei Pang
Ximing Li
Fausto Giunchiglia
Xiaoyue Feng
Renchu Guan
Venue: NeurIPS 2025 poster ()
Keywords: Graph few-shot learning
Distribution calibration
Primary area: general_machine_learning
TL;DR: GRACE

Abstract: Graph few-shot learning has attracted increasing attention due to its ability to rapidly adapt models to new tasks with only limited labeled nodes. Despite the remarkable progress made by existing graph few-shot learning methods, several key limitations remain. First, most current approaches rely on predefined and unified graph filters (e.g., low-pass or high-pass filters) to globally enhance or suppress node frequency signals. Such fixed spectral operations fail to account for the heterogeneity of local topological structures inherent in real-world graphs. Moreover, these methods often assume that the support and query sets are drawn from the same distribution. However, under few-shot conditions, the limited labeled data in the support set may not sufficiently capture the complex distribution of the query set, leading to suboptimal generalization. To address these challenges, we propose GRACE, a novel Graph few-shot leaRning framework that integrates Adaptive spectrum experts with Cross-sEt distribution calibration techniques. Theoretically, the proposed approach enhances model generalization by adapting to both local structural variations and cross-set distribution calibration. Empirically, GRACE consistently outperforms state-of-the-art baselines across a wide range of experimental settings. Our code can be found here.

Graph Few-Shot Learning via Adaptive Spectrum Experts and Cross-Set Distribution Calibration
Yonghao Liu Yajun Wang'*, Chunli Guo?", Wei Pang Ximing Li Fausto Giunchiglia' Xiaoyue Feng' Renchu Guan '1
Key Laboratory of Symbolic Computation and Knowledge Engineering of the Ministry Education, College of Computer Science and Technology, Jilin University College of Software, Jilin University
School of Mathematical and Computer Sciences, -aat University
*RIKEN Center for Advanced Intelligence Project
DDepartment of Information Engineering and Computer Science, University of Trento
(yonghao20, yajun24, guac124)0mails,
@mails. jlu. edu. cn, glu.edu...
w. w.p.annehwccomm uk, 1iximing860gmail. com, fausto. giwnghiiigggeee illggggniiiii it, {fengxy, guanrenchu @ edu.
Abstract
Graph few-shot learning has attracted increasing attention due to its ability to rapidly adapt models to new tasks with only limited labeled nodes. Despite the remarkable progress made by existing graph few-shot learning methods, several key limitations remain. First, most current approaches rely predefined and unified graph filters (e.g., low-pass or high-pass filters) to globally enhance or suppress node frequency signals. Such fixed spectral operations fail to account for the heterogeneity of local topological structures inherent in real-world graphs. Moreover, these methods often assume that the support and query sets are drawn from the same distribution. However, under few-shot conditions, the limited labeled data in the support set may not sufficiently capture the complex distribution of the query set, leading to suboptimal generalization. To address these challenges, we propose GRACE, novel Graph few-shot leaRning framework that integrates Adaptive spectrum experts with Cross-sEt distribution calibration techniques. The- oretically, the proposed approach enhances model generalization by adapting both local structural variations and cross-set distribution calibration. Empirically, GRACE consistently outperforms state-of-the-art baselines across wide range of experimental settings. Our code can be found here.
Introduction
Graphs, as fundamental and expressive data structure, are widely employed to model variety of complex systems in the real world 21, including social networks 3 4 transportation networks
5 6.. and pootiin-protein interaction networks 7 []. Recently, graph neural networks (GNNs) emerged as the facto standard for learning on graph-structure
data due their powerful representation capabilities. However, the effectiveness of GNN-based models heavily relies on the availability large number labeled nodes. A major challenge lies in the fact that annotating large-scale datasets is often impractical in real-world scenarios [9] This process is not only time- and aassurce-intensing but also demands extensive somain-specific expertise in certain specialized fields [10) [1]. For example, in the biomedical domain, accurately annotating unknown genes
'Equal Contribution
Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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often requires substantial knowledge of molecular biology, which is difficult even for experienced researchers [[2] In such scenarios where labeled data are scarce, these models often suffer from severe overfitting issues 13]. Thus, graph few-shot learning (FSL) has attracted increasing attention as a promising paradigm that enables rapid adaptation to novel tasks using only small number of labeled samples. Existing graph FSL models typically follow a two-stage paradigm [1) These models first employ the graph encoder to learn low-dimensional embeddings of nodes, and then apply the few-shot learning algorithm to enable rapid generalization to new tasks. While several graph few-shot learning methods have achieved impressive results [7 18], they still face several critical limitations that hinder their expressivity.
First, most existing graph FSL methods are grounded in either the homophily assumption (i.e., nodes with the same label tend to be connected) or the heterophily assumption (i.e., nodes with different labels tend to be connected) 19]. Based on these assumptions, they typically adopt predefined, uniform graph filters such as low-pass or high-pass filters (2).. This one-size-fits-al design implicitly applies global enhancement or suppression to node frequency signals. However, real-world graph data often exhibit significant local topological heterogeneity, where both homophilic and heterophilic connection patterns may coexist across different local regions of the graph [21 22). To substantiate our claim, we visualize the local link distribution of nodes in the Cora dataset 123, As shown in Fig. T it is evident that different nodes exhibit diverse local connectivity patterns. Applying a single, globally designed fiter-optimizees for specific connectivity assumption to all nodes can lead to suboptimal performance and may adversely affect nodes whose local structures deviate from the assumed model. This naturally leads to a fundamental question: Is it possible to develop method that enables node-specific filtering strategies to better accommodate the diverse local structures present in real-world graphs?
Second, these graph FSL methods implicitly assume that the support and query sets within each task are drawn from the same underlying distribution. However, this as- sumption is often challenged in real-world scenarios. On the one hand, the limited labeled data in the support set may fail to adequately capture the complex distribution of the query set [24]. On the other hand, the random sampling process during meta-task construction duce systematic biases-sure as oversampling from dense Sabgrrapss-wiihe in turn leads to performance degrada- tion under distribution shift conditions. The above claims are further supported by Fig. 2 where we visualize the node distributions of randomly sampled support and query sets on the Cora dataset. As shown in Fig. [ there exists a clear distributional discrepancy between the two sets, highlighting the presence of distribution shift in practical task construction. Hence, effectively narrowing the distribution gap between the support and query sets is essential under distribution shift.
Harrshd cdpe
intro-
Figure 1: Diversity of local connectivity patterns in the Cora. Node colors indi- cate their class labels.
To address the aforementioned challenges, we propose novel framework named GRACE, which integrates both adaptive spectrum experts and cross-set distribution cali- bration to facilitate effective graph FSL. Specifically, in- (MoE) paradigm, we
Suport durulty Query denc
Supooit point
Quary 2E
spired by the mixture-of-expprt develop a node-specific filtering mechanism that lever- ages multiple experts to model diverse local connectivity patterns. Each expert is responsible for capturing a dis- tinct graph filtering behavior, while gating mechanism adaptively assigns expert weights based on the structural characteristics of each node. Next, to alleviate the dis- tributional mismatch between the support and query sets, we initially derive class prototypes from the support set, which are subsequently refined through an explicit cali- bration process guided by the query set. Theoretically, GRACE enhances the model's generalization lower bound by incorporating adaptive spectrum experts that align with local graph structures. Empirically, it
Figure 2: Visualization of distributional discrepancy between support and query sets in the Cora.

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achieves substantial performance gains over competitive baselines on several standard benchmarks. In summary, our contributions are as follows.
(I) We propose a novel framework, GRACE, which integrates adaptive spectrum experts and cross-set distribution calibration to address the challenges of graph FSI..
(II) We provide theoretical analysis showing that GRACE offers improved generalization guarantees by adapting to local structural heterogeneity and mitigating distribution shift.
(III) We conduct extensive experiments on multiple benchmark datasets, demonstrating that GRACE consistently outperforms existing state-of-the fi-the--rt art methods.
2 Related Work
Graph Neural Networks. GNNs have become the cornerstone in the field of graph-structured data analysis, providing a powerful solution for graph representation learning [5). Typically, most GNNs follow the message passing mechanism [26], where the nodes continuously aggregate information from their neighboring nodes, gradually extracting local information. This characteristic enables GNNs based on this mechanism to perform excellently when dealing with homophilic graphs. However, when faced with heterophilic graphs, traditional GNNs are clearly inadequate. To this end, researchers have developed a series of specialized models 27 28 Recent studies have found that graphs in the real world often exhibit mixed structural patterns 22]. However, traditional GNNs generally adopt a -one-size-fits-lll" approach, applying the same global filter to all nodes. This practice cannot fully exploit the characteristics of each node when dealing with graphs with mixed patterns, and it is difficult to achieve the optimal effect. Therefore, our model introduces a node-specific adaptive filtering method, which selects appropriate filter for each node according to its characteristics.
Few-Shot Learning. FSL aims to solve new tasks using limited number of samples and the knowledge accumulated from previous experiences. This approach has received great attention due to its effectiveness in handling data with rare labels [1]. Generally speaking, the existing FSL models can divided mainly into two categories: (i) optimization-banae
methods [15] 18 10] and
(ii) metric-based methods [17
32 I1. The former focuses on designing different mechanisms to utilize the gradients of samples. For example, the Model-Agnostic Meta-Learning algorithm (MAML)
33 proposes inner-outer loop mechanism for gradient updates learn good initial parameters, allowing the model to quickly adapt to new tasks with a small amount of training data. The latter aims to learn transferable distance metric to evaluate the similarity degree of association between given samples and query samples. For instance, Prototypical Network [3] calculates the prototype of each category by taking the mean vector of the support examples and classifies query instances by measuring the Euclidean distances between these query instances and the prototypes.
The MoF architecture 35 is mainly based on the principle of "divide and conquer" (66, that is, first dividing the problem space, and then having specialized sub-models or experts handle their respective parts of the tasks. It has been widely applied in the fields of natural language processing (37 38 and computer vision [39 40 to improve the efficiency and performance of large-scale models. Recently, several studies 20 4 in the graph domain have also explored the integration of MoE architectures to enhance graph representation learning. For example, GMoE 42) uses the MoE architecture to adaptively select the propagation hops for different nodes. According to the features of nodes and the information of neighboring nodes, it selects the most suitable propagation hops for each node through a gating mechanism. GraphMETRO [4] utilizes the MoE architecture to address the problem of graph distribution shift. Despite recent progress in applying MoE architectures to general graph learning tasks, their potential remains unexplored in graph FSL scenarios.
Mixture-of-
3 Preliminary Study
In this section, we formally define the studied problem in this work. We focus on few-shot node classification (FSNC), one of the most representative tasks in graph FSL, to evaluate the performance of our proposed model. Formally, we consider input graph G {V. E,E A), where V and E denote the sets of nodes and edges, respectively; X E gaxd is the node feature matrix; and
3

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A E 10,1]axm is the adjacency matrix, where A, 1 if there is an edge between node i and node j. and A,3 = 0 otherwise. Typically, FSNC consists of two stages: tetaattaining and meta- testing. The label space of meta-training is denoted as Iuusee and that of meta-testing as Vew where Vhuse U Veew = 3 and Vhuve nevew 0. Moreover, we adopt the episodic training paradigm widely used in FSL by constructing series of meta-tasks. In both in the meta-training and meta-testing phases, the construction of each meta-task follows a consistent procedure. Specifically, each meta- task consists of support set and query set, i.e., T {Se, 2r). The support set is formed by randomly sampling N classes from a particular label space V.. and selecting K labeled nodes per glass-yielding an N-way K-shot classification problem, i.e., S. = {(X ) The query set is then constructed by sampling M additional nodes per class from the remaining labeled data of those same N classes, i.e., Qi {(X,, (. Y1, (7 W Note that the only difference between meta-training and meta-testing tasks lies the label space from which classes are sampled: the former samples classes from Vasse. while the latter samples from D V'eww The goal of FSNC is to extract generalizable knowledge from a collection meta-training tasks Tuain = (T:)i= such that the model can swiftly adapt to a meta-testing task Tes {Swat Qwes by leveraging a small support set
Swst {
Y i / K containing only few labeled instances per class, and accurately predict
labels for unseen nodes in the corresponding query set Qeest = {X% lest, Y Y N
4 Method
In this section, we provide detailed descriptions of our proposed model, GRACE, which consists of two key components: adaptive spectrum experts and cross-set distribution calibration. The former dynamically assigns expert weights for each node based on its local connectivity patterns, enabling the model learn more discriminative node embeddings. The latter leverages class prototypes to explicitly calibrate the distribution shift between the support and query sets, thereby enhancing the model's s generalization across tasks. To facilitate the better understanding of our model, we illustrate the overall framework of GRACE in Fig. 3
4.1 Adaptive Spectrum Expert
Generally, the first step of FSNC is to learn expressive node embeddings. As previously discussed, existing graph FSL models adopt a fixed graph filter and fail to consider the diverse local connectivity patterns of individual nodes. To this end, introduce MoE-based architecture designed to adaptively capture different structural patterns across nodes. Given that real-world graph-structured heterophily, we instantiate
data often exhibit either homophily ical connectivity types: one with low-pass filtering characteristics to smooth node features under homophilic settings, and the other with high-pass filtering behavior emphasize feature differences in heterophilic regions.
experts model these typ-
4.1.1 The Low-Pass Expert
It is widely recognized that graph convolutional networks (GCNs) 3 function as low-pass filters 45 46), effectively capturing smooth node signals. Hence, we select GCNs as one of the experts. The core idea of GCNs is to iteratively aggregate information from the target node's neighbors to update its representation. This process can be formally expressed as:
H o OD AD- (OOO))
where Á = A + I is the adjacency matrix with added self-loops, and D is the corresponding degree matrix. (() and (()) denote the node embeddings layer and the learned weight matrix, respectively. (0) = X is the initialized original node feature when l = 0. Moreover, (()) is the non-linear activation function such as ReLU.
Through the low-pass expert, we can obtain the smoothed node representations Hiw E R that characterize homophilic connectivity patterns.
4.1.2 The High-Pass Expert
The high-pass expert designed to amplify the feature differences between connected nodes, thus effectively capturing heterophilic structures where nodes with dissimilar labels are more likely to be

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(
Seltodi-TTriningg
Meta- Trainng
0) Generate prototypes using the enoodddings of the support sei
Sampling
Twan
Meta-Testing
50 Callbrate the protocypes using the embedklings the query set
Gating
Experts
Embeddings
Low Pacs
0 A....
High
(W0) Classifiation
(b) Adaptive Spectrum Experts
Cross-Set Distribution Calibration
Figure 3: The overall framework of GRACE. (a) Illustration of episodic training. In each episode, an FSNC task is constructed by randomly sampling from the original graph. (b) Adaptive spectrum experts. By introducing multiple experts to capture the diverse frequency components of nodes, we employ gating module to adaptively weight the spectrum experts. (c) Cross-set distribution calibration. We first compute class prototypes based on support set. If classification performed by directly assigning the query sample to the nearest prototype using Euclidean distance, it would be incorrectly assigned to the prototype p2. However, after applying prototype calibration, the query sample can be correctly classified.
linked. To achieve this, we design the following strategy. First, we employ a linear transformation to project the original node features X into the feature space where smoothed representations Hjo reside. We then compute the difference F between the original and smoothed features, which explicitly captures the local discrepancy of the node. Finally, we apply an attention mechanism over the resulting differential features, assigning higher weights to neighboring nodes that are significantly different from the target node, thereby enhancing the model's sensitivity to heterophilic connections. The above procedure can be defined as follows:
X' XW', F F
H
= LayerNormmA FF,
where W dxd is the trainable weight. To ensure stable model training, we apply scaling factor to the differential features to control their magnitude, followed by a layer normalization operation.
FOF
T K
F6 = FWQ: Fx FWK. Fy FWv,
Hnigh = softmax
Fv.
(3)
Vd
where W Q. WK. and Wy E R xd' are the projection matrices. Hnigh E Ruud is the desired high
frequency feature, which measures heterophilic connectivity patterns.
4.1.3 Gating Module
To effectively integrate the outputs of the low-pass and high-pass experts, we employ gating mechanism that adaptively assigns weights each expert's output. Specifically, we concatenate the raw node features X, the absolute difference between the node and its one-hop neighbors
N Ax X), the feature-wisc standard deviation ó of the raw node features, and the node degree

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D to form the composite representation X E Rax4d which is then fed into the gating module. This design enables the gating module dynamically allocate appropriate expert weights based on each node's local topological structure. The procedure can be defined as follows:
x
X [D;
softsax g/T), Z Hiow + a:, Highh
(4)
where a E I x is the gating weights and W E R the trainable weight. t is the temperature parameter. Z Ruxd is the learned final node embeddings through the adaptive spectrum expert architecture.
4.2 Cross-Set Distribution Calibration
Due the distributional discrepancy between the support and query within meta-task, directly inferring the label of a query node as the nearest prototype in Euclidean space, as done in standard prototypical networks, can easily lead suboptimal or erroneous decision boundaries. To this end, we propose a cross-set distribution calibration strategy. Specifically, we first compute class prototypes P E Raxd' based on the support set, i.e., P = I = k) JZ where I[[] is the indicator function. Next, inspired by the concept of kernel density estimation (KDE), we calibrate the class prototypes using samples located in high-density regions of the query distribution, which are considered to be more reliable, defined as follows:
1111 20 )),
= Z P. V = softmax(exp((
(5)
where E N represents the feature difference between query samples and class prototypes. E NMxd denotes the weight that quantifies the contribution of the query sample to the prototype calibration. is the bandwidth parameter of the kernel function, which controls the smoothness of the correction process.
Next, we compute correction vector by performing weighted summation over the feature differ- ences A, using the normalized weights V. The calibrated class prototype is then obtained based on this correction vector. The process can be formulated
AP A P AP,
where (35(tan)(3) + 1) trainable parameter that controls the magnitude of prototype calibration, in which 3 is predefined scalar value.
4.3 Model Optimization
After applying the adaptive spectral experts and the cross-set distribution calibration, we adopt the classical metric-based episodic training paradigm for FSNC. Specifically, we optimize the model parameters by minimizing distance-based cross-entropy loss computed over the query sets of all meta-training tasks in Tuain- The objective be formulated follows:
T NM
IYY, = k] log exp(-e(Zi, W Pb)
(7)
Σn exp(-e(Z)) W. P)))
where e(.,-) is the Euclidean function and W, denotes the trainable vector.
In the meta-testing phase, we also compute the calibrated prototypes using the same strategy as described in Bnd Then, each query instance is assigned to the class of the nearest calibrated prototype based on Euclidean distance. Formally, the predicted label Y for a query instance is defined as follows:
Ps
Σ
1|Yiest,i K)Zies, P Calibration(P)) Y argmin, eZZWi, Pk)..
Stest,
(Ziaa.r Vin.))
(8)
We present the detailed training procedure and the complexity analysis of GRACE in Appendices A.I and A.2.

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Theoretical Analysis
In this section, theoretically analyze the effectiveness of the proposed model. Specifically, present the following theorem to establish the connection between the model's generalization error and the employed techniques.
Theorem 5.1. Suppose that the loss function & is I.-Lipschitz continuous, and Eg > 0, the gating module satisfies Evg-Py [o I(d > d }[ S Cg. where a, denotes the gating weight for node and dhom, duct measure the degrees of homophily and heterophily, respectively. Furthermore, for ò > we assume that the Wasserstein distance between the support and query distributions satisfies Wi(Ps, Pe) S 5. Then the generalization error Egen of the proposed model is bounded by:
log T + +22cg Cos +C2e+CC((+00037 +0100))-1110)-22)))
Egen S &CIV
(9)
where C₁ Cz. and C3 are the constants. and [2] are the number of training tasks and query samplex. is the bandwidth.
Theorem 5.1
indicates that, given fixed number of training tasks and query samples, our model achieves a tighter generalization error bound compared to that of standard approaches. This improve- ment is attributed to the reduction of the discrepancy measures eg and ö, which is accomplished through the use of adaptive spectrum experts and the cross-domain distribution calibration strategy.
Moreover, spectral experts.
derive the following corollary to further illustrate the advantage of the adaptive
Corollary 5.2. When local topology exhibits strong heterogeneity (eg 0), our model achieves strictly better bound MoE than that of single-filter methods Sin gen
"gen"
MoE
Sin
0(12)-1/2)
(10)
gen
gen
Corollary 5.2 indicates that the generalization error of GRACE is clearly lower than that of models using single filter. The proofs of Theorem 5.1 and Corollary 5.2 can be found in Appendix A.3.
Experiments
6.1
Datasets
To empirically validate the effectiveness of our proposed model, we utilize several widely adopted
datasets for FSNC tasks, including Cora (23) CiteSeer [X]], Amazon-Computer [47) Coauthor-
CS [4]. DBLP [88) CoraFull [49], and, a large-scale dataset, ogbn-arxiv [50]. The statistics of
these datasets are presented in Table We present detailed descriptions of these adopted datasets in Appendix A.4.
6.2 Baselines
To comprehensively evaluate the effectiveness of the proposed model, we compare against the following three representative categories of base- lines. Graph embedding methods contain Deep- Walk [51], node2vee [52]. GCN B and SGC
Table 1: Statistics of the evaluated datasets.
#Nodes
#Eigges
#iccatures
#Labels
Cora
2.708
5,278
1.433
CiteSeer
3,327
4,552
Amazon-Computerr
13.381
245,778
767
[5]. Meta-learning methods include Prototypi- cal Network (ProtoNet) (34] and MAML (33)
Coauthor-CS
18,353
81,894
DBLP
40,672
144,135
7.202
137
CoraFull
19,793
65,311
8,710
Graph meta-learning methods consist of GPN
ogbn-arxiv arxiv
169,343
1,166,243
128
40
17
G-Meta (18). TENT (16), Meta-GPS
15
TEG [53], COSMIC (54), and Meta-BP
55
Detailed descriptions of these baselines are presented in Appendix A.5,
6.3
Implementation Details
In the stage of adaptive spectrum experts, the low-pass expert is implemented using a two-layer GCN, with each layer followed by batch normalization and ReLU activation. For the high-pass
7

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expert, the dimensions of all projection matrices are uniformly set to 32, i.e., d' = 32. The gating network is implemented as a two-layer fully connected network. with the hidden dimension of 96. The temperature T in Eq set to 2. Additionally, in the cross-set distribution calibration stage, the Gaussian kernel bandwidth a is set to 1. During training, we use the Adam optimizer [56] with an initial learning rate of 0.001. For evaluation, we randomly generate multiple meta-testing tasks from the test set. Specifically, 100 tasks are sampled per evaluation, with each task comprising 10 query samples. To ensure the fairess and stability of our results, we conduct 5 independent experiments and report the average accuracy, standard deviation, and 95% confidence interval across these runs. All experiments are carried out NVIDIA 3090Ti GPU to maintain consistent computational conditions and reproducibility.
Results
Model Performance. We conduct extensive experiments across various few-shot settings multiple datasets. As shown in Tables 2 3 and our proposed model GRACE consistently achieves superior performance under all experimental configurations, demonstrating its effectiveness for graph FSL compared to other competitive baselines. We attribute the performance improvements to the two key components introduced in our model. The adaptive spectrum experts module leverages MoE architecture to assign different weights to high-pass and low-pass experts based on the local topology of each target node. This design mitigates the limitations of using single graph filter, which may fail to accommodate diverse structural patterns. Moreover, the cross-set distribution calibration module leverages the distributional characteristics of high-density samples in the query set to explicitly calibrate the support-set prototypes, effectively narrowing the support-query distribution gap and improving the discriminative power of the classification boundary.
Moreover, it is evident that graph meta-learning models significantly outperform other types of baselines, owing to their tailored designs for addressing the challenges inherent in graph FSL tasks. In contrast, graph embedding methods and conventional meta-learning models exhibit unsatisfactory performance. This performance gap can be attributed to two main reasons: the former lacks mecha- nisms to cope with the scarcity of labeled nodes and is prone to overfitting, while the latter fails to exploit the inherent structural information of graphs.
Table 2: Accuracies (%) of different models on the three datasets.
Model
Cor
ClteSeer
Anazot-Compitt way
wwwy shot
way
way
way
wny
2 5 way
way shot
DeepWalk
32.95=2.70
36 7.9:
21.50
30. 00:56:22770 79
30: 1.42
43:224319
46 2..5
49.20=2.44 2.46
$1.24 3..2442..71
andelvve
31,17=3.16
20.00=2000
3.:12:3.15
22.00
20.25+2.56
51,46-2.25
$3.49 2.699
OCN
26.4611.166
6996112.52
67.9512236
51.9512.46 45
11.7911.00
25.5612.56
10116.2200
63:46-2.16
SGC
26.75-22.1
70.15+11999
70.67+42.11
53.72=2.55
55.12+2..99
57.25-2279
61.29:42.45
65.29-2206
09.35-+2211
ProcolNe
20.39-1252
52.67:-2.28
$7.92-62.34
49.15 29
52.19:12.96
13:75-1::49
57.15:1:2.55
2.09
2.01
MAMI.
22.40=2.20
55.07
27.50:22.29
40.15:: 25
53.75:22.75
54.3612239 39
53.72::2.25
59,20
2.:90
Mata-GNN
58.62=2.66
70.40:-2.644
11.91
55.45=2.115 15
99.71:22.79
61.32243222
62.36-t2.70
67.49=211
70. 10115122116
GPN
60.12=2.12
74.05+11.9
76.39 2.33
57 37.36--22.2 20
64.22+22.22
49
65.56-+ 2.60
72.39 2.30
2.21
G-Mets
50.73-1115
14 391
1.08
54.
57. 27.50
60.40 90
3..16:1..110
2.42
3.92
TENT
66.75 222.5
60003
33.20.1.3.19
2.95
85.12
Matu-GPS
62,19=2112
101994-2.15
23.79:42.10
58.95
20.95+2.002
82. 12:12:42.555
87.10=2.65
X FNC
25947=299
52.70-13.19
58.79-22.56
67.96-1-.310
70.29 3.05
$1.50-+-2.2
36.39-2.11 2:29
90.25 20-25-42 2.26
TEG
20.50-2.55
1065+1155
64 2.002.01
59. 20200-220000 69
73. 73.79 1.50
76 76 12
86.40=22.10 10
29.00-2.57
92. 2.05
COSMIC
63 2.47
65.37-22.49
69. 2.330.
60.55=2.75 75
70.25+2.56
75 10:00-2230 30
R5.4942.46
18.36-22 2.02
91, 21.59H22.00
TIP
30 792
71 101:011:00 66
85 15:12.19
61. 12:1222211 10
71, 2.11
75 2.3
83.36:12.07
89.49 2.06
92. 1.
MassR
66.4224.12
76
63.12:2.116
6015522445 45
73, 3.19
11:20
10:24.10
99:5-4455
GRACE
66,48=2.88
82.40-22..03
16.19:
63.90:22.84
75,67=2..44
7.664
90.23:00000
92.46-11555
94.06-t00.50
Ablation Study. To validate the effectiveness of the adopted strategies, we design multiple model variants under differrnt few-shot settings on different datasets. (I) w/o high: We exclude the high- pass expert. (II) w/o low: We discard the low-pass expert. (III) w/o cal: We climinate cross- set distribution calibration. (IV) w/o both: We omit both adaptive spectrum expert and cross-set distribution calibration, resulting in a variant that follows the standard training paradigm of graph meta-learning models. We present the ablation results in Table 5 with additional results provided in Appendix A.6. Based on the results, we have the following in-depth analysis. (1) Our proposed GRACE outperforms all four variants, which validates the necessity of the proposed modules. (II) It can be observed that the variant without the cross-set distribution calibration generally exhibits inferior performance.
8

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Table 3: Accuracies (%) of different models on the two datasets.
Model
Cozuthoe-CS
DBLP
way shot
2 way shot
way 3 shot
way shot
way 3 shot
way 5 shot
10 way 3 sbot
shot
DeepWalk
59.52:42.72
63.12433112
33.76:33.11
40.15:::2.66
49.12=2.25
59.1244..52
37.111:2119
49.16-::2.99
node2vee
56.16:2-4.19
60.22:4-.06
30.35=3003
39.16:33799
4565=2279
55.92:2233
25.7222.42
46. 26.19:22.75
GCN
73.52++11.7
77.20:13.01
$2.19=22.31
56.25:1:2.99
61.12-2.15
67.26:42.39
42. 42.16:22.39
56.12:4:2.10
SGC
75.49:
79.62-+2..1
26.39:
59.25-4:2.16
66.32=2225
20.19:42..6
40.19::2.26
55.16:::2.56
ProtoNet
31.18::382
75.5143.119
47.71
51.66::2.51
59.95-2.56
62.95:2.772
32.35::1662
52.95:2:190
MAML
62.32:4-4.0
65.20:1:420
36,99:4.33 4.32
42.12:::2443
55.05= 2.30
60.67:1:244
29 2,99
40.22:4:2.61
Meta GNN
85.76:4-..74
87.86-1-479
1..87
68.59
73,41 3.20
77.95
65 2.722:22.79
69.12:4/2.51
GPN
25.60:22.155
88, 2.22
25.88=27755
3.119
15.39-33. 3.41
79.90=
67 2.40
71,12 1.87
32.1443..0
75.72-1:.59
74.18:13.2
7649-1220
N0.12:1:2.4
2.700
72.19:12.11
TENT
89.55:24.49
50.001
78.38:25.22 5.21
78. 78.56-2-.42
78.22-2.10
81. 21.30:22.022
(9 2.15
79.200==1.95
Meta-GPS
20.16:42.72
92. 1.66
2:35
1.79
79.12=11 192
61.66:222.16 16
TO 2.22
73,59-2:120 1.26
92.00
62.93-+2.02
84.26-+-3.00
77.45
80.69-+-2.52
72.95-+-120 1.76
TEG
92.36:t11.59
19.00.11.222
80.78 40
84.70:t:144
79 79.26=2.44
82.19:::2.40
72. 2.12
75.99
COSMIC
89.35:444499
93.32
5..38
85.47 1,42
78.34 2.06
81881+2.005
66.53-4
10.09:
TLP
90.35:4-4.49
90.90:::1244
22.30:22.05
78.56:2:4.12
77.49-3222
81,95:422.39
2..19:2.35
73.16:+:2.50
Meta-BP
91.19:42221
92.32.42.111
21.35
82.12:+-2.15
78.22 2.10
81,13-+2..55
71 21.30+22:12
73.15:+-2.39
GRACE
95.50:1 1,30
96.20-10.97
86.03 1.05
86.82 1.01
81.72 2.05
85.30:::1900
74.22 in 1,56
76.70:1-1446
Table 4: Accuracies (%) of different models on the two datasets.
CoraFull
ogbn-aras
Model
5 way 3 shot
way 5 shot
10 way shot 10 way shot
S way shot
5 way 5 shot
way 3 shot
10 way 5 shot
DeepWWlk
23.00:43.09
25.93:3..45
15.3244410
17.7443.73
34.12:3.10 1.16
2.99
2.35
23.7621.02
mude2vec
23.75
25/12:1.61
13.90:13333 3.32
15.1122.
25.29=2.00
27. 17.39:12.35 56
22.99:13.15
25.95
GCN
34,68 2-7.6
39.83-42.49
29:23-4-3225
34.144-2.15
92.26-22.11
36.29-4-2.99
30.21 1.95
33.96+t1.55
39.56:1...52
44.53:8:2.2
25.12-8:.71
39.53-13.32
35.19
29.76:t:2995
31.99:12.112
35.22::2.52
ProtoNer
33.67-22.55
36.83-33.76
24.90
27:244:2.67
39.99-3.288
47.31
32.79-42.22
37.19411992
MAML
37.12433.16
47.51 3.009
26.61 4:2.1
31.60+-2.91
1.49 28.35
29.09 1.62
30.19:4:2.97
36.19:-2.29
Meta GNN
52.23-4-2.41
59.12:42.36
47.21
53.32:13.155
40.14 1.94
45.52 1.71
15.19:1:..2
39,02:1:
GPN
53.24-H2235
60.31
30.93-422 30
56.21+222099
42.81 2.34
50.50:t::11
37 $7.364 $7.36+:1.99
42.16
G-Meta
37.52:4..91
6.14323.11
53.92-12.91
1.1:3.02
1.70
2.12
2.775
TENT
64.80-24.10 10
51.73:24.0
56.00-33.53
50.26: 1.73
61.38
19:19:1:111
46.29+1..20
Meta-GPS
19:19.55.55
2.52
61. 61.23:1:311
64.22.1:2
52.16 2.01
62.55:11.99
42 2.096-22.02
46.86122.1 10
X-FNC
69.32.1..11
71,26:1-.199
19.63 1.4-5-4.45
53.00133.93
$2.36 2.75
63.19:1:2:22
41 2.772
46.10:1:2.16
TEG
12.04:1..06
76.20:2:133
61.0311111
65.36:1:.03
6..07:11.72
01.11:10.33
COSMIC
13.00-+1.788
71.24 1.52
65.79:+11 36
70.0-+11.93
52.99 2.19
65.42-+1100
23.19:12:722
21.5912.19
TLP
66.32:1...10
71.36114.19
51.73-1-133 34
56.00113.53
41.95
$2.99:12.05
39.12:1:2.15
42.62:12.009
72.90:11.90
67.26.12..9
55.12::411
65.39:144.55
46.25:1:4522
50.12:23.39
GRACE
1.32
11.60221.28
70.91111.08
74.5411.98
62.
68.34121.73
50.18:11001
55.07:10.11
This validates that this strategy can succeed in reducing the distributional discrepancy between the support and query sets within the meta-task. (III) Since real-world graphs often exhibit diverse local connectivity patterns, relying solely on high-pass or low-pass expert leads suboptimal performance, highlighting the advantage of GRACE's adaptive combination of both.
Table 5: Results of different model variants on all datasets.
Cora
CiteSeer
Amazon Computer
Coauthoe CS
DBLP
CoraFull
ogbn-arxáv
Model
way shot
way shot
way sbot
5 way 3 shot
way shot
way shot
5 way shot
w/o high
64.01 4:2.67
62. 22.26:12..6
23 90.08::0.79
79.05 1.23
79.35.1..00
76.73 1.45
59.32.1: .0
w/o low
63. 63.94::2.79
59. 29.64422.75
1.11
85.05+ 883
77.23= 1.49
61.9 61.98:t11
who cal
65.666112.80
58.61-12.58
89.58.1 1.02
1.197
83.52.1 1.89
77.1811 1.45
61.84.11.90
wo
60.12:4:2.12
25.36+22.00
66.56442.60
75.68:42.75
79.90
23.2442.33
42.81
Ours
66.48-4-2888
63.90-t:2.84
90.23++0.90
86.03-+1.05
85.30-t11.00
78.22 1.38
62.31=11.94
Hyperparameter Sensitivity. We primarily analyze the impact of two crucial hyperparameters- the bandwidth and the gating temperature 7-on model performance under the 2 way 5 shot experimental setting across several datasets, as shown in Figs. 4(a) and and 4(b) We observe that the model performance with respect to the bandwidth parameter generally exhibits a rise-then-fall trend. When a too small, the model only leverages a limited number of neighboring samples. Conversely, an excessively large introduces many irrelevant or noisy nodes, thereby impairing the model's is discriminative capability. Regarding the gating temperature т, the model performance remains relatively stable across different values. A plausible explanation is that within the explored

---

range, whether the softmax distribution becomes slightly sharper or smoother, both the low-pas- and high-pass experts maintain sufficient representational capacity.
97.5
100.0
95.0
97.5
02.5
95.0
Accuracy (%)
92.5
Accurscy
67.5
87.5
65.0-
CoraFull
CiteSeer
CoraFull
CiteSeer
02.5
DBLP
Coauthor-CS
82.5-
DOLP
Coauthor-C5
80.0
80.0
(a)
(h)
Figure 4: Hyperparameter sensitivity analysis: (a) Model performance varies with the bandwidth a.
(b) Model performance varies with the gating temperature
Case Study. We visualize the weights learned by the gating module to verify whether the proposed adaptive spectral expert strategy can effectively assign different weights to the experts based on varying local connectivity patterns. Specifically, on the Coauthor-CS dataset, nodes are grouped into 20 equal-width bins according to their homophily scores d For each bin, we compute and plot the normalized mean weights assigned to the low-pass expert (nww and the high-pass expert Whigh (Figs. 5(a) and 5(b).. The results show clear trend: node homophily increases, the weight allocated to the low-pass expert steadily increases, while that the high-pass expert decreases accordingly. This behavior is consistent with intuition and provides empirical evidence that the proposed adaptive spectral expert strategy effectively captures the local structural patterns of nodes.
Moreover, we visualizes the cross-set distribution calibration strategy under the 2-way 1-shot setting in Fig. [(c) We observe that the uncalibrated prototypes coincide with the corresponding support samples, which often lie in sparse regions relative to the query samples, potentially leading to misclassification. In contrast, the calibrated prototypes are shifted toward the dense regions of their corresponding query points, bringing them closer to the query cluster centers.
.ce
www.ing
(a)
(b)
Figure 5: (a) Normalized low-pass expert weight across node homophily d (b) Normalized high-pass expert weight across node homophily dhom. (c) Cross-set distribution calibration via KDE contours, showing support (stars), query (circles), and corrected prototypes (diamonds).
8 Conclusion
In this work, we propose a novel model, named GRACE for graph FSL. Specifically, our model incor- porates two key techniques. First, an adaptive spectral expert strategy is employed to assign different weights to multiple experts based on the diverse local connectivity patterns of nodes, thereby learning expressive node embeddings. Second, a cross-set distribution calibration strategy is introduced to mitigate the distributional shift between the support and query sets, enabling the model to establish more accurate decision boundaries. Theoretically, GRACE offers stronger generalization guarantees by adapting to local structural heterogeneity and mitigating distributional shifts. Empirically, GRACE consistently outperforms other competitive models across multiple benchmark datasets.
10

---

Acknowledgments
Our work supported by the National Science and Technology Major Project under Grant No. 20212D01 12500, the National Natural Science Foundation of China (No. 62172181 87 and No. 62372209). Fausto Giunchiglia's work is funded by European Union's Horizon 2020 FET Proactive Project (No.823783).
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A Appendix
A.1 Training Procedure
Algorithm 1 Training Procedure of GRACE
Require: A graph H
Ensure: The trained GRACE.
1: Perform the low-pass expert using Eq.1.
2: Perform the high-pass expert using Eqs.2 and 3.
3: Intergrate the outputs of low-pass and high-pass experts using Eq.4
4: Perform cross-set distribution calibration using Eqs.5 and 6.
5: Optimize the proposed model by minimizing the loss in Eq.7
6: Evaluate the model performance using query set with Eq.8.
We present the detailed training procedure of GRACE in Algorithm
A.2 Complexity Analysis
In this section, we provide a detailed analysis of the time complexity of the proposed model. During the graph feature extraction phase, the primary computational cost arises from the low-pass branch and the high-pass expert's ' forward propagation. The low-pass branch employs two graph convolutional layers implemented using sparse matrix multiplications, resulting in an approximate complexity of El d'), where |E] denotes the number of edges and d' represents the dimensionality of the hidden units. In the high-pass expert module, aside from initial linear projection, sparse self- attention computation is performed on all edges, incurring a complexity of O([E) - d'). Furthermore, the gating network integrates the raw node features with their first- and second-order neighborhood differences via fully-connected mappings, and its forward pass operates with a complexity of O( d), where n is the total number of nodes and d is the input feature dimension. Regarding the few-shot prototype correction mechanism, the complexity is primarily determined by the Euclidean distance computations and subsequent weighted corrections between the support and query samples, which is approximately ONNo d'), with No denoting the number of query samples. Additionally, the supervised contrastive loss employed in the model necessitates concatenating, normalizing, and computing the similarity matrix for the features of both support and query samples, leading to an overall complexity of ((Nss + N² d'), where Ns represents the number of samples in the support set. In summary, the overall time complexity of the model is chiefly influenced by the number of edges, nodes, and the feature dimensions; by employing sparse matrix operations and localized sampling strategies, we have effectively reduced the computational burden, ensuring that the model's runtime efficiency remains within acceptable bounds for practical applications.
A.3 Theoretical Proofs
A.3.1 Proof of Theorem 5.1
Before formally proving Theorem 5.1, we first present several key definitions.
1. (Lipschitz Continuity) The loss function L: RNN x y the following is satisified:
+
RR is L-Lipschitz continuous if
[C(Z,) L(Z', v)1 < LIZ
Z'
Vy e.
2. (Heterogenity Balance) For node E V, define homophily degree d:om = [((, v) E E
V/. = vo }1 and heterophily degree dhet |1, dhom. For fg > 0, the gating network satisfies:
Eo
[aa I(dioom dbet)]] Eg.
3. (Distribution Shift) For 5 > 0, the Wasserstein-1 distance between support set distribution Ps and query set distribution Pe satisfies:
Wi(Ps, < 8.
22

---

The complete eπror decomposition is:
gen
Moo
Gate
Ditt
(I)
Expert Variance
Gating Eirrrr
Distribution
Next, we present the following lemmas to assist the proof of Theorem 5.1.
Lemma A.1 (Expert Variance Bound). Let FMEE be the hypothesis class of the adaptive spetrum experts module. The expected error from expert diversity satisfies:
log T
(MoE' S 2L (FMoE) I CiV
T
where Ry is the Rademacher complexity.
Proof. The proof follows three key steps:
Step 1: Define Empirical Rademacher Complexity. For T i.idd tasks {T:) and Rademacher variables B, {+1}:
Ri (FME)) E
sup fEJ'm MaR
Σ (T)
Step Apply Rademacher Bound for Ensembles. Using the theorem in [1 for II-expert models:
llo T T
RT(FMoE)
S
[r
log T
II
Step 3: Link to Generalization Error. By Talagrand's contraction lemma 2
2T (FMMe)
log T
- 21
T
log T T
Ciy
Lemma A.2 (Gating Error Propagation). Under Definition 2 (Heterogenity Balance), the gating- induced error satisfies:
EGate S L LV (a. - < C2Eg.
Proof. The proof consists of three key phases:
Step 1: Error Vector Representation. Define the representation discrepancy between ideal and actual gating:
AH, (a. a Hlow, (a a. Hiight
Using the Lipschitz continuity of the loss function:
(HH,) L(H;) S L|AH,12
Step 2: Norm Analysis. By the filter energy bound representations):
Howw 1|,, H Hnigh S (normalized
AAH 1l2 S Jas, ag1(( H olo + H 112) < 2/ agl
Taking expectation over nodes:
E. AH < 2E, ja. af S 2cg
Step 3: Concentration Inequality. Applying Cauchy-Schward inequality to the loss difference:
EGate E (HH,)) [(H))] s LE |l2 - 2Le, C2
23

---

Lemma A.3 (Distribution Calibration Error). Let Ps be the calibrated support distribution using KDE with bandwidth o, and Po be the query distribution. Under Definition (Wi (Ps.Ps.Po) S 6). the distribution shift error satisfies:
Diit S C3 (6+ 0(02) -
where C3 I. diimmm)) depends the label space diameter.
Proof. We analyze the distribution calibration error via three steps:
Step 1: Error Decomposition. Using the triangle inequality of Wasserstein distance:
Wi Wi(Ps, Pe) S (P(,ssPo)) Po) + Wi (i
Original shift
KDF estimation
By definition 3, the first term is bounded by 5.
Step 2: KDE Estimation Error. Let Ps(y) ब Ex Ko - 81) be the KDE-calibrated distribution, where y are perturbed prototypes. Using the Kantorovich-Rubinsttci duality (3):
W1 Wasss
A [f(1)] E Ps [(v)]]
sup ||
where is I-Lipschitz. This can be bounded by:
Wi (P Ps) S E Ps(v) Ps(1)) + Var Ps(
Bias
Variance
Step 3: Variane Analysis. For Gaussian kernel Kr with bandwidth a:
Bias term: By Taylor expansion.
E P[Ps(v) Ps(i) = O
Variance term: By the central limit theorem,
Var Var(Ps(y)) =0 - 10/0
where d is the feature dimension. Choosing 1Q1-1/((+4) optimizes the trade-off:
Var(Ps()) = (101-1/2)
Step 4: Final Bound. Combining all terms with the Lipschitz loss:
Epi L d)am()) Wi(Ps, Po) SCss (0 (8+0)))) +o 10000)+00111101000000)0 where diam()) = supg.y'e D.y''E ey |ly - y'll2.
Next, we formally prove the Theorem 5.1.
Proof.
Recall Eq I and Lemmas A.l
A.2
A.3
the following inequality holds:
Egen
EMoE
+
EGate
+
EDiat
Expert
Gating Fimrr
Distribution
(2)
loo T T
(5 (5+00))+00(11111))
< sCy
+ C2c, + Cs
Thus, complete the proof of Theorem 5.1.
24

---

A.3.2 Proof of Corollary 5.2
Proof. We compare the generalization error of the proposed model (e with baseline using single graph filter (egen)
Step 1: Baseline Error Characterization. For the single-fitte baseline, Theorem 5.1 implies:
log T + C2
Sin gen S CiV
T
Step 2: Error Difference Analysis. Subtract the proposed model's bound (Theorem 5.1) from the baseline:
A
gen
"gen
< C2 (eg
Sin =g + +0 (1
Step 3: Gating Advantage. Under the strong heterogeneity (eg - 0), and noting Sin eg
2 eg:
C2(Eg - Sin) S LiEg - Eg)
Step 4: Final Inequality. Combining these results:
Ae < o (10
Thus, complete the proof of Corallary 5.2.
A.4
Dataset Descriptions
We conduct experiments variety of graph datasets from different domains. Each dataset is divided into disjoint class sets for veta-training, meta-validation, and meta-testing. The details are as follows:
Cora 4 A citation graph where nodes represent academic papers and edges indicate citation relationships. Each node is assigned label based on the paper's research topic. We divide the dataset into 2, and 2 classes for meta-training,
validation, and meta-testing, respectively.
CiteSeer [4: A document-level citation network consisting of scientific publications as nodes and citation links edges. Labels reflect the thematic area of each document. The dataset is split into classes for each of the three meta-learning phases.
Amazon-Compn Computer [5]: A co-purchase network constructed from Amazon product data. Nodes denote products, and edges connect items frequently purchased together. Each product is categorized based on its functional type. We apply 4/3/3 class split for training, validation, and testing.
Coauthor-CS [5): collaboration graph in which nodes correspond to authors and edges indicate co-authored publications within the computer science domain. Labels are derived from research specialties. A 5-class split is used for each meta stage.
bibliographic co-authorship network where each node denotes a researcher and edges indicate joint publications. Node labels reflect academic fields. We partition the dataset into 77, 30, and 30 classes for training, validation, and testing.
DBLP 66:
CoraFull 7 An extended version of the Cora dataset that includes a broader range of categories. Nodes represent papers, and citation links define the graph structure. We use 40 classes for meta- training. 15 for validation, and 15 for testing.
ogbn-arxiv 8) A large-scale graph built from arXiv submissions in computer science. Each node corresponds to paper, and edges are formed based on citation patterns. Labels are based on subject areas defined the arXiv taxonomy. The dataset is split into 20 classes for training and 10 classes each for validation and testing.
25

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A.5 Baseline Descriptions
A.5.1 Graph Embedding Methods
DeepWalk 9: It leverages random walks inspired by the word2vec algorithm generate low-
dimensional node embeddings for graphs.
GCN [[O]: employs first-order Chebyshev approximation graph filter to derive hidden node embeddings, which are then utilized for downstream task analysis.
SGC Mi It streamlines the GCN architecture by eliminating non-linear activations and collapsing weight matrices, resulting in simpler yet efficient model.
A.5.2 Meta-Learning Methods
It learns metric space and predicts query sample categories by measuring their similarity to class prototypes derived from support samples.
ProtoNet [
MAML, T3 By optimizing model parameters through one or few gradient updates, enables fast adaptation to new tasks with limited labeled data, providing a well-initialized meta-learner.
A.5.3
Graph Meta-Learning Methods
GPN 14]
It adapts ProtoNet by integrating graph encoder and evaluator to learn node embeddings, assess node importance, and classify new samples based on their proximity to the nearest class prototype.
G-Meta [15]: By constructing node-specific subgraphs, it propagates localized node information and employs meta-gradients to extract transferable knowledge across tasks.
TENT [6]] It introduces adaptive framework with node-level, class-level, and task-level com- ponents to bridge the generalization gap between meta-training and meta-testing, while minimizing performance fluctuations caused by task variations.
Meta-GPS [17]: Enhancing MAML, it incorporates prototype-based parameter initialization, scaling, and shifting transformations to improve meta- meta-knowledge transfer and enable faster adaptation to new tasks.
TEG [18] It designs task-equivariant graph framework using equivariant neural networks to learn adsk-tde strategies, effectively capturing inductive biases from diverse tasks.
COSMIC [9]: proposes a contrastive meta-learning framework that aligns node embeddings within each episode through a two-step optimization process for improved few-shot learning.
Meta-BP 20) It proposes lightweight graph meta-learner that extracts relevant knowledge from -lx pre-trained GNN and leverages task-relevant information to quickly adapt to new tasks, while pruning the meta-learnr to enhance its generalization ability on unseen tasks.
A.6 More Ablation Study
We conduct extensive ablation studies examine the contribution of individual components in our proposed framework. By systematically removing or altering specific modules, we aim to assess their impact on overall performance and provide insights into the design choices. The detailed results are summarized in Tables A.
A.2 A.3 A.4. Specifically, Table presents an additional ablation on the gating inputs defined Eq.4, where the input vector is constructed as X, = X [|||| with
X denoting the original node feature, N = AÄ - X the one-hop neighborhood difference, & the feature-wise standard deviation, and D the node degree. We design four variants accordingly: w/o X: We remove the original feature; (II) w/o N: We discard the neighborhood difference; (III) w/o ø: We eliminate the standard deviation; (IV) w/o D: We exclude the degree information.
The ablation results clearly demonstrate that each designed module contributes significantly to the overall performance, which is consistent with analysis in the ablation study section of the main text.
A.7 Limitation
Although our model achieves outstanding performance in graph few-shot learning. it currently considers only high-pass and low-pass filters. Incorporating broader range of spectrum experts could potentially further enhance the model's performance. Moreover, it introduces several critical
26

---

Table A.1: Results of different model variants three datasets.
Cora
CiteSeer
Jiaazon-Compinn
Model
way shot
way 5 shot
way shot
way
way shot
way shot
w/o high
74.824:2.49
82.89:12.04
73.76:1:..3
77.62:42.03
1.33
10.57:11.13
w/o low
78.11
1.937=11993
67.4611..39
70.62::2.23
92.06=00.00
94,31
w/o cal
82.35+:2.04
1.77
71.17=22.44
79.32:1..99
92.32:1:.55
94.62:10.52
w/o both
1..6
76.3
64.22:4:2.22
65.59:
72.19:2.330
76.19::2.21
82.4011:2.03
86819:11.80
75.67=12.44
79.64:11.79
92.46.10.55
94.66.10.50
Table A.2: Results of different model variants on two datasets.
Coauthor-CS
DBLP
Model
way shot
2 way 5 shot
way shot
5 way 3 shot
10 way 3 shot
10 way shot
w/o high
93,46+ 1.41
93.00=11.40
1.19
76.85+2.11
66,81=1.63
70.08
w/o low
94.60+11.34
18-
85.31=1.03
79.75+42.003
12.50=
76.65+1..2
w/o cal
9.39
1..3
86.27=0.95
80.14:4..008
13.5
75.90+
w/o both
85.60+2..15
88.70-+2.21
81.79+3.18
75.39++3.41
67.20-+2.40
71.12+1.87
Ours
95.50:11.30
96.20=10.97
86.82=1.01
81.72::2.05
74.22::1.56
76.70=1146
Table A.3: Results of different model variants on two datasets.
CoraFull
ogbn-arxit arxiv
Model
5 way 5 shot
10 way shot
10 way 5 shot
5 way 5 shot
10 way 3 shot
10 way 5 shot
w/o high
19.07:11.35
1.
7..55=11000
1.764=1.77
47 1.01
51.55:10.2
wfo low
81.32+1 1.23
1.557+1.11
73.95+0.97
67.01+1.63
49.98+ 1.04
54.94+00.1
w/o cul
80.38 1.30
1..09
74.20
1.75
1.04
53.77-10.95
w/o both
29.31+2.19
50.93+22.30
56.21#2.09
50.50+2.13
37.36=
42.16=22.19
Ours
8..60
70.91-1.08
74.54
68.34
50.18:1.01
55.07
Table A.4: Results of different model variants seven datasets.
Model
Cora
CiteSeer
AmazonnComppnn
Coauthor-CS
DBLP
CoraFull
ogbn-arxiv
2 way 1 shot
2 way shot
2 way shot
way shot
way shot
5 way 5 shot
5 way shot
w/o
63 63.46:22
63.83+22.74
89. 89.95=00.80
1.13
84.81+1.91
80.91=1.30
62.46#
63.12++2.93
60.99++2.91
89.53++0884
84.63+1.199
84.55+1884
80.80 1.27
62.06+ 1.93
w/o
61.4
63.68-13.07
89.47 1.01
85.39-1..10
84,83-1:1.90
81.01::1.20
62.19
w/o D
63.80-+2.84
62.27442.93
89.41 1.03
85.26:t:1.09
85.01+11.83
$1.52+11.28
62.26 1.93
Ours
66.48-+2.88
63.90
0.90
86.03++1.006 +.05
85.30++1.00
1..28
62.31 1,94
hyperparameters that influence the final performance. Determining the optimal settings for these enhancements remains challenging task. This indicates that there is still room for improvement in our model's performance due to the impact of hyperparameters.
A.8 Broader Impacts
This study aims develop an effective approach for graph few-shot learning. Our proposed method not only advances the development of graph-based few-shot learning but may also offer insights for few-shot learning in other domains. While our work does not involve any ethical concerns, it may carry potential societal implications. However, we believe it is not necessary to emphasize them here.
References
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Reviews:
[{"review_id": "kEbbUGDfvH", "reviewer": "Reviewer_6Yjk", "summary": "This paper proposes the GRACE framework for graph few-shot learning tasks. The framework introduces adaptive spectrum experts to adapt to the heterogeneity of local topological structures in the graph, and combines the cross-set distribution calibration technology to solve the problem of inconsistent distribution of support sets and query sets, thereby improving the generalization ability of the model. Experiments show that GRACE outperforms existing few-shot learning methods in a variety of experimental settings, verifying its effectiveness.", "questions": "Please respond to each item in [Weakness] one by one.", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper provides a thorough analysis of the issues that need to be addressed in Graph Few-Shot Learning, highlighting the necessity of developing node-specific filtering strategies and narrowing the distribution gap between the support and query sets.\n2. To tackle the aforementioned problems, the paper introduces Adaptive Spectrum Experts and Cross-Set Distribution Calibration.\n3. Experimental results on seven graph datasets, including Cora and CiteSeer, demonstrate the effectiveness of the model. The experiments are comprehensive, and the ablation studies and visual analyses effectively validate the rationale behind the two targeted designs.\n\nWeaknesses:\nThe quality of the paper is relatively high, but there are still some shortcomings:\n1. Areas that need improvement in writing:\n  1) Figure 3 lacks a legend.\n  2) The related work section is missing in the main text, which is quite important and should be included.\n2. There is a lack of discussion on the limitations of the research work in the main text.\n3. 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?", "was_revised": true, "final_justification": "The work is of high quality and therefore receives a reasonable initial score. The only drawback is that the paper places a significant amount of key content in the appendix, which significantly hinders reading. During the rebuttal period, the original paper could not be directly revised, making the quality of the revisions difficult to judge. We hope the authors will address this issue in the future.", "rebuttal": "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.\n\n```\nW1.1: Figure 3 lacks a legend.\n```\n**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.\n\n```\nW1.2: The related work section is missing in the main text, which is quite important and should be included.\n```\n**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.\n\n```\nW2: There is a lack of discussion on the limitations of the research work in the main text.\n```\n**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.\n\n```\nW3: 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?\n```\n**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**."}, {"review_id": "s8OparUlhu", "reviewer": "Reviewer_bCQK", "summary": "This paper tackles two critical challenges in **graph few-shot learning (GFSL)**:\n\n1. Handling **diverse local structures** in real-world graphs.\n2. Narrowing the **distribution gap** between support and query sets.\n\nThe authors propose a framework GRACE incorporating adaptive spectrum experts and cross-set distribution calibration.  They further validate their claims through theoretical analysis and experiments.", "questions": "1. The authors primarily selected homophilic datasets. Can additional experiments on heterophilic datasets be provided to support the claim of adaptive handling of heterogeneity?\n\n2. In Table 5, removing the **low-pass expert** (w/o low) yields better performance than removing the **high-pass expert** (w/o high) on 5 homophilic datasets, which contradicts intuition. Theoretically, the low-pass expert should offer more benefits for homophilic datasets, and the authors should provide deeper analysis. \n\n3. The parameter $\\lambda$ in Equ. (2) lacks comprehensive analysis.", "limitations": "see weaknesses.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths and Weakness:\n\n#### Strength:\n\n- The paper proposes a novel approach to address the graph few-shot learning task.\n- Theoretical derivations and experimental results are provided to demonstrate the method’s effectiveness.\n\n#### Weakness:\n\nMethodological Concerns.\n\n1.  Prototype Calibration Novelty. The prototype-based strategy in Cross-set distribution calibration lacks originality, as similar concepts have been adopted in methods like PrototypeNet. The authors should offer more clarifications. \n2.  The design of attention mechanism in Equ. (3)  lacks clear motivation and experimental validation. \n3.  The dimension of the node degree matrix D in Equ. (4) may not align with $d$ and is dependent on the number of nodes. How is this issue addressed across datasets with varying node sizes?\n4.  Why use $|\\hat{A}X - X|$ instead of $\\hat{A}X - X$ in Equ. (4) ?\n5.  The $\\hat{\\beta}=0.5(tanh(\\beta) + 1)$ should yield a scalar if $\\beta$ is scalar value, which contradicts the statement in line 184: _$\\hat{\\beta}$ is a trainable parameter_.", "was_revised": true, "final_justification": "The author has addressed some of my concerns and I will maintain the score.", "rebuttal": "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.\n\n```\nW1: Prototype Calibration Novelty.\n```\n**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.\n\n```\nW2: The design of attention mechanism in Eq. (3).\n```\n**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.\n\n|CoraFull|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|w/o attn|90.20±1.47|89.88±1.28|81.92±1.11|83.33±1.05|\n|Ours|90.22±1.38|91.60±1.28|85.91±1.08|87.54±0.98|\n\n|ogbn-arxiv|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|w/o attn|60.30±1.94|66.00±1.62|48.45±1.10|52.36±0.90|\n|Ours|64.31±1.94|68.34±1.73|52.18±1.01|56.07±0.91|\n\n|Coauthor-CS|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||2 way 3 shot|2 way 5 shot|5 way 3 shot|5 way 5 shot|\n|w/o attn|91.85±1.52|93.05±1.35|81.90±1.18|82.58±1.23|\n|Ours|95.50±1.30|96.20±0.97|86.03±1.05|86.82±1.01|\n\n|Cora||||\n|:----|:--------:|:--------:|:--------:|\n||1 way 1 shot|2 way 3 shot|2 way 5 shot|\n|w/o attn|62.55±2.70|69.15±2.79|73.40±2.13|\n|Ours|71.48±2.88|82.40±2.03|86.19±1.80|\n\n|CiteSeer||||\n|:----|:--------:|:--------:|:--------:|\n||1 way 1 shot|2 way 3 shot|2 way 5 shot|\n|w/o attn|64.20±2.98|68.55±2.95|70.35±2.30|\n|Ours|65.90±2.84|75.67±2.44|79.64±1.79|\n\n|Amazon-Computer||||\n|:----|:--------:|:--------:|:--------:|\n||2 way 1 shot|2 way 3 shot|2 way 5 shot|\n|w/o attn|88.70±2.16|95.30±1.29|93.90±1.38|\n|Ours|98.23±0.90|98.46±0.55|98.66±0.50|\n\n|DBLP|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|w/o attn|69.46±2.32|77.66±1.84|66.37±1.52|69.82±1.50|\n|Ours|81.72±2.05|85.30±1.90|74.22±1.56|76.70±1.46|\n\n\nFrom 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.\n\n```\nW3: The dimension of the node degree matrix.\n```\n**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 $n$.\n\n```\nW4: Why use |AX-X|?\n```\n**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.\n\n**W5: Why $\\hat{\\beta}$ is a trainable parameter?**\n\n**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.\n\n```\nQ1: Can additional experiments on heterophilic datasets be provided?\n```\n**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.\n\n**Table: The homophily values of different datasets.**\n| Dataset | Homophily |\n|:---:|:---:|\n| Cora | 0.767 |\n| CiteSeer | 0.627 |\n| Amazon-Computer | 0.700 |\n| Coauthor-CS | 0.755 |\n| DBLP | 0.278 |\n| CoraFull | 0.496 |\n| ogbn-arxiv | 0.445 |\n\nThe **CoraFull**, **ogbn-arxiv**, and **DBLP** datasets exhibit heterophilic property. This demonstrates that our model achieves superior performance even on heterophilic datasets.\n\n[1] Geom-GCN: Geometric Graph Convolutional Networks. In ICLR. 2020.\n\n```\nQ2: 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?\n```\n**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.\n\n\n**Q3: The parameter $\\lambda$ in Eq. (2) lacks comprehensive analysis.**\\\n**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.\n\n|CoraFull|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|w/o $\\lambda$|89.68±1.38|91.44±1.42|84.69±1.07|87.41±1.07|\n|Ours|90.22±1.38|91.60±1.28|85.91±1.08|87.54±0.98|\n\n|ogbn-arxiv|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|w/o $\\lambda$|65.92±1.76|69.29±1.68|51.33±1.10|57.47±0.84|\n|Ours|64.31±1.94|68.34±1.73|52.18±1.01|56.07±0.91|\n\n|Coauthor-CS|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||2 way 3 shot|2 way 5 shot|5 way 3 shot|5 way 5 shot|\n|w/o $\\lambda$|95.85±1.10|97.00±1.06|86.44±1.06|87.20±0.99|\n|Ours|95.50±1.30|96.20±0.97|86.03±1.05|86.82±1.01|\n\n|Cora||||\n|:----|:--------:|:--------:|:--------:|\n||1 way 1 shot|2 way 3 shot|2 way 5 shot|\n|w/o $\\lambda$|70.15±2.91|82.33±1.97|84.74±1.64|\n|Ours|71.48±2.88|82.40±2.03|86.19±1.80|\n\n|CiteSeer||||\n|:----|:--------:|:--------:|:--------:|\n||1 way 1 shot|2 way 3 shot|2 way 5 shot|\n|w/o $\\lambda$|67.19±2.67|72.75±2.65|75.44±1.99|\n|Ours|65.90±2.84|75.67±2.44|79.64±1.79|\n\n|Amazon-Computer||||\n|:----|:--------:|:--------:|:--------:|\n||2 way 1 shot|2 way 3 shot|2 way 5 shot|\n|w/o $\\lambda$|98.80±0.46|97.54±0.65|98.84±0.47|\n|Ours|98.23±0.90|98.46±0.55|98.66±0.50|\n\n|dblp|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|w/o $\\lambda$|79.26±2.07|84.22±1.62|74.76±1.62|77.15±1.40|\n|Ours|81.72±2.05|85.30±1.90|74.22±1.56|76.70±1.46|\n\nFrom 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."}, {"review_id": "d7IaxcuI8H", "reviewer": "Reviewer_ZVRV", "summary": "The authors argue that real-world graph data often exhibit significant local topological heterogeneity, making the use of a single fixed graph convolutional filter potentially suboptimal. They also highlight that existing baselines typically assume the support and query sets within each task are drawn from the same underlying distribution, which limits their ability to accurately represent the query set under distribution shift conditions.\nTo address these challenges, the authors propose GRACE, a method that employs adaptive spectrum experts leveraging both low-pass and high-pass filters, integrated via a gating mechanism within a Mixture-of-Experts framework to accommodate diverse local connectivity patterns. Additionally, GRACE introduces cross-set distribution calibration, which refines class prototypes using high-density samples to mitigate distributional discrepancies between the support and query sets in a meta-task.", "questions": "1) Regarding the first weakness I mentioned, could the authors clarify why handling nodes with diverse connectivity patterns is particularly emphasized in the graph few-shot learning context? This issue is a general challenge in graph learning and has been extensively studied in the context of heterophilic graphs. If possible, please include a baseline that combines graph few-shot learning methods with convolutional networks specifically designed for heterophilic graphs.\n\n2) As noted in my second point, while the qualitative results in Figure 5a and 5b are promising, it would strengthen the analysis to include the final accuracy values for those cases. Additionally, please include experiments comparing the accuracy with and without prototype calibration under varying levels of distributional shift to highlight the contribution of this component.\n\n3) As stated in lines 24–29, I agree that in some domains, labeled data may be scarce. However, few-shot learning typically targets generalization to new categories, which differs from the task of learning GNNs with limited labels. Could you clarify the specific scenarios in the graph domain where this meta-learning framework is particularly needed? If possible, it would be helpful to include small-scale experiments on such data (beyond citation networks) to support the motivation.\n\nI am willing to raise my score if all of my concerns are adequately addressed.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "* Strengths\n\n1) The authors propose a simple yet effective method that addresses well-known challenges in the graph domain, namely heterophilic nodes and distribution shift.\n\n2) The authors provide code to promote reproducibility.\n\n* Weakness\n\n1) While the limitation of using a single graph convolutional filter in capturing nodes with diverse connectivity patterns is a well-known issue in the graph domain, it has not been particularly emphasized in the few-shot learning context. The challenge of modeling heterophilic nodes [1] has been widely explored in a separate line of research, independent of few-shot learning. In this case, incorporating convolutional layers that account for structural heterogeneity into existing few-shot learning baselines (e.g., TENT) may already help mitigate the issue.\n\n2) The ablation studies are well conducted, and the case study in Figure 5 shows promising results—demonstrating that the model assigns appropriate weights based on node homophily and calibrates the prototype effectively in the direction of the query sample. However, the analysis would be more complete if the final accuracy were reported with respect to different levels of node homophily, to better clarify the effect of the proposed framework.\nAdditionally, it would be helpful to show the difference in accuracy with and without prototype calibration under varying degrees of distributional shift.\n\n[1] Graph Neural Networks for Graphs with Heterophily: A Survey", "was_revised": true, "final_justification": "This work proposes a simple yet effective method for addressing heterophilic nodes and distribution shift. Initially, I was concerned that important experiments were missing; however, the authors addressed this concern during the rebuttal period.", "rebuttal": "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.\n\n```\nW1 & 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.\n```\n**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.\n\nMoreover, 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.\n\nTo 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.\n\n|Amazon-Computer||||\n|:----|:------------:|:--------:|:--------:|\n||2 way 1 shot|2 way 3 shot|2 way 5 shot|\n|TENT|80.75±2.91|85.32±2.10|89.22±2.16|\n|TENT+H2GCN|66.02±2.46|79.45±2.50|85.86±2.40|\n|Ours|98.23±0.90|98.46±0.55|98.66±0.50|\n\n|Coauthor-CS|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||2 way 3 shot|2 way 5 shot|5 way 3 shot|5 way 5 shot|\n|TENT|89.35±4.49|90.90±4.24|78.38±5.21|78.56±4.42|\n|TENT+H2GCN|85.75±2.55|88.25±1.97|60.36±1.61|64.06±1.47|\n|Ours|95.50±1.30|96.20±0.97|86.03±1.05|86.82±1.01|\n\n|CoraFull|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|TENT|64.80±4.10|69.24±4.49|51.73±4.34|56.00±3.53|\n|TENT+H2GCN|63.94±2.03|67.47±1.77|49.54±1.18|53.15±1.15|\n|Ours|90.22±1.38|91.60±1.28|85.91±1.08|87.54±0.98|\n\n|DBLP|||||\n|:----|:--------:|:--------:|:--------:|:--------:|\n||5 way 3 shot|5 way 5 shot|10 way 3 shot|10 way 5 shot|\n|TENT|78.22±2.10|81.30±2.02|69.52±2.16|73.20±1.95|\n|TENT+H2GCN|76.62±2.26|78.56±2.16|66.67±1.40|70.15±1.37|\n|Ours|81.72±2.05|85.30±1.90|74.22±1.56|76.70±1.46|\n\n|Cora||||\n|:----|:--------:|:--------:|:--------:|\n||2 way 1 shot|2 way 3 shot|2 way 5 shot|\n|TENT|55.39±2.16|58.25±2.23|66.75±2.19|\n|TENT+H2GCN|57.25±2.65|60.64±2.21|68.55±2.14|\n|Ours|71.48±2.88|82.40±2.03|86.19±1.80|\n\nFrom 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.\n\n[1] Graph prototypical networks for few-shot learning on attributed networks. In CIKM. 2020.\\\n[2] Few-shot learning on graphs. In IJCAI. 2022.\\\n[3] Heterophily and graph neural networks: Past, present and future. In IEEE Data Engineering Bulletin. 2023\\\n[4] Beyond homophily in graph neural networks: Current limitations and effective designs. In NeurIPS. 2020.\n\n```\nW2 & 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.\n```\n**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.\n\n**Table: Results of our model under different levels of node homophily.**\n| Coauthor-CS 2 way 3 shot ||||\n| :----------------------: | :------: | :------------------: | :---------------: |\n|Homophily Range| Accuracy | Correctly Classified | Total Query Nodes |\n|[0.0 - 0.1)|0.9104|61|67|\n|[0.1 - 0.2)| 0.8889 |16|18|\n|[0.2 - 0.3) | 0.9574 | 45| 47|\n|[0.3 - 0.4) | 0.9500 |57|60|\n|[0.4 - 0.5) | 0.9388 |46|49|\n|[0.5 - 0.6) | 0.9205 |139|151|\n|[0.6 - 0.7) | 0.9471 |215|227|\n|[0.7 - 0.8) | 0.9448 |154|163|\n|[0.8 - 0.9) | 0.9664 |259|268|\n|[0.9 - 1.0) | 0.9737 |925|950|\n|Overall| 0.9585 |1917|2000|\n\n|Amazon-Computer 2 way 3 shot ||||\n| :--------------------------: | :------: | :------------------: | :---------------: |\n|Homophily Range|Accuracy|Correctly Classified | Total Query Nodes |\n| [0.0 - 0.1) | 0.7391 |51 |69|\n| [0.1 - 0.2) | 0.7027 |26|37|\n| [0.2 - 0.3) | 0.9714 |34|35|\n| [0.3 - 0.4) | 0.9531 |61|64|\n| [0.4 - 0.5) | 0.9524 |80|84|\n| [0.5 - 0.6) | 0.9929 |140|141|\n| [0.6 - 0.7) | 0.9919 |123|124|\n| [0.7 - 0.8) | 1.0000 |153|153|\n| [0.8 - 0.9) | 0.9960 |246|247|\n| [0.9 - 1.0) | 0.9981 |1044|1046|\n|Overall|0.9790|1958|2000|\n\n| DBLP 5 way 3 shot ||||\n| :---------------: | :------: | :------------------: | :---------------: |\n|  Homophily Range | Accuracy | Correctly Classified | Total Query Nodes |\n| [0.0 - 0.1)| 0.7534 |1751|2324|\n| [0.1 - 0.2)| 0.8384 |249|297|\n| [0.2 - 0.3)| 0.8608 |365|424|\n| [0.3 - 0.4) | 0.8781 |281|320|\n| [0.4 - 0.5) | 0.9013 |137|152|\n| [0.5 - 0.6) | 0.8753 |323|369|\n| [0.6 - 0.7) | 0.9301 |173|186|\n| [0.7 - 0.8) | 0.9615 |100|104|\n| [0.8 - 0.9) | 0.9714 |136|140|\n| [0.9 - 1.0) | 0.9196 |629|684|\n| Overall|0.8288|4144|5000|\n\n| CoraFull 5 way 3 shot ||||\n| :-------------------: | :------: | :------------------: | :---------------: |\n| Homophily Range    | Accuracy | Correctly Classified | Total Query Nodes |\n| [0.0 - 0.1) | 0.8562 | 792|925|\n| [0.1 - 0.2) | 0.9257 |187|202|\n| [0.2 - 0.3) | 0.8680 |309|356|\n| [0.3 - 0.4) | 0.8972 |358|399|\n| [0.4 - 0.5) | 0.9422 |261|277|\n| [0.5 - 0.6) | 0.9145 |567|620|\n| [0.6 - 0.7) | 0.9308 |444|477|\n| [0.7 - 0.8) | 0.9320 |274|294|\n| [0.8 - 0.9) | 0.9263 |264|285|\n| [0.9 - 1.0) | 0.9159 |1067|1165|\n|Overall| 0.9046 |4523|5000|\n\nFrom the results in the table above, it is evident that our model demonstrates superior recognition capability across nodes with varying levels of homophily.\n\n[1] Geom-GCN: Geometric Graph Convolutional Networks. In ICLR. 2020.\n\nMoreover, 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.\n\n|Coauthor-CS 2 way 3 shot|||||\n|:----------------------:|:--------------:|:-----------:|:----------:|:-----------:|\n|Shift Level|Avg. Shift (MMD)|Acc (w/o Cal)|Acc (w/ Cal)|Accuracy Gain|\n|Low Shift|0.1100|0.9726|0.9732|+0.0006|\n|Medium Shift|0.1404|0.9599|0.9633|+0.0033|\n|High Shift|0.1842|0.9390|0.9458|+0.0068|\n\n|Amazon-Computer 2 way 3 shot|||||\n|:--------------------------:|:--------------:|:-----------:|:----------:|:-----------:|\n|Shift Level|Avg. Shift (MMD)|Acc (w/o Cal)|Acc (w/ Cal)|Accuracy Gain|\n|Low Shift|0.1089 |0.9798|0.9804|+0.0006|\n|Medium Shift|0.1401|0.9798|0.9813|+0.0015|\n|High Shift|0.1840|0.9744|0.9771|+0.0027|\n\n|DBLP 5 way 3 shot|||||\n|:---------------:|:--------------:|:-----------:|:----------:|:-----------:|\n|Shift Level|Avg. Shift (MMD)|Acc (w/o Cal)|Acc (w/ Cal)|Accuracy Gain|\n|Low Shift|0.0677|0.8269|0.8363|+0.0094|\n|Medium Shift|0.0748|0.8275|0.8377|+0.0102|\n|High Shift|0.0827|0.7925|0.8029|+0.0104|\n\n|CoraFull 5 way 3 shot|||||\n|:-------------------:|:--------------:|:-----------:|:----------:|:-----------:|\n|Shift Level|Avg. Shift (MMD)|Acc (w/o Cal)|Acc (w/ Cal)|Accuracy Gain|\n|Low Shift|0.0622|0.9108|0.9171|+0.0063|\n|Medium Shift|0.0700|0.8931|0.8982|+0.0051|\n|High Shift|0.0791|0.8782|0.8944|+0.0162|\n\nFrom 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.\n\n```\nQ3: Could you clarify the specific scenarios in the graph domain where this meta-learning framework is needed?\n```\n**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.\n\nWe 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.\n\n**Table: Results of different models on the cell type annotation.**\n| Models | 5 way 3 shot | 5 way 5 shot |\n|:---:|:---:|:---:|\n| TEG | 69.55$\\pm$2.29 | 73.52$\\pm$2.20 |\n| COSMIC | 71.52$\\pm$2.15 | 76.19$\\pm$2.82 |\n| Ours | 76.52$\\pm$1.29 | 80.03$\\pm$1.15 |\n\n[1] High resolution mapping of the tumor microenvironment using integrated single-cell, spatial and in situ analysis. In Nature Communications. 2024."}, {"review_id": "YHY5tdDCH8", "reviewer": "Reviewer_bH8n", "summary": "GRACE gracefully handles hetero/homo-homophilic edges in graph few-shot learning. It consists of two key ingredients: (1) adaptive spectral expert strategy and (2) cross-set distribution calibration strategy. Empirical analysis is done comparing the proposed method to other recent approaches such as Meta-BP. Theoretical results examine the generalization error.", "questions": "Do you have a hypothesis for why CiteSeer seems to show a different pattern for the ablation in Table 5 than the other datasets? For the other datasets it seems \"w/o cal\" is next best, but on CiteSeer \"w/o high\" is next best?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "This is a nicely constructed paper, it clearly outlines challenges in the space of graph FSL and offers intriguing solutions to them. \n\nStrengths: \n1) Quality: To the best of my understanding the choice of baseline comparisons is quite comprehensive and current. The proposed method seems to be well motivated and clearly presented. \n2) Clarity: The paper is written clearly, results are presented clearly. \n3) Originality: Perhaps not groundbreaking, but a nice method that seems well suited to spark interest in those working in this space. \n\nWeaknesses: \n1) Originality: The approach follows a tried and true paradigm of graph FSL, it does not revolutionize things. It is a nice contribution, but leaves the reader thinking if there are things that can be done beyond this structure. \n2) Significance: I do not discount the scientific merit of the paper, however, I do wonder about the use cases of these particular datasets / data types in the presence of todays LLM-universe. It is not clear to me whether the same datasets would be easy or difficult for say a simple prompted LLM. That said this is merely commentary and does not factor into my decision of scoring the paper. \n\nPerhaps relevant: https://mlg.eng.cam.ac.uk/zoubin/papers/zgl.pdf", "was_revised": true, "final_justification": "The author response addresses my major doubts regarding the paper. I think the paper is solid and has nice contributions, however not overwhelmingly so, hence borderline rating.", "rebuttal": "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.\n\n```\nW1: It is a nice contribution, but leaves the reader thinking if there are things that can be done beyond this structure.\n```\n**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.\n\n```\nW2: It is not clear to me whether the same datasets would be easy or difficult for say a simple prompted LLM.\n```\n**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.\n\nTo 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.\n\n**Table: Results of the LLM across different datasets.**\n| Dataset | LLama3-8B | Ours |\n|:---:|:---:|:---:|\n| Cora (2 way 1 shot) | 67.52$\\pm$2.19 | 71.48$\\pm$2.88 |\n| CiteSeer (2 way 1 shot) | 57.59$\\pm$2.25 | 65.90$\\pm$2.84 |\n| Coauthor-CS (5 way 3 shot) | 75.52$\\pm$2.49 | 86.03$\\pm$1.05 |\n| ogbn-arxiv (5 way 3 shot) | 49.72$\\pm$2.36 | 64.31$\\pm$1.94 |\n\nFrom the results, we can observe that our model outperforms the LLM on this task.\n\n[1] A survey of large language models for graphs. In KDD. 2024.\\\n[2] Exploring the potential of large language models (llms) in learning on graphs. In SIGKDD Explorations Newsletter. 2024.\n\n```\nQ1: Why CiteSeer seems to show a different pattern for the ablation in Table 5?\n```\n**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."}]

Author rebuttal:

Meta-review: The paper introduces a method for graph few-shot learning that combines adaptive spectrum experts with cross-set distribution calibration to better handle data scarcity and distributional shifts. The core idea is to leverage multiple spectral experts that capture structural information at different frequencies, while an adaptive mechanism selects among them for each task. A distribution calibration module is further applied to align support and query sets, reducing bias in few-shot settings. Extensive experiments on benchmark graph classification and node classification datasets show consistent improvements over state-of-the-art baselines. 

Reviewers highlight several strengths.
- The adaptive spectrum experts are a novel and concrete mechanism for automatically balancing low- and high-frequency structural signals, and ablation studies demonstrate that without this module accuracy drops significantly. 
- Empirical performance is strong: the method consistently outperforms state-of-the-art baselines across multiple datasets, often by a significant margin, and detailed ablations confirm the necessity of both modules.
- The paper is also clearly written, with reproducibility support.

Some limitations were raised, including the computational overhead of maintaining multiple spectral experts, a need for broader evaluation on large-scale graphs, and limited theoretical discussion of why adaptive spectral selection is particularly suited to few-shot scenarios. Nonetheless, reviewers agreed these do not undermine the contribution. The rebuttal further clarified scalability, provided additional runtime analysis, and reinforced the novelty relative to prior spectral and calibration approaches, which reviewers found satisfactory.

We recommend acceptance, with the following suggestions for the camera-ready: (1) expanding discussion of scalability, providing clearer guidance on practical hyperparameter choices, (2) situating the approach more explicitly relative to meta-learning methods in graph domains, and (3) including the experiments added during the rebuttal.
Decision: Accept (poster)