L2DGCN: Learnable Enhancement and Label Selection Dynamic Graph Convolutional Networks for Mitigating Degree Bias
Authors: jingxiao zhang
Shifei Ding
Jian Zhang
Lili Guo
Xuan Li
Venue: NeurIPS 2025 spotlight ()
Keywords: Missing Data
few-Label Learning
graph convolutional networks (GCNs)
graph representation learning
Primary area: deep_learning
TL;DR: DR

Abstract: Graph Neural Networks (GNNs) are powerful models for node classification, but their performance is heavily reliant on manually labeled data, which is often costly and results in insufficient labeling. Recent studies have shown that message-passing neural networks struggle to propagate information in low-degree nodes, negatively affecting overall performance. To address the information bias caused by degree imbalance, we propose a Learnable Enhancement and Label Selection Dynamic Graph Convolutional Network (L2DGCN). L2DGCN consists of a teacher model and a student model. The teacher model employs an improved label propagation mechanism that enables remote label information dissemination among all nodes. The student model introduces a dynamically learnable graph enhancement strategy, perturbing edges to facilitate information exchange among low-degree nodes. This approach maintains the global graph structure while learning graph representations. Additionally, we have designed a label selector to mitigate the impact of unreliable pseudo-labels on model learning. To validate the effectiveness of our proposed model with limited labeled data, we conducted comprehensive evaluations of semi-supervised node classification across various scenarios with a limited number of annotated nodes. Experimental results demonstrate that our data enhancement model significantly contributes to node classification tasks under sparse labeling conditions.

L2DGCN: Learnable Enhancement and Label Selection Dynamic Graph Convolutional Networks for Mitigating Degree Bias
Jingxiao Zhang', Shifei Ding! Jian Zhang', Lili Guo', , Xuan Li"
School of Computer Science and Technology/ School of Artificial Intelligence,
China University of Mining and Technology. Xuzhou 221116, China
2 Mine Digitization Engineering Research Center of Ministry of Education, Xuzhou 221116, China (zhangjingxiao, dingsf, 2hangjian10231209, liliguo, 1ixuan23)@cumt. edu.cn
Abstract
Graph Neural Networks (GNNs) powerful models for node classification. but their performance is heavily reliant on manually labeled data, which is of- ten costly and results in insufficient labeling. Recent studies have shown that message-passing neural networks struggle to propagate information low-degree nodes, negatively affecting overall performance. To address the information bias caused by degree imbalance, we propose Learnable Enhancement and Label Selection Dynamic Graph Convolutional Network (L22DGN). L2DGCN con- sists of a teacher model and a student model. The teacher model employs an improved label propagation mechanism that enables remote label information dis- semination among all nodes. The student model introduces a dynamically learn- able graph enhancement strategy, perturbing edges facilitate information ex- change among low-degree nodes. This approach maintains the global graph struc- ture while learning graph representations. Additionally, we have designed la- bel selector to mitigate the impact of unreliable pseudo-labels on model learning.
To validate the effectiveness of our proposed model with limited labeled data, we conducted comprehensive evaluations of semi- supervipe node classification across various scenarios with a limited number of annotated nodes. Experimental results demonstrate that our data enhancement model significantly contributes node classification tasks under sparse labeling conditions.
1 Introduction
Graphs model structured and relational systems and are used in fields like traffic networks [I) molec- ular structures 2 and protein networks Graph learning algorithms analyze graph-structuee data by considering node features and their relationships (edges), achieving success in many domains.
Graph neural networks (GNNs), based on message-passing mechanisms, are a key technology for handling graph data. Node classification, core task related graphs, has received much atten- tion. Traditional GNN methods rely supervised learning with numerous labeled nodes, but high labeling costs limit their practicality. Researchers have combined self- self-training and lscudo-labeling techniques with GNNs to improve semi-supervised node classification under limited labeled data. However, these methods still struggle when labeled nodes are scarce or unlabeled nodes are abun- dant.
*Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

(a)
(c)
Figure 1: The number of nodes corresponding the node degree.
In a graph. node's degree usually refers to the number of edges connected to that node, reflect- ing its connection strength and importance within the network, significantly influencing the path and speed of information propagation. However, in real-world scenarios, the degree distribution of nodes often follows power-law distribution[4]. where most nodes are low-degree nodes, and only few have very high degrees. We believe that this degree imbalance is a primary reason for the model's 's failure in situations with few labeled nodes. According to related influence theories the label of a target node is affected by the cumulative influence of the normalized features of its neigh- boring nodes within a K-hop propagation range. For low-degree nodes, every connection is crucial for their correct classification, but due to their limited number of connections, their information propagation capacity is significantly restricted, thus affecting the effectiveness of the propagation path. Figure [ illuusraaess the impact of the degree of the node on the propagation of information when the number of labeled nodes is limited. In Figure [ (a), the degree-O node (labeled node 1 and unlabeled nodes 2 and 3) cannot transmit information; in Figure (b). the I-degree node is misclas- sified due to incorrect connections; whereas in Figure (c), despite the presence of some erroneous connections, nodes with degrees greater than 1 still achieve correct classification. The insufficient connections of low-degree nodes limit information propagation, especially in the case of scarce la- beled nodes. Therefore, in this context, graph neural networks require multi-step propagation to effectively transmit information, highlighting the importance of addressing low-degree nodes in the effective dissemination of information.
In the research on the degree bias problem in Graph Neural Networks (GNNs), several studies have explored solutions from different perspectives: DegFairGT [6] proposes a learnable structural en- hancement and structural self-attention mechanism, which generates new edges by calculating the structural similarity between node pairs to balance message passing, and retains the global topology with the help of sulf-super task based on p-step transition probability matrices, thereby allevi- ating the problem of insufficient information in low-degree nodes and over-smoothing in high-degree nodes; DAHGN 77, on the other hand, focuses on heterogeneous information networks, constructs a dual-view contrast framework of heterogeneous views and homogeneous subgraphs, combines semi-supervised task loss and contrast loss, and adopts differentiated strategies for low-degree and high-degree nodes to eliminate degree bias, filling the gap in research on heterogeneous scenar- ios; GraphPatcher [8] innovatively realizes model-agnostic degree bias mitigation through test-time augmentation, iteratively generates virtual nodes to repair damaged neighborhoods of low-degree nodes, improving the performance of low-degree nodes (by an average of 6.5%) while preserving the advantages of high-degree nodes, with an overall performance improvement of 3.6% on average. However, existing methods still have limitations in sparse labeling scenarios: DegFairGT's struc- tural enhancement has limited adaptability to dynamic topologies and is difficult to directly cope with the challenge of insufficient labeled data; DAHGN's contrastive learning framework is insuffi cient in handling the reliability of pseudo-labels in complex heterogeneous networks; GraphPatcher, as a test-phase strategy, cannot fundamentally optimize the information aggregation of low-degree nodes during training.
Our proposed learnable enhanced and label selection dynamic graph convolutional network aims to address the poor node classification performance caused by degree bias in the absence of labeled nodes. The model comprises teacher model and a student model. The teacher model generates pseudo-labels for unlabeled nodes via an improved label propagation method. The student model dynamically learns from the graph through two approaches: 1) Structural Optimization: It prunes edges based on node degree, retains core edges, and uses high-order feature information from a de- coupled GCN to enhance the topological structure of low-degree nodes, ensuring balanced informa- tion flow. 2) Pseudo- Label Selection: A pseudo-label selector combines nodes with high confidence and removes those with low confidence, dynamically updating the training set. Our contributions include:

---

Proposing a dynamic graph convolutional network based on learnable augmentation and label selectors address degree bias caused by the scarcity of labeled nodes.
Introducing teacher model that uses soft pseudo-label propagation to expand the training set.
Designing student model that performs edge pruning based on node degree and integrates higher-order node features for dynamic topology learning, thereby mitigating degree bias effects while using the label selector to enhance the training set.
Demonstrating through extensive experiments on multiple datasets that our model is highly effective for semi-supervised node classification with extremely limited labeled nodes, par- ticularly in alleviating degree bias.
2
Related Work
Graph Convolutional Networks Graph Convolutional Networks (GCNs) have significantly ad- vanced graph learning, being mainly divided into spectral and spatial graph convolutions. Spectral graph convolution processes graph signals using graph spectral theory, Fourier transforms, and con- volution theorems 2 [0), while spatial graph convolution extracts features by passing and aggregat- ing information from neighboring nodes. Common GCN models such as GCN [.]. GAT [12), and SGC [13 typically employ a coupled structure of propagation and aggregation. However, in scenar- ios with scarce labeled nodes, increasing model depth is often considered solution, though deeper models like [4 see a significant increase in computational complexity. Consequently, de- coupled GCNs have gained attention for their stability and flexibility. For instance, some approaches expand the receptive field through decoupled transformation and propagation, APPNP optimizes global information utilization by combining personalized PageRank, GAMLP [16] maintains high scalability during pre-computation, while DecGCN 17 focuses on improving model stability and generalization capabilities.
Node Classification With Few Labels In semi-supervised node classification tasks with limited labeled nodes, traditional GCN models often face performance issues due to insufficient supervi- sion. Recent graph learning methods aim to address this challenge. For example, CGPN [88] uses Poisson learning to counteract Laplacian performance degradation, M3S [19] enhances GCN gener- alization through a self-supervised multi-stage training framework, IGCN (00 introduces a unified
graph filtering approach to reduce overfitting and training parameters, GraphHop 22 improves graph signal smoothing with a two-stage training process, AGST [22] enhances decision boundary separation by capturing remote node interactions through self- telf-training. and CMPGNN 23 presents
a noise-resistant framework via contrastive message passing. PASTEL (24] addresses the prob- lems of insufficient information and excessive suppression caused by "topological imbalance" by proposing a position-aware graph structure learning framework. It enhances intra-class connections and optimizes edge weights through anchor position encoding, alleviating structural biases at the level of propagation paths. NodeMixup (25) focuses on the insufficient reachability between labeled and unlabeled nodes, designing a cross-set mixing strategy and neighbor label distribution-avwe sampling to enhance information interaction through node pair mixing without adjusting the GNN architecture. Another study (26] expands the GNN's receptive field to skip neighborhoods through position encoding, adding virtual nodes/edges to the input graph and injecting position features to achieve model-agnostic receptive field expansion, avoiding complex architectural modifications. Despite these advances, existing methods often overlook the reliability of pseudo-labels, which can lead to inaccuracies model training, MSP-LR 27 introduces a label regularization method and proposes graph neural network with basic learning and label regularization modules to enhance label reliability through pscudolabeling and regularization based on the cluster assumption.
Graph Representation Learning In graph representation learning, edges are crucial for informa- tion dissemination, but real-world graphs often contain noisy edges. Researchers have developed several approaches to optimize graph structures. JLGCN (28) transforms graph optimization into distance metric learning using the Mahalanobis distance metric. [29] proposes an end-to-end joint fusion framework aiming for consistent feature integration and adaptive topology tuning. IDGL 30 frames graph learning as similarity metric learning, iteratively refining graph structures and embeddings. KI introduces a self-supervised framework that combines graph structure learning, clustering for pseudo-labels, and sample selection for clean labels. [2] leverages information the- ory to maximize mutual information for reconstructing topological transformations.
33 presents

---

Label Matrix (Y)
y(k)
Teacher
Label Propagation
slpp propagation
Contrastive 4y
Edge Pruming
Seructual Optimization
precest
Structural Optimizaton
Gomphical
Enhancement
Optimized adjacency matrix(,d))
Similarity Matrix
Pscado Label
Cross-cnloopy loss Ais
Classifier
Cross- entropy loss 1-+
Ecalure
Propagarion
Edge
Deleted edge
Feature MalriA (X)
propagation
TM-step
X
Festure Transfommation
8
Student
Figure Overview of the proposed framework. In each iteration, the teacher model generates pseudo-labels for all nodes, while the student model enhances the graph structure using higher-order features. Based on the student model's pseudo-labels, reliable nodes are selected to dynamically update the training set and optimize pseudo-labeling via weakly supervised contrastive loss.
method that simultaneously integrates graph learning and graph convolution into unified network architecture and enforces label smoothing through unsupervised loss terms. (34] graph structure refinement to eliminate irrelevant noise and simultancously maximizes view-shared and view-unique task-relevant information, thereby tackling the frontier of non-redundant multiplex graph.
Proposed Method
This section describes our proposed node classification model for under-labeled scenarios. We start with a mathematical formulation of the problem, followed by an overview of the model's architec- tural framework and a detailed exposition of its key components in the subsequent subsections.
3.1 Problem formulation
An undirected graph with e edges and n nodes can be represented as a quintuple:
G = (V, X)
(I)
where V and E denote the set of nodes and edges, respectively, and X Raxd denotes the initial feature matrix of the graph G with n nodes each having d features. The adjacency matrix A e (0, 10axn represents the connections between nodes, and À includes self-loops. Let ò be the diagonal matrix of Á, and S.y = 1-1/2 AD denotes the symmetric normalized adjacency matrix with self-loops. The labeling matrix is denoted by Y E IRaxe where c is the number of classes. In semi-supervised setup, the node V is divided into labeled VL and unlabeled Vu sets. Our focus is on predicting labels for Vy given few labeled nodes in V which may be balanced or unbalanced across classes. each class has K labeled nodes, the problem becomes under-shot semi-supervised node classification.
3.2 Architecture Overview
In this section, we will provide detailed introduction to our proposed L2DGCN, a self-training graph convolutional network model. This model effectively improves the performance of GCN when labeled nodes are scarce by mitigating degree bias through three innovative designs across two key modules. Figure illlssrrates the overall architecture of L2DGCN.

---

3.2.1 Teacher model based on the propagation of soft pseudo-labels
In self-training models, teacher models typically use labelled data to predict unlabelled data, provid- ing pseudo-labelling information for unlabelled nodes. Whereas in the label propagation algorithm [35], the labels of the tagged nodes are reset to their true labels after each iteration, which means that the influence of other nodes on the labels the tagged nodes is absorbed in the subsequent iter- ations. Therefore, we make use of soft pseudo labels for long range propagation in order to generate pseudo labels for unlabelled nodes. The improved soft label propagation formula as follows:
y(K) (1 a) 3 Siler Y (K- + aY (0)
(2)
Syyn (D 1/2 A (Dirr)-
where ( = E is the initial label matrix, K is the order of propagation, Atter. = Aijer. + denotes the adjacency matrix with self-loop added after the iter.th matrix optimization, and Diter is the diagonal matrix of Axer, where diter. Σド= Atter, Djjer d:ter. SSter is the normalized adjacency matrices, and for the convenience of writing, in the following expressions omit the superscript iter. a is the balanced higher-order pseudo-labels with the initial pseudo-labels hyper- parameters. By setting an appropriate the model can effectively maintain accurate perception of local structures even after multiple propagations, thus improving the overall learning effect and model performance.
3.2.2 Student model based on dynamic learnable graph augmentation and label selector
Decoupled GCN backbone
Graph Convolutional Networks (GCNs) combine neighbourhood aggregation and feature transfor- mation for node representation learning. However, recent studies indicate that this coupled design can cause issues like training difficulties, underutilisation of graph structures, and excessive smooth- ing. To address these, we adopt a decoupled GCN model for graph feature propagation, enabling higher-order feature interactions.
( = (1 3)) (TT- + +,x (T) = (ReI.U(X(T)))
T21 1
(3)
where 3 is positive parameter that balances the initial and higher-order feature information, similar to a. By setting 3 appropriately, the model can preserve initial feature information even with infinite propagation. At the first iteration, X0)) X represents the initial feature information. While large number of propagation steps T allows for extensive higher-order interaction, excessive T introduces noise, making the classification boundaries less distinct.
Dynamic Learnable Graph Enhancement
Real-world graphs have many low low-degree nodes whose edges are crucial for information dissemina- tion. Incorrect or missing edges can significantly affect these nodes. To boost model performance, especially with limited labeled data, we dynamically optimize the graph topology using node de- grees and features.
Edge Pruning Based on Node Degrees A node's degree is its edge count. high-degree nodes are central to the graph's structure and information flow, while edges of low-degree nodes are especially important. We propose pruning the graph by keeping edges of high-degree nodes and removing those of low-degree nodes to reduce the impact of incorrect edges. The steps are as follows.
Step 1: Determine the number of nodes to preserve the edges:
(4) where Bnr is the pruning rate B E [0, 1].(1 B..)) is the ratio of the number of total nodes to the number of nodes whose edges are to be retained, n is the total number of nodes, and M is the number of nodes to be retained. When 3 1 our model can degenerate into an MLP with self arantrrainng. 8,, = our model can be seen as an APPNP model with self self-ttrinnng.
M = - (1-3w) n
Step 2: Sort the nodes in descending order based on the node degree d(v) and select the first M
nodes, denoted as Vj:
V. = {11, 02 02.-...70 UM
(5)

---

where d(v1) ... ) D is the degree matrix A E R is the initial adjacency matrix, where the choice of optimising the initial graph structure each time avoids introducing cumulative emvors and local optimal solution problems in the optimisation process, and ensures the controllabil- ity and stability of the optimisation process.
Step 3:
For the selected node Vs, all edges E. connected to it are retained, while all edges of the nodes that not selected and those that are also not selected when the retained edges are selected are removed. The obtained selected edges and the pruned adjacency matrix Aw are
E, = E3 Je,,, or E V
(6)
1. Cjj E E. Aw (i.)) = (o, otherwise,
(7)
This operation filters the top M nodes by degree and retains the edges between them. By selecting the right q value, the model retain the minimal edges for optimal results, offering insights into graph data compression and preservation.
Graph enhancement based on dynamic similarity matrix The decoupled GCN's backbone sup- ports long-range feature propagation and local attention, enabling the feature matrix to capture global and local features. The similarity matrix from this feature matrix effectively expresses both types of features and is calculated as:
Trans 5 (T)
(8)
where S(z, ) denotes the similarity between nodes and j.
To refine the graph structure and ensure low-degree nodes primarily have core edges, we use a KNN graph for unselected discrete nodes Va. guarantecing each has at least P neighbors. The graph structure is enhanced by:
1, if ei Au S( (7) ( min(r(a) 1T) (P, P)), 0, otherwise.
Aa(i,))
(9)
Here, eij E An indicates Aw contains edge eij, and r(5!?), P) returns the similarity between a:(") and the P-th similar row vector in X This approach leverages the mutual reinforcement between quality features and good structural information to optimize the graph structure for subsequent model iterations.
Self-training label enhancement Self-training augments GNNs by generating pseudo-labels for unlabeled nodes using a teacher model, but initial pseudo-labels can be unreliable. We introduce method with confidence threshold μ. where only pseudo-labels above μ are used, ensuring high- confidence contributions. The student model determines node confidence via the formula:
(:()) (ReI.U(WW:))22 (TT) (1 3ym (T--) ()
T21 1
(10)
(T-1)
In the student model, parameter controls information dissemination. larger T captures broader node info, aiding complex graph understanding but risking noise overload in suboptimal graphs. A smaller T' limits info to local nodes, possibly missing higher-order relationships. Balancing info coverage and noise is key for effective learning.
Next, according to the set threshold μ,, the high confidence unlabelled nodes are selected for super- vised learning of the model, i.e:
V = V U (o, ( for i E V such that 2
(11)
where V is the initial set of unlabelled nodes and Ve is the set of reliable unlabelled nodes.
In order to utilise reliable pseudo-labels to assist in labelling the training set for model training, the standard semi-supervised learning objective function can be modified into the following form:
L.e U
(12)

---

where L is the cross-entropy loss of the labelled nodes and L is the cross-entropy loss of the unlabelled nodes in the student model with a confidence level greater than μ.. i.::
I =
Σ
y log Vi
(13)
VEVL
L = E
Σ VEEV =01
oe log Df
(14)
where of denotes the pseudo-labelling information obtained by the teacher model and yf denotes the pseudo-labelling obtained through the student model.Also, in order maintain the consistency of the information obtained from the teacher model and the student model, we motivate the simi- larity function assign large values to the positive pairs and small values to the negative pairs by introducing the infoNCE contrast loss [36 37).
LinfoNCE = Σ log exp(zi 2, /T)
n
(15)
El= exp(2 -2///
Let zft be the positive sample of 2i, and žj consist of one positive and negative embeddings. adjusts the model's ability distinguish negative samples; a large T may equalize negative sample treatment, while a small 7 can hinder convergence or generalization. The contrast loss aims to enhance pseudo-label validity by caleulating the distance between reliable pseudo-labeled nodes U and class prototypes. The formula for class prototypes is:
Ce =
Σ
T
VV. + V
(16)
where V.2 denotes the set of labelled nodes belonging class c, V denotes the set of reliable pseudo-labelled nodes belonging to class c, and C. denotes the corresponding class prototype of class The hard pseudo-tag of the reliable pseudo-tag tag set U" is Or = arg max 0/ The contrast loss
function after correction using reliable pseudo-tags is:
explx: Co,/T) Σ (-108
Ler. =
(17)
De exp(x; Co/T)
where Cg. is the corresponding prototype of node u4. For any node its corresponding class proto- type is used as a positive sample, and the embedding of other class prototypes negative sample. Then the loss function of the whole model is:
L = L ALL +7LCI.
(18)
where À and yy are hyperparameters that balance the loss of unlabelled nodes and contrast.
3.3 Computational Complexity Analysis
The computational complexity of the proposed model is determined by the core operations of both the teacher model (for pseudo-label generation) and the student model (for dynamic graph enhance- ment, feature propagation, and pseudo-label selection), depending on key parameters: graph scale (number of nodes n, number of edges E)), feature dimension d, and propagation steps K (for the teacher model) or T' (for the student model); to align the labels (including pseudo-labels) generated by the teacher model with the node pseudo-labels obtained by the student model and ensure con- sistency in their iterative propagation processes, we set K T. Specifically, the teacher model generates pseudo-labels via improved soft label propagation, with time complexity of O(K n²²)) for K iterations (where e denotes the number of classes), as each iteration involves matrix multi- label matrix. For the student
plication between an X n adjacency-related matrix and an model, its complexity comes from three modules: dynamic graph enhancement (with complexity On log + E + n2d + P. d), including node sorting, edge traversal, KNN graph construction

---

based on cosine similarity calculation, and neighbor supplementation, where P is the number of neighbors per node), decoupled GCN propagation (with complexity O E d) for T iiterations, as each iteration requires feature aggregation over E edges for d-dimensional features), and pseudo- label selection (with complexity (n c) from traversing all n nodes compute label confidence). Combining the teacher and student modules, the overall computational complexity is dominated by terms related to n (notably n² from matrix operations), (notably d from graph propagation), and the unified propagation step K = TT
4 Experiments
In this section, we conduct experiments to validate our model's effectiveness and robustness with extremely few labeled nodes. Experimental design is follows:
4.1 Experimental setup
Datasets We validated our model's effectiveness in semi-supervised node classification on six ho- mogeneous graph datasets of varying sizes. These include citation networks Cora, Citeseer, and
Pubmed 38) widely used for semi-supervised node classification; Coauthor-CS and Coauthor-
Physics 39 datasets for academic collaboration analysis; and Amazon-Photo 33], which comprises
product images with metadata labels. Detailed dataset information is in Table
Table 1: Dataset statistics
Table 2: Hyperparameters range
Dalasel
BNodes
#Edges
#Features
#Claoess
#Edge Density
Hyperparameters
#Range
Cora
2,708
5.275
1,433
0.3014
Her.
(1.2,3, 1.5)
Clesserr
3,327
4,552
3,703
0.000
8n
(0.12, 0.10 0.08, 0.06, 0.04, 0.02, 0.00) 110,112 16, 2.03 (1, 21,2.3,4, 5, G. 7, & 10)
Puhmed
19.717
44,321
500
0,0002
Comnboe-CS CS
18.333
0.0005
Coanthoe Physics
34,493
8,415
P
Amazon- Plotoo
7,087
119,013
745
0.0012
T
6,
Balancing setup low labelling rates: We built the training set by randomly selecting 3, or 10 labeled nodes per category (3-shot, 5-shot, 10-shot). The validation set had 30 nodes per category, with the rest used for testing 222]
Balancing setup under standard segmentation: Following we used 20 labeled nodes per class for training, with 500-node validation set and the remaining nodes in the test set.
Compared Methods: We compared our model with classical and state-of-the-art methods, includ- ing GCN Σ. GAT [1), SGC [13], label-efficient GCN models (GLP [40], IGCN [40], CGPN
41, CMPGNN 23
GraphHop (21). and self-trained GNN models (PTA 15 ST-GCNs [2),
M3S [19) AGST
22
Muse [3
4.2
Implementation Details
We implemented all algorithms in PyTorch with the Adam optimizer, following original settings when available. Results reported are average accuracies from 10 independent runs. Our model was trained with a maximum of 100 iterations, a learning rate of 0.01, and a regularization weight of x 10- To prevent overfitting, early stopping was applied, halting training if validation loss didn't improve for 1000 steps. Default parameters included K=T, matrix optimization iterations (iter.), pruning rate B.. P neighboring nodes added, and T feature propagation steps for the decoupled GCN. Hyperparameter ranges are in Table 2 with variations based on dataset labeling rates.For the selection of optimal values of the parameters listed in 2 we adopted the grid search method. Specifically, within the preset parameter ranges, we exhaustively combined the possible values of each parameter, evaluated the model performance the validation set, and finally selected the parameter combination that made the model perform optimally.
4.3
Main results
In the experiments, we evaluate our model and baselines in semi-supervised node classification across various labeling rates. The top three models are labeled, with the best bold and the other two underlined, combining results from [22 and our experiments.

---

Table 3: Accuracy (%) of semi-supervised node classification test with low labeling rate under balanced training
Mallod
Corn
Clieseer
Pilmal
3-dbot
S-bbx
T0-shos
S-bbet
T0-shoc
3-4hot
S-Jbot
T0-sbox
TF
02.78
= 0.02
08.72:00:08
61.05 +
31.57
0.005
31.55
F08T
0.30
59.8
00.05
02.57
6y 02 0.75
OON
56.31 - 0.81
64.15 +
72.87 + +0.33
47.30
1000-0000 -0.00
64.27 +.81
60.26 + 0.57
50.94 + 00.51
66.40 0.85
72.57 1 0.74
GAT
65.30 - 0.98
69.53 1 0.84
76.44 1 0.35
51.62 1..97
58.67 1.881
65.13 0.51
64.72 0.91
08.52 0.90
73.85 0.60
02.00 0.32
08.94
64.92
08.74
0.92
64.72 0.91
0.84
77:50
0.03
IOCN
50.50 0.97
66.51
06.23 0.97
CGPN
71.53
74.85
02.54
02.20 1.03
63,78 1.00
08:21
71.21
CMPGNN
00.35
27.08 1.
77.80 1.27
65U85 + 1.55
00.50
64.43 1.50
07:49 2.09
71.75 2.53
72.06
GrughHop
09.06 2:23
74.00 18
70.40
0:30
07:26 0:46
60.29 8:25
64.43 4.71
64:11 6.56
72.61
NACiphormer
03.80
70.25
74.88
0.97
48.50 0.08
63.22 0.72
50.26 0.58
07:07 0.53
68. 13 0.38
73.
0.00
PTA
09:21 0.333
10.35 0.20
25.09 1 10.25
S1.15 1.31
G1.15 1:.8
06.10 0.35
07:00 0.32
12:25 0.82
70.41 0.:1
STAGUNA
65:45 0.994
71.16 0.87
76.64 + 0:45
49.85 + 11335
61.89 00.91
Cx 08.66-4 0.36
65
0.94
70.
0.98
74.10 0.63
MESS
64.01 = 0.71
69.26
0.77
77:20 + 0:41
GouS1 11.88
50.72
de 0.89
C0.39 0:41
08:01
01.00
72
88 0.85
76.81
0.49
AGST
21.00 0.55
70.
72
0.35
20.02 + 0.58
52:53
+ 0.02
53:
12 0.80
66. 84 0.29
T6 06
0.633
78. 26
0.77
73. 20.36 0.53
OURS
15.00:00.21
$1.07
1 0.43
82
1 0.26
0S 08.90 0.11
70:35 0:23
71:64 0:30
TL 17,7020000
15:07 20:00
90.85 0:000
(16.62)
(11.5))
(12.37)
(16.45)
(72.2))
(1306)
(11.89)
(20.19)
(14.41)
Table 4: Accuracy (%) of semi-supervised node classification test with low labeling rate under balanced training
Method
Counthor-CS
Coanthor Poysies
Amazon Photo
3-shor
S-chot
10-shot
3-shor
5-shot
10-sher
3-shot
S-shor
10-shor
57.77=0.77
62.0910060
66.1820.5 36
13.46-0.93
76.91:00.61
803550011
69:2410022
13.43=0.22
77.781061
GCN
77.17-0.79
84 0.509
89.01=09%
N2. 0.88
87. 0.00
90.78-00.80
69. 50:54
74.42-0.97
00.30=00
GAT
79.66-0.75
85. 1.+10.4449
89.34+0.10 19
86.07-1.15
89. 35-35----48
0..4++0.48
7044++1.19
77.89-1.00 1.05
82. 62.39+
SGC
84.93-0.57
88. 35.11
90.13+0.99 99
87.55=0.64
87 0.768..939
91.38-0.31
75.05+0888
78.73-0.69
04.1440445
CTP
34.38-0.61
361066
01122-0
75.11E1
JGCN
01.26.00.47
36.1510.333
90.8210.15 13
89 0.57
91 91.3510.229
92.78.10.21
75.36110998
82, 10..0..0889
85.5011 0.3.
CGPN
88 3.39
89. 141:3 27
90.37: 14
90,06-3.48 3.48
91 76.7662222 33
92.56 02.56:::.22 22
83.57:33.24 24
64.74-2.6
87.78
CMPGNN
20.224-2.57
24.299--2.21
81.33
83
87.68--2.36
01.50:3..5 35
4.15
GraphHop
71.15++4.98
85.05-1.18
68.42+100
84.43-111
NAGphommer
85.61=0.38
89 50.08840.85
90.55:00499
86. 0.55
$9.91=00.22
92.54=00224
74.79+00335
83.58-0.33
$7.85 19
PTA
86.36-0.466
804340
90. 18
88.62
77ATH029
8263 8.73-0076
ST-OCNs
88.31-0.16
91.39
87.61=0.69
73.86:1.55
81.93-1009
85.54110.6 67
M3S
84.11=0.46
56 91
91.08:0.0 11
89, 0.55
91 07:27700331
92.93:20:25
74, 94-96-09997
88-0
85 37
AGST
07.14-0.25
91. M-+--53
89.83+0 39
91 01.44-0.47
90 888+0.53
93. 93.26-60.88 36
81.63+0775
81 81.83-0.99
85.97+0 5%
OURS
91.45 0.33
91 02:005
92.1810.68
03 33.09
9100310.44
04.65100.88
86.10:20.53
87. 90.069
88 5.33
(72.49)
(10.52)
(10.59)
(11.75)
(12.27)
(11.39)
(12.53)
(T2.48)
(10.71)
Low-labeling rates setting: Tables 3 and 4 show our model outperforms others, achieving up to 8.28% higher accuracy in the 5-shot. This highlights its effectiveness with few labeled nodes. Clas- sical shallow GCNs struggle with limited data, while models using higher-order and pseudo-label info perform better.
Standard Divisions experiments: Table shows our model gains up to 2.39% accuracy over base- lines on Cora, Citeseer, and Pubmed datasets, despite the low-labeling focus, underscoring its supe- rior performance.
4.4 Ablation Study
In this section, we evaluated the performance gains of each model component through ablation ex- periments, including graph structure optimization based on node degree, pseudo-label reliability, and the effectiveness of contrastive loss. Experiments are performed on the Cora and Citeseer datasets under 3-shot, 5-shot, and 10-shot labeling ResullR in Figure show that in the Cora dataset, label selection significantly improves performance in 3-shot and 5-shot tasks, while learnable graph augmentation is more effective the 10-shot task. Conversely, this pattern is reversed in the Citeseer dataset, which is attributed to the dataset's 's unique characteristics. Compared with models retaining contrastive loss L2DGCN-LC shows significant performance gaps: on Cora, the gap reaches over 20 percentage points in 3-shot scenarios narrowing to 8 and 5 percentage points in 5-shot and 10-shot scenarios, respectively; on the more complex Citeseer, the gaps are over 20, 14, and 7-8 per- centage points in 3-shot, 5-shot, and 10-shot scenarios. These results confirm that contrastive loss helps capture feature associations from limited data, suppresses interference noisy datasets, and is critical for enhancing model adaptability and classification stability. We will supplement these experiments and analyses to clarify the independent role of contrastive loss, making the conclusions more robust.

---

4.5 Parameter Analysis
In this section, order to verify the impact of each hyperparameter on the model performance, we conduct series of experiments the Cora and Citeseer datasets under 3 and 5 settings. These experiments are divided into three main parts, and their results are shown in Figure
1)Matrix Optimization Hyperparameters: Evaluated pruning rate (3wz) and number of nearest neigh- bors (P) on Cora and Citeseen, On Cora, both showed minor fluctuations in accuracy. On Cite- seer's 3-shot task, accuracy rose with higher (3w)) and more neighbors, but fluctuated; for 5-shot, no clear trend for (Bw)), but P showed rapid improvement before declining if too large. 2) Pseudo- Labelling Selection Threshold (µ): On 5-shot Cora and Citeseer, performance was stable but in Citeseer's 3-shot task, performance varied significantly and dropped sharply as increased. 3) De- coupled GCN Propagation Steps (T): Cora showed minimal variation. Citeseer had notable fluc- tuations, especially in the 3-shot task, due to many discrete nodes and random training selection.
Table 5: Test accuracy of node classification
Cora
Method
Cora
Cileseer
Pubmed
LP
67.04 0.41
45.29
0.34
69.78 = 0.54
95.0
GCN
77.85
0.33
65.95 + 0.42
76.33 + 0.47
75.0
GAT
65.12 + 0.72
73.20 = 0.49
SGC
71.19 0.29
69.20 + 0.37
72.13 + 0.66
33.0
GLP
79.33
08.94 0.28
78.49 = 0.39
3-dui
S-slet
10-bbo
IGCN
0.31
67.89 0.29
78.64 0.39
LZDGCNALS LOOOHALE LEDGONACE
CGPN
14.12+1.55
67.34 + 1.07
75.81 + 1.26
Citeseer
CMPGNN
72.54 +.54++3.33 3.32
60.80 + 1.99
73.94 + 2.61
Graphllpp
1.10
67.23 1 2.40
75.62 1 3.01
Accuncy
25.0
PTA
0.35
78.66 + 0.44
65.0
ST GCNs
0.27
70.26 0.23
78.12 = 0.30
55.0
M3S
0..11
70.42 0.29
77.98 = 0.29
45.0
AGST
80.57 0.12
67.60
0.01
76.50 - 0.35
Muse
78.80 + 0.50
73.50 1.40
73.60 + 3.10
L30GENASS L.DGGNALE ESDOUNALC
L3DGEN
OURS
83.93 0.11
71.79
80.02 0.01
(12.39)
(11.71)
(1.36
Figure 3: Visualization of ablation results
Cora 3-shot
Cora 5-shot
Citeseer 3-shot
Citeseer 5-shot
50
Apgminyy
25-
2
70
m
60
0,20
000
0.10
0.15
10
255
3.0
7.5
10.0
1.00
1.2
1.30
1.75
240
Bi
P
Figure 4: Model performance with varied hyperparameters
5
Conclusion
To address the problem that existing models perform poorly with limited labelled nodes, we propose new solution, L2DGCN. The model contains two modules and is designed with three key elements aimed at optimising graph structure learning and efficiently propagating semantic information, thus mitigating the problem of model performance degradation due insufficiently labelled nodes. We have conducted extensive experiments on several benchmark datasets with low labelling rates, and the results show the effectiveness of solving the graph structure problem terms of node degree, as well as the precise selection of pseudo-labes labels to address their unreliability. We realise that con- sidering only features for learnable graph augmentation the current study is not comprehensive enough, especially for low-homogeneous graphs that may introduce undesirable edges.Thhrrffone Therefore, future work will focus on a multifaceted exploration of graph augmentation, aiming to develop more robust classification models.

---

Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grants 62276265, 62576344, 62406326, and 62206297.
References
[1] B. Du, X. Hu, L. Sun, J. Liu, Y. Qiao, and W. Lv, "Traffic demand prediction based on dynamic transition convolutional neural network," IEEE transactions on intelligent transportation sys- lems, vol. 22, no. 2, pp. 1237-1247, 2021.
[2] Jimenez, S. Doerr, Martinez- A. S. Rose, and G. De Fabritiis, "Deepsite: protein- binding site predictor using 3d-convolutional neural networks," Bioinformatics, vol. 33, no. 19, pp. 3036-3042, 2017.
[3] Y. Zhou, Y. Myung, C. H. M. Rodrigues, and D. B. Ascher, "Ddmut-ppi: predicting effects of mutations on protein-protett interactions using graph-based deep learning," Nucleic acids research, vol. 52, pp. 207-214, 2024.
[4] X. Tang, H. Yao, Y. Sun, Y. Wang. J. Tang, C. Aggarwal, P. Mitra, and S. Wang, "Investigating and mitigating degree-related biases graph convolutional networks," in Proceedings of the 29th ACM International Conference Information and Knowledge Management, 2020, pp- 1435 1444.
[5] H. Wang and J. Leskovec, "Combining graph convolutional neural networks and label propa- gation," ACM Transactions on Information Systems, vol. 40, no. 4, pp. 1-27, 2022.
[6] V. T. Hoang, H.-J Jeon, and O.-J. Lee, "Mitigating degree bias in graph representation learning with learnable structural augmentation and structural self-attention." IEEE Transactions on Network Science and Engineering, vol. 12, no. 5, pp. 3656-3670, 2025.
[7] M. Zhao and A. L. Jia, "Dahgn: Degree-aware heterogeneous graph neural network," Knowledge-Bard Baseed Systems, vol. 285, p. 11 111355, 2024.
[8] M. Ju, T. Zhao, W. Yu, N. Shah, and Y. Ye, "Graphpatcher: mitigating degree bias for graph neural networks via test-time augmentation," " in Proceedings of the 37th International Confer- ence Neural Information Processing Systems, 2023.
[9] Bruna, W. Zaremba, Szlam, and Lecun, "Spectral networks and locally connected networks graphs," in 2nd International Conference on Learning Representations, 2014.
[10] M. Defferrard, X. Bresson, and P. Vandergheynst, "Convolutional neural networks graphs with fast localized spectral filtering," Proceedings of the 30th International Conference on Neural Information Processing Systems, 2016, pp. 3844-3852.
[11] T. N. Kipf and M. Welling, "Semi-supervised classification with graph convolutional net- works," in 5th International Conference Learning Representationss 2017.
[12] Velickovie, Cucurull, Casanova, Romero, Liò, and Bengio, "Graph attention networks," in 6th International Conference on Learning Representations, 2018.
[13] Wu, A. H. S. Jr., T. Zhang, C. Fifty, T. Yu, and K. Q. Weinberger, "Simplifying graph convolutional networks," Proceedings of the 36th International Conference on Machine Learning, vol. 97, 2019, pp. 6861-6871.
[14] M. Chen, Z. Wei, Z. Huang, B. Ding, and Y. Li, "Simple and deep graph convolutional net- works," in Proceedings of the 37th International Conference Machine Learning, vol. 119, 2020, pp. 1725-1735.
[15] H. Dong. J. Chen, F. Feng, X. He, S. Bi, 7. Ding, and P. Cui, "On the equivalence of decoupled graph convolution network and label propagation," " in Proceedings of the Web Conference 2021, 2021, pp. 3651-3662.

---

[16] W. Zhang, Z. Yin, Z. Sheng, Y. Li, W. Ouyang, X. Li, Y. Tao, Z. Yang, and B. Cui, "Graph attention multi-laye perceptron." in Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2022, pp. 4560-45445 4570.
[17] Y. Liu, Y. Gu, Z. Ding, J. Gao, Z. Guo, Y. Bao, and W. Yan. "Decoupled graph convolution network for inferring substitutable and complementary items," in Proceedings of the 29th ACM International Conference on Information & Knowledge Management, 2020, pp. 2621-62222222 -6288.
[18) S. Wan, Y. Zhan, L. Liu, B. Yu, S. Pan, and C. Gong, "Contrastive graph poisson networks: Semi-supervised learning with extremely limited labels," in Advances in Neural Information Processing Systems 34, 2021, pp. 6316-6327.
[19] K. Sun, Z. Lin, and Z. Zhu, "Multi-stage self-supervised learning for graph convolutional networks graphs with few labeled nodes," vol. 34, no. 4, 2020, pp. 5892-5899.
[20] L. Wu, H. Liu, X. Zhang, and Z. Guan, "Label efficient semi-supervised learning via graph filtering." in 2019 JEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 9574-9583.
[21] T. Xie, B. Wang, and C.-C. J. Kuo, "Graphhop: An enhanced label propagation method for node classification." IEEE Transactions On Neural Networks and Learning Systems, vol. 34, no. 11, pp. 9287-9301, 2023.
[22] K. Ding, E. Nouri, G. Zheng, H. Liu, and R. White, "Toward robust graph semi semi-supervised learning against extreme data scarcity," IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 9, pp. 11 661-11 670, 2024.
[23] "Contrastive message passing for robust graph neural networks with sparse labels," Neural Networks, vol. 182, p. 106912,22 2025.
[24] Q. Sun, J. Li, H. Yuan, X. Fu, H. Peng, C. Jí. Q. Li, and P. S. Yu, "Position-aware structure learning for graph topology-imbalan -mbalance by relieving under-reaching and over-squashing," in Proceedings of the s1 ACM International Conference on Information & Knowledge Man- agement, 2022, P. 1848-1857.
[25] W. Lu, Z. Guan, W. Zhao, Y. Yang, and L. Jin, "Nodemixup: tackling under-reaching for graph neural networks," in Proceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence, 2024.
[26] R. Gabrielsson, M. Yurochkin, and J. Solomon, "Rewiring with positional encodings for graph neural networks," Transactions on Machine Learning Research, vol. 2023, 2022. [Online]. Available:
[27] J. Zhang, S. Ding, J. Zhang, L. Guo, and L. Ding, "Multi-channel set polynomial based label regularized graph neural networks against extreme data scarcity," Pattern Recognition, vol. 166. p. 111754, 2025.
[28] Tang, W. Hu, X. Gao, and Z. Guo, "Joint learning of graph representation and node features in graph convolutional neural networks," CoRR, vol. (bss/1999.04931, 2019.
[29] Y. Chen, Z. Wu, Z. Chen, M. Dong, and S. Wang, "Joint learning of feature and topology for multi-view graph convolutional network." Neural Networks, vol. 168, pp. 161-170, 2023.
[30] Y. Chen, L. Wu, and M. Zaki, "Iterative deep graph learning for graph neural networks: Better and robust node embeddings." in Advances in Neural Information Processing Systems, vol. 33, 2020, pp. 19 31 394-19313 326.
[31] J. Yuan, H. Yu, M. Cao. J. Song, J. Xie, and C. Wang, "Self-supervised robust graph neural networks against noisy graphs and noisy labels," Applied Intelligence, vol. 53, no. 21, pp. 25 154 25 170, 2023.
[32] X. Gao, W. Hu, and G.-J. Qi, "Self-supervised graph representation learning via topology transformations," IEEE Trunsactions on Knowledge and Data Engineering, vol. 35, no. 4, pp- 4202-4215, 2023.

---

[33] F. Dornaika, J. Bi, and C. Zhang, "A unified deep semi-supervvsed graph learning scheme based on nodes re-weighting and manifold regularization." " Neural Networks, vol. 158, pp. 188-196, 2023.
[34] Z. Shen, S. Wang, and Z. Kang. "Beyond redundancy: Information-aware unsupervised multi- plex graph structure learning," in Advances Neural Information Processing Systems, vol. 37, 2024, pp. 31 629-31 658.
[35] D. Zhou, O. Bousquet, T. Lal, J. Weston, and B. Scholkopf, "Learning with local and global consistency," in Advances in Neural Information Processing Systems, vol. 16, 2004, pp. 321- 328.
[36] K. He, H. Fan, Y. Wu, S. Xie, and B. Girshick, "Momentum contrast for unsupervised vi- sual representation learning," in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 9726 9735.
[37] A. van den Oord, Li, and Vinyals, "Representation learning with contrastive predictive coding," CoRR, vol. abs/1807.00 0007003748, 2018.
[38] P. Sen, G. Namata, M. Bilgic, L. Getoor, B. Gallagher, and T. Eliassi-Rad, Rad, "Collective classi- fication in network data," " Al magazine, vol. 29, no. 3, pp. 93-106, 2008.
[39] O. Shehur, M. Mumme, A. Bojchevski, and S. Günnemann, "Pitfalls of graph neural network evaluation," " CoRR, vol. abs/1811.00 1.05668, 2018.
[40] Q. Li, X.-M. Wu, H. Liu, Zhang, and Z. Guan, "Label efficient superisee learning via graph filtering," in 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2019, pp. 9574-9583.
[41] Wan, Y. Zhan, L. Liu, Yu, Pan, and C. Gong, "Contrastive graph poisson networks: Semi-supervised learning with extremely limited labels," in Advances in Neural Information Processing Systems 34, 2021, pp. 6316-6327.
[42] Q. Li, Z. Han, and X.-M. Wu, "Deeper insights into graph convolutional networks for semi- supervised learning." in Proceedings of the 32nd AAAI Conference Artificial Intelligence, 2018, pp. 3538-3545.
[43] Z. Wang, Q. Zeng, W. Lin, M. Jiang, and K. C. Tan, "Multiview subgraph neural networks: Self-supervised learning with scarce labeled data," IEEE Transactions on Neural Networks and Learning Systems, pp. 1-14, 2024.

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: blue[Yes]
Justification:
The main claims made in the abstract and introduction accurately reflect our contributions and scope.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals motivation as long as it is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: blue[Yes]
Justification:
The authors have discussed the limitations of the new method in the Conclu- sion section.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The au- thors should reflect on how these assumptions might be violated practice and what the implications would be.
The authors should reflect the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the ap- proach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech- speech-to-tex system might not be used reliably provide closed captions for online lectures because fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to ad- dress problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?

---

Answer: gray[NA]
Justification:
No theoretical result.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theo- rems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be comple- mented by formal proofs provided appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclu- sions of the paper (regardless of whether the code and data are provided or not)?
Answer: blue[Yes]
Justification: Our algorithm is easy to understand, and we have provided detailed explana- tions of the implementation details.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is a dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can accomplished various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or the contribution a specific model and empirical evaluation, it may be necessary either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data often one good way accomplish this, but reproducibility detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of model checkpoint, other means that are appropriate to the research performed.
also be provided via
While NeurIPS does not require releasing code, the conference does require all sub- missions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily new algorithm, the paper should make it clear how to reproduce that algorithm.
(b) the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (c.g., a large language model), then there should either be way to access this model for reproducing the results or a way re- produce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which thors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers have some path reproducing or verifying the results.
5. Open access to data and code

---

Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: orange[No]
Justification:
We use the publicly available dataset.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips...
for more details.
While we encourage the release code and data, we understand that this might not be possible, so "No" is acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (c.g., for a new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https:
//appsscc/pbbllc..///cc www.c//gwugeeeeeeeeee Stte//CooeSeuiiiee onPolicy)
more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Question:
Answer: blue[Yes]
Justification: We have provided detailed parameter analysis the experimental section, as well as the basis for setting some parameters fixed values.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropri- ate information about the statistical significance of the experiments?
Question:
Answer: [Nay[NA]
Justification: N.A.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi-
dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).

---

The method for calculating the error bars should be explained (closed form formula, call a library function, bootstrap, etc.)
The assumptions made should be given (e.g,, Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report I-sigma error bars, but one should state it. The authors should prefer- ably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative enror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: blue[Yes, YYe]
Justification: We have provided the computational resources.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't t make it into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics httppp///aaurrppp.cppp///////hep
Answer: blue[Yes]
Justification: We have carefully read the NeurIPS Code of Ethics and our research conforms with it.
Guidelines:
The answer NA means that the authors have not reviewed the NeurlPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: gray[NA]
Justification: The research is an improvement of existing classification algorithms and does not address social impacts.
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.

---

Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact spe- cific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitiga- tion strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Question: Does the paper deseribe safeguards that have been put in place for responsible release of data or models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Answer: gray[NA]
Justification: N.A.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by re- quiring that users adhere to usage guidelines restrictions access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: Yes)
Justification:
We have cited the utilized papers.
Guidelines:
The answer NA means that the paper does not use existing assets. The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include URL.
The name of the license (e.g.. CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
license, copyright information, and terms of use the pack- age should be provided. For popular datasets, haperswithcode com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the li- cense of dataset.
If assets are released,

---

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's s creators.
13. New assets
Are new assets introduced in the paper well documented and the documenta- tion provided alongside the assets?
Question:
Answer: gray[NA]
Justification: N.A.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
For crowdsourcing experiments and research with human subjects, does the pa- per include the full text of instructions given participants and screenshots, if applicable, as well as details about compensation (if any)?
Question:
Answer: gray [NA]
Justification: N.A.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contri- bution of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According the NeurIPS Code of Ethies, workers involved in data collection, cura- tion, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country or institution) were obtained?
Answer: gray[NA]
Justification: N.A.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research
with human subjects.
Depending on the country in which research is conducted, IRB approval (or equiva- lent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

---

16. Declaration of LLM usage
Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, originality of the research, declaration is not required.
Question:
Answer: gray[NA]
Justification: N.A.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to LLM policy for what should or should not be described.


Reviews:
[{"review_id": "L9Lc89QiXV", "reviewer": "Reviewer_1mpJ", "summary": "The paper focuses on addressing the performance issues of graph neural networks (GNNs) in low-label data and low-degree node scenarios, proposing the L2DGCN model. The model employs a teacher model to improve label propagation for cross-node remote information interaction and a student model to dynamically enhance graph structures, promoting communication among low-degree nodes while maintaining topology. A label selector is used to optimize pseudo-labels. Experiments validate its effectiveness in mitigating degree bias and improving performance in low-label scenarios.", "questions": "For questions, please see the weakness in the above section.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths \n1. The method is innovative, proposing a dual-model architecture that combines decoupled GCN and dynamic graph enhancement techniques to specifically address the information propagation challenges of low-degree nodes. \n2. The motivation behind the proposed model is well-founded, and the experimental design is robust. It is validated in low-label scenarios across multiple different types of datasets, with results showing that the accuracy outperforms 14 baseline methods, demonstrating the model's effectiveness.\n\nWeaknesses\n\n1. In Section 4.2, the value range of $\\mu$ in Table 2 is inconsistent with that in Figure 4 of Section 5.4. Please carefully check and verify. \n2. Generalizability of the label selector: The setting of the confidence threshold $\\mu$  relies on dataset characteristics. It is recommended to add comparative results with (  $\\mu$=0 ) (full pseudo-labels) in the ablation experiment of Section 4.4 to validate the necessity of the filtering mechanism.", "was_revised": false, "final_justification": "", "rebuttal": "We would like to express our sincere gratitude to the reviewer for the meticulous review and constructive comments. Your professional insights have provided important guidance for us to improve the quality of the paper, and we deeply appreciate this.\n\n   1.Regarding the inconsistency in the numerical range between Table 2 in Section 4.2 and Figure 4 in Section 5.4 that you pointed out, we are fully aware that this is an oversight in the manuscript proofreading process. After careful revision, we have adjusted the numerical range in Table 2 to [1.0, 1.2, 1.4, 1.6, 1.8, 2.0], where the newly added value of 2.0 corresponds to the model performance when pseudo-labels are not used. Meanwhile, we have supplemented this result to Figure 4 to ensure that the data in the table and the figure are completely consistent, so as to more clearly present the impact of pseudo-labels on model performance.\n\n    2. With respect to your suggestion of adding the comparison result of μ=0 (full pseudo-labels) in the ablation experiment of Section 4.4 to verify the necessity of the filtering mechanism, we believe this suggestion is helpful for more comprehensively highlighting the generality of the label selector and the core value of the filtering mechanism. The full pseudo-label result you suggested to supplement corresponds to the situation when μ=1.0 mentioned earlier in our paper. We will incorporate this result into the ablation experiment section. By comparing the differences in model performance between the full pseudo-label scenario and different confidence thresholds, we will intuitively demonstrate the key role of the filtering mechanism in eliminating noisy pseudo-labels and improving model robustness, thereby further verifying the necessity of the label selector design.\n\n  Once again, we thank you for your valuable comments. We will further strengthen the proofreading of the manuscript to ensure the accuracy of data and charts and improve the quality of the paper."}, {"review_id": "9nerqlzeHw", "reviewer": "Reviewer_eGGT", "summary": "This paper proposes a new model, L2DGCN, to address the challenge of semi-supervised node classification on graphs with very few labeled nodes. The authors identify \"degree bias\" as a primary cause for performance degradation in this setting. The model consists of a teacher-student architecture.", "questions": "Please address Weakness part.", "limitations": "N/A", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "# Strength \n\n* The paper is motivated by the degree bias problem in GNNs, which is well recognized in the literature.\n* The authors have conducted a comprehensive set of experiments across six benchmark datasets and multiple low-data settings.\n* The proposed L2DGCN framework is modular, integrating several popular techniques like teacher-student learning, label propagation, graph enhancement, and self-training, which are relevant to the problem at hand.\n\n# Weakness\n\n* The paper's primary motivation is to mitigate the negative effects of degree bias on low-degree nodes, which suffer from insufficient information propagation. However, the proposed \"Edge Pruning Based on Node Degrees\" component explicitly states that it retains edges for high-degree nodes while removing edges connected to low-degree nodes.  This seems to be in direct contradiction with the stated goal of the paper.\n* Individual component (self-training with pseudo-labels, soft label propagation, learnable structure augmentation, contrastive loss, and pseudo-label selection) is based on existing techniques. The novelty of each component is limited, and their integration feels more like an ad-hoc ensemble than a principled, unified model.  Besides, it has a large number of sensitive hyperparameters.\n* The effectiveness of the label selector depends on the accuracy of soft pseudo-label assignment in ultra-low label regimes. Despite the claimed robustness, quantitative evidence for reduction in label noise or comparisons with alternative confidence estimation approaches are absent.\n* While the ablation study (Figure 3) quantitatively shows the contributions of label selection and graph enhancement, there is little qualitative or visualization analysis regarding how graph structure actually changes and how degree bias is mitigated in practice\n* Some related works about under-reaching issue should also be inclued [1,2,3,4].\n\nRefs:\n[1] Position-aware structure learning for graph topology-imbalance by relieving under-reaching and over-squashing, CIKM 2022.\n[2] NodeMixup:  Tackling Under-Reaching for Graph Neural Networks, AAAI 2024.\n[3] Rewiring with positional encodings for graph neural networks.", "was_revised": true, "final_justification": "The authors have addressed my concerns. And I would like to raise my rating to 4.", "rebuttal": "Dear Reviewer,\n\nThank you sincerely for your valuable comments and profound insights, which are of great significance for enhancing the logical rigor, innovation expression, and result interpretability of our paper. Below are detailed responses to your points:\n\n\n1. You pointed out that the practice of retaining edges of high-degree nodes and removing connections of low-degree nodes in the proposed \"node degree-based edge pruning\" component seems to contradict the paper's goal of mitigating degree bias and improving information propagation for low-degree nodes. This observation is very much to the point: viewed in isolation, this operation may indeed give the impression of being contrary to the goal. However, in the overall design of the model, this component and the \"graph enhancement based on dynamic similarity matrix\" module form a complementary collaboration. The former reduces interference by pruning redundant or noisy connections of low-degree nodes (such as weak associations with heterogeneous nodes), while the latter, based on dynamically calculated node similarity, directionally adds effective connections between low-degree nodes and their homogeneous nodes. They work together from the two aspects of \"denoising\" and \"supplementing connections\": not only preventing low-degree nodes from being misled by invalid information, but also actively supplementing high-quality information propagation paths for them, ultimately achieving targeted optimization of the problem of insufficient information propagation for low-degree nodes. We will further clarify the collaborative logic of these two modules in the paper, and through clearer mechanism descriptions and comparative experiments, intuitively show how their combination can effectively alleviate degree bias, making the consistency between the model design and the research goal easier to understand.\n\n\n2. You noted that individual components are based on existing technologies with limited novelty, and that their integration lacks a principled unity. Indeed, each component of the model is built upon relevant research, but we have incorporated original improvements targeting the degree bias issue of low-degree nodes in key modules:  \n\n    In the learnable structure enhancement module, existing methods mostly adopt a strategy of uniformly enhancing all nodes, while we focus on the particularity of low-degree nodes—their limited connections are more sensitive to noise, and the quality of a single edge has a significant impact on information propagation. To address this, we first remove the original connections of low-degree nodes (including potential noisy edges) through edge pruning, and then, combined with the characteristics of homogeneous graphs, directionally add reliable connections with nodes of the same class for them through a dynamic similarity matrix. This \"first reduce, then increase\" strategy is not a simple superposition of operations, but designed based on the information propagation rules of low-degree nodes: if the original edge is a key connection, it will be regenerated through dynamic similarity under the homogeneity assumption; if it is not reconstructed, it confirms its noisy nature, thereby achieving precise optimization of the connection quality of low-degree nodes.   \n\n    In the pseudo-label self-training module, instead of directly adopting the traditional self-training framework, we screen high-confidence pseudo-labels through a label selector, specifically alleviating the interference of low-quality pseudo-labels on the model. This mechanism has a clear gain in improving stability in sparse labeling scenarios.  \n\n    In addition, the integration of various components forms an organic collaboration around the core goal of \"alleviating the degree bias of low-degree nodes\": edge pruning \"denoises\" for low-degree nodes, dynamic enhancement \"supplements connections\" for them, and pseudo-label screening provides reliable supervision signals for them. The three together constitute a complete solution to the shortcomings of information propagation in low-degree nodes, rather than a simple pile-up of independent technologies.  \nRegarding the issue of hyperparameter sensitivity, we have completed systematic experimental verification in the hyperparameter analysis section. The results show that the model has good stability under perturbations of key parameters, further supporting the rigor of the research. We will focus on strengthening the elaboration of the above mechanisms in the revised manuscript to highlight the principle and unity of the model design.\n\n\n3. You raised points regarding the connection between the effectiveness of the label selector and the accuracy of soft pseudo-label assignment, as well as the lack of quantitative evidence for noise reduction and comparisons with other confidence methods. In the existing analysis, through gradient tests on the confidence threshold μ in the hyperparameter section, we observed the trend of model performance changes under different thresholds—the higher the μ value, the more stable the model's performance in sparse labeling scenarios. This indirectly reflects the potential noise suppression effect of the label selector by regulating the number of pseudo-labels (screening high-confidence samples). We will more clearly present the connection between this observation result and the performance of the label selector in the revised manuscript, and strengthen the support of existing experimental results for its effectiveness.\n\n\n4. You suggested that although the ablation study quantitatively demonstrates the contributions of label selection and graph enhancement, it lacks qualitative or visual analysis on the actual changes in graph structure and the mitigation of degree bias. We will supplement the analysis from the following aspects: First, visually compare the changes in topological structure before and after graph enhancement. By drawing local subgraphs of key nodes (especially low-degree nodes), we will show the adjustment of neighbor distribution caused by added or deleted edges, intuitively presenting how dynamic graph enhancement supplements effective connections for low-degree nodes. Second, statistically analyze the proportion of edge additions and deletions in different node degree intervals, and combine with changes in node classification accuracy to quantitatively illustrate the correlation between graph structure adjustment and degree bias mitigation. Third, select typical cases to show the changes in feature embedding distribution of low-degree nodes before and after graph enhancement, revealing the process from being indistinguishable to clustering with nodes of the same class, and clarifying the specific effect of degree bias mitigation. These supplementary analyses will make the working mechanism of the model clearer and further enhance the credibility of the paper's conclusions.\n\n\n5. You opined that incorporating relevant works addressing uncovered issues is helpful for enriching the literature review section of the paper and enhancing the completeness and relevance of the research background. In the task of semi-supervised node classification, existing studies have been dedicated to solving the performance bottlenecks of Graph Neural Networks (GNNs) in scenarios with sparse labeled data, focusing on optimizing issues such as limited information propagation, unbalanced topological structures, and insufficient learning of low-degree nodes. Specifically, PASTEL [1] addresses the problems of insufficient information and excessive suppression caused by \"topological imbalance\" by proposing a position-aware graph structure learning framework. It enhances intra-class connections and optimizes edge weights through anchor position encoding, alleviating structural biases at the level of propagation paths. NodeMixup [2] focuses on the insufficient reachability between labeled and unlabeled nodes, designing a cross-set mixing strategy and neighbor label distribution-aware sampling to enhance information interaction through node pair mixing without adjusting the GNN architecture. Another study [3] expands the GNN's receptive field to skip neighborhoods through position encoding, adding virtual nodes/edges to the input graph and injecting position features to achieve model-agnostic receptive field expansion, avoiding complex architectural modifications. In contrast, the proposed model adopts a teacher-student dual-model collaborative mechanism: the teacher model realizes global long-range label diffusion through improved label propagation, the student model introduces a dynamically learnable graph enhancement strategy to promote interactions among low-degree nodes, and a label selector is designed to filter pseudo-label noise. This architecture not only balances global structure preservation and local information enhancement but also specifically solves the problem of pseudo-label reliability. Its dynamic edge perturbation strategy has stronger adaptability to complex topologies, and the optimization for information acquisition of low-degree nodes is more direct, showing unique advantages in sparse labeling scenarios. We will supplement the citations and analyses of relevant works as suggested, making the related work section of the paper more comprehensive and in-depth, and better highlighting the innovation and necessity of this research.\n\nRefs: [1] Position-aware structure learning for graph topology-imbalance by relieving under-reaching and over-squashing, CIKM 2022.\n\n[2]NodeMixup: Tackling Under-Reaching for Graph Neural Networks, AAAI 2024. \n\n[3]Rewiring with positional encodings for graph neural networks."}, {"review_id": "QGyY2KRgl6", "reviewer": "Reviewer_FjSS", "summary": "To address the challenges of labeling costs and low-degree node propagation in GNN node classification, the L2DGCN model is proposed. Its teacher-student architecture solves the problems of long-range information transmission and low-degree node interaction through improved label propagation and dynamic graph augmentation strategies, respectively. By integrating a label selector to optimize the learning process, the model significantly enhances performance in semi-supervised classification experiments with limited labeled data.", "questions": "Please refer to the above weakness.", "limitations": "Yes.", "rating": 6, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n1. It solves a major challenge in graph neural networks, namely degree bias in semi-supervised node classification, and proposes an innovative method to address this problem. I appreciate the depth of your analysis, the clarity of the methodology, and the extensive experiments you conducted to validate the model. Your combination of pseudo-label propagation and dynamic graph augmentation is a promising direction, and the improvements reported on various datasets are commendable. \n2. Validating node classification performance in 3 low-label-rate scenarios on 6 datasets is thorough and extensive.\n\n**Weaknesses**\n1. This work addresses the degree bias problem in graph convolutional networks, which has also been widely studied in previous works. The authors are required to enrich the Related Work section. Below are some papers related to solving degree bias for the authors' reference.\n\n[1] Van Thuy Hoang, Hyeon-Ju Jeon and  O-Joun Lee. \"Mitigating Degree Bias in Graph Representation Learning With Learnable Structural Augmentation and Structural Self-Attention,\" IEEE Transactions on Network Science and Engineering, 2025, doi: 10.1109/TNSE.2025.3563697.\n\n[2] Mingxia Zhao, Adele Lu Jia, “DAHGN: Degree-Aware Heterogeneous Graph Neural Network,” Knowledge-Based Systems, 2014, 285: 111355.\n\n[3] Mingxuan Ju, Tong Zhao, Wenhao Yu, Neil Shah, and Yanfang Ye. 2023. GRAPHPATCHER: mitigating degree bias for graph neural networks via test-time augmentation. In Proceedings of the 37th International Conference on Neural Information Processing Systems (NIPS '23). pp. 55785–55801.\n\n2. In Section 4.2, K is fixed at 10. The correlation between this value and the dataset scale or node degree is not clarified. It is recommended to add an experiment on \"the correlation between K and model performance\" in the parameter analysis of Section 4.5. \n\n3. Formula (18) includes the contrastive loss $L_{CL}$, but its individual impact is not tested in the ablation experiments. It is suggested to add a control group in Figure 3 that \"removes only $L_{CL}$\" to clarify its improvement ratio on classification accuracy.", "was_revised": true, "final_justification": "The authors' response  has adequately addressed all of my concerns. I think this is a well-motivated and solid work. So I raise my rating to 6.", "rebuttal": "Dear Reviewer,\n\nThank you sincerely for your valuable comments and insightful suggestions, which are crucial for enhancing the quality, rigor, and comprehensiveness of our paper. We have carefully addressed each of your points, and the detailed responses are as follows:\n\n\n1. In the research on the degree bias problem in Graph Neural Networks (GNNs), several studies have explored solutions from different perspectives: DegFairGT [1] proposes a learnable structural enhancement and structural self-attention mechanism, which generates new edges by calculating the structural similarity between node pairs to balance message passing, and retains the global topology with the help of a self-supervised task based on p-step transition probability matrices, thereby alleviating the problem of insufficient information in low-degree nodes and over-smoothing in high-degree nodes; DAHGN [2], on the other hand, focuses on heterogeneous information networks, constructs a dual-view contrast framework of heterogeneous views and homogeneous subgraphs, combines semi-supervised task loss and contrast loss, and adopts differentiated strategies for low-degree and high-degree nodes to eliminate degree bias, filling the gap in research on heterogeneous scenarios; GraphPatcher [3] innovatively realizes model-agnostic degree bias mitigation through test-time augmentation, iteratively generates virtual nodes to repair damaged neighborhoods of low-degree nodes, improving the performance of low-degree nodes (by an average of 6.5%) while preserving the advantages of high-degree nodes, with an overall performance improvement of 3.6% on average. However, existing methods still have limitations in sparse labeling scenarios: DegFairGT's structural enhancement has limited adaptability to dynamic topologies and is difficult to directly cope with the challenge of insufficient labeled data; DAHGN's contrastive learning framework is insufficient in handling the reliability of pseudo-labels in complex heterogeneous networks; GraphPatcher, as a test-phase strategy, cannot fundamentally optimize the information aggregation of low-degree nodes during training. To address these issues, the L2DGCN proposed in this paper achieves a breakthrough through a teacher-student dual-model collaborative mechanism: the teacher model adopts an improved label propagation mechanism to realize long-range label information dissemination among global nodes, alleviating the insufficiency of supervision signals under sparse labeling; the student model introduces a dynamically learnable graph enhancement strategy, perturbing edges to facilitate information exchange among low-degree nodes while taking into account the preservation of the global structure; in addition, a specially designed label selector effectively mitigates the impact of unreliable pseudo-labels on model learning. This integrated framework of \"global label diffusion - local dynamic enhancement - pseudo-label screening\" demonstrates significant advantages in semi-supervised node classification tasks under sparse labeling scenarios, which not only specifically solves the information bias problem of low-degree nodes but also adapts to complex topologies through flexible dynamic learning mechanisms, providing a new and effective solution for mitigating degree bias in scenarios with insufficient labels.\n\n\n2. Your suggestions on clarifying the correlation between the value of K and dataset size, node degree, as well as supplementing experiments on \"the correlation between K and model performance\" are of great significance for improving the parameter analysis section. We will add relevant experiments in Section 4.5's parameter analysis: by testing the model's performance when K takes values such as 5, 10, 15, and 20 on datasets like Cora and Citeseer, we will analyze the correlation between K and dataset size (number of nodes, edge density) and node degree distribution, clarify the trend of K's influence on model performance, verify the rationality of setting K=10, and provide references for K selection in different scenarios. This supplement will make the parameter analysis more comprehensive and enhance the reliability and practicability of the conclusions.\n\n\n3. Your opinion on testing the individual impact of contrastive loss in ablation experiments and adding a control group is valuable for improving experimental design and clarifying the role of key components. The experimental results are as follows: On the Cora dataset, the accuracy of the model without contrastive loss (L2DGCN-LC) is 59.69 (3-shot), 76.53 (5-shot), and 78.23 (10-shot); on the Citeseer dataset, it is 49.02 (3-shot), 55.81 (5-shot), and 67.74 (10-shot). Compared with models retaining contrastive loss (L2DGCN, L2DGCN-LS, L2DGCN-LE), L2DGCN-LC shows significant performance gaps: on Cora, the gap reaches over 20 percentage points in 3-shot scenarios (vs. L2DGCN's 80.43), narrowing to ~8 and ~5 percentage points in 5-shot and 10-shot scenarios, respectively; on the more complex Citeseer, the gaps are over 20, ~14, and 7-8 percentage points in 3-shot, 5-shot, and 10-shot scenarios (vs. L2DGCN's 69.61 in 3-shot). These results confirm that contrastive loss helps capture feature associations from limited data, suppresses interference in noisy datasets, and is critical for enhancing model adaptability and classification stability. We will supplement these experiments and analyses to clarify the independent role of contrastive loss, making the conclusions more robust.\n\n\nThank you again for your careful review and guidance. We will revise the manuscript in accordance with your suggestions to further improve its quality."}, {"review_id": "vAEW8QYbWs", "reviewer": "Reviewer_XADT", "summary": "This paper addresses the degree bias problem in node classification when there are insufficient labeled nodes. The authors demonstrate that the proposed method enhances graph structures by focusing on low-degree nodes, enabling effective information propagation and significantly improving performance on various homogeneous and heterogeneous graphs.", "questions": "1. The authors should analyze the potential drawbacks of the proposed method to provide readers with a more comprehensive understanding of the solution. \n2. Table 2 lists the parameter ranges but does not specify how the optimal values were selected (e.g., whether grid search or Bayesian optimization was used). It is recommended to supplement the description of \"hyperparameter optimization strategies\" in Section 4.2. \n3. Some recent models related to mitigating degree bias have emerged, but they are missing from the comparative experiments. \n4. The improved model mentioned in the paper is a self-training model, which may lead to higher time complexity. However, the paper lacks an analysis of time complexity.", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "### Strengths \n1. The article has a complete structure and clear writing style. \n2. Some experimental results seem promising.\n### Weaknesses\n1. The authors should analyze the potential drawbacks of the proposed method to provide readers with a more comprehensive understanding of the solution. \n2.Table 2 lists the parameter ranges but does not specify how the optimal values were selected (e.g., whether grid search or Bayesian optimization was used). It is recommended to supplement the description of \"hyperparameter optimization strategies\" in Section 4.2. \n3.Some recent models related to mitigating degree bias have emerged, but they are missing from the comparative experiments. \n4. The improved model mentioned in the paper is a self-training model, which may lead to higher time complexity. However, the paper lacks an analysis of time complexity.", "was_revised": true, "final_justification": "The rebuttal fully resolved my concerns. The paper is insightful and meets the acceptance standard.", "rebuttal": "Dear Reviewer,\n\nThank you sincerely for your valuable comments and insightful suggestions, which are of great significance for improving the completeness, rigor, and persuasiveness of our paper. We have carefully addressed each point, and the detailed responses are as follows:\n\n\n1. **Potential drawbacks of the proposed method and solutions**  \nYour opinion on analyzing the potential drawbacks of the proposed method is extremely valuable and helps improve the completeness and rigor of the paper. The following is a detailed explanation of the potential shortcomings of the L2DGCN model and their solutions:  \n- **High computational complexity with limited adaptability to large-scale graphs**: The teacher model's soft label propagation (with complexity O(K • N²c)) and the student model's dynamic graph enhancement (with O(N²D)) involve operations with a square level of the number of nodes. This leads to a significant increase in time consumption for large-scale graphs (such as Pubmed).  \n  Solutions: Adopt a sparse node sampling strategy, retaining only high-impact nodes (e.g., high-degree nodes, classification boundary nodes) for core operations, converting full-node pair calculations into local ones; introduce approximate similarity algorithms (like random projection) to reduce the feature dimension D and lower the cost of a single similarity calculation.  \n- **Insufficient optimization of dynamic graph enhancement for low-homophily graphs**: Relies on feature similarity to construct KNN graphs without fully integrating graph structural properties (e.g., clustering coefficient, betweenness centrality), which may introduce redundant edges or miss key connections in low-homophily graphs.  \n  Solutions: Combine structural and attribute features to calculate similarity (e.g., weighted fusion of cosine similarity and random walk structural similarity), ensuring edge supplementation considers both feature correlation and structural dependence; dynamically adjust the number of KNN neighbors P based on graph homophily, reducing P for low-homophily graphs to minimize redundancy.  \n\n\n2. **Hyperparameter optimization strategy**  \nThank you for the reviewer's detailed suggestions. We have supplemented the detailed description of the hyperparameter optimization strategy in Section 4.2: For the selection of optimal values of the parameters listed in Table 2, we adopted the grid search method. Specifically, within the preset parameter ranges, we exhaustively combined the possible values of each parameter, evaluated the model performance on the validation set, and finally selected the parameter combination that made the model perform optimally. Although the grid search method needs to traverse many parameter combinations, it can ensure a comprehensive examination of the parameter impact within the set range. For the parameter dimensions and ranges involved in our experiments, it can effectively find a better solution and ensure the stability of the experimental results.  \n\n\n3. **Supplementary comparative experiments with recent related models**  \nThank you for pointing out that some recently emerging models related to mitigating degree bias are missing from the comparative experiments. Your comment is of great significance for improving the experimental design and enhancing the comprehensiveness and persuasiveness of the research.  \nWe have noticed a series of related models that have emerged in recent years (such as [specific model names can be listed here if known]). Due to the relatively recent publication of these works, they were not included in the comparative experiments during the initial experimental design phase of the first draft. To address your suggestion, we will supplement comparative experiments with these emerging models in the revised manuscript:  \nFirst, we will select representative state-of-the-art models in the field of degree bias mitigation, ensuring their comparability with the research scenarios of this paper (such as semi-supervised node classification, sparse labeling conditions, etc.). Second, we will adopt a unified experimental setup (including datasets, evaluation metrics, hyperparameter tuning criteria, etc.) to fairly compare the performance of our model with these emerging methods in key dimensions such as overall performance, the magnitude of performance improvement for low-degree nodes, and adaptability to dynamic topologies. Finally, through quantitative analysis and mechanism comparison, we will further clarify the unique advantages of our model in addressing degree bias under sparse labeling scenarios, such as the innovative value of designs like \"teacher-student dual-model collaboration\" and \"combination of dynamic graph enhancement and pseudo-label screening\" compared to existing methods. After supplementing these comparative experiments, we will be able to more comprehensively verify the advancement and practicality of our model.  \n\n\n4. **Computational complexity of the model**  \nThe computational complexity of this model is composed of the core operations of the teacher model and the student model, and is directly related to parameters such as graph scale (number of nodes (N), number of edges (E)), feature dimension (D), and propagation steps. The specific breakdown is as follows:  \n- **Complexity of the Teacher Model (Soft Label Propagation)**: The teacher model generates pseudo-labels through improved soft label propagation, with the core involving matrix multiplication (multiplying an N×N matrix by an N×c matrix). Complexity of a single propagation is O(N²c); total complexity after K propagations is O(K • N²c).  \n- **Complexity of the Student Model**:  \n  1. Dynamic Graph Enhancement: Edge pruning involves node sorting (O(N log N)) and edge traversal (O(E)); similarity matrix and KNN graph construction involve cosine similarity calculation (O(N²D)) and neighbor supplementation (O(N • P • D)). Total: O(N log N + E + N²D + N • P • D).  \n  2. Decoupled GCN Propagation: After T propagations, with single propagation complexity O(E • D), total complexity is O(T • E • D).  \n  3. Pseudo-Label Selection: Traversing nodes to calculate confidence, with complexity O(N • c).  \n- **Total Complexity of the Model**: Combining the above modules, the total computational complexity is dominated by the number of nodes N (affecting the N² term), number of edges E (affecting the E • D term), and propagation steps K/T.  \n\n\nThank you again for your constructive comments. We will revise the manuscript accordingly to enhance its quality."}]

Author rebuttal:

Meta-review: The paper presents the L2DGCN model, which aims to address GNN performance in few-labels and low-degree node scenarios. Most reviewers agree that the approach presented is novel, the presentation is clear (at least after the rebuttal) and the experiments are promising. The reviewers also agree that the degree bias problem tackled in this work is a major problem in GNN. Although initial reviews have posted weaknesses such as hyperparameter analysis and novelty concerns, these issues are sufficiently addressed in author rebuttals.

In sum, given that the significance of the problem tackled and the novelty of the approach, I recommend accepting the paper.
Decision: Accept (spotlight)