GD$^2$: Robust Graph Learning under Label Noise via Dual-View Prediction Discrepancy
Authors: Kailai Li
Jiong Lou
Jiawei Sun
Honghong Zeng
Wen Li
Chentao Wu
Yuan Luo
Wei Zhao
Shouguo Du
Jie LI
Venue: NeurIPS 2025 poster ()
Keywords: Graph Neural Network
label noise
Primary area: general_machine_learning
TL;DR: We propose a dual-view graph learning framework that detects label noise by capturing semantic discrepancies between node-level and structure-level predictions.

Abstract: Graph Neural Networks (GNNs) achieve strong performance in node classification tasks but exhibit substantial performance degradation under label noise. Despite recent advances in noise-robust learning, a principled approach that exploits the node-neighbor interdependencies inherent in graph data for label noise detection remains underexplored. To address this gap, we propose GD$^2$, a noise-aware \underline{G}raph learning framework that detects label noise by leveraging \underline{D}ual-view prediction \underline{D}iscrepancies. The framework contrasts the \textit{ego-view}, constructed from node-specific features, with the \textit{structure-view}, derived through the aggregation of neighboring representations. The resulting discrepancy captures disruptions in semantic coherence between individual node representations and the structural context, enabling effective identification of mislabeled nodes. Building upon this insight, we further introduce a view-specific training strategy that enhances noise detection by amplifying prediction divergence through differentiated view-specific supervision. Extensive experiments on multiple datasets and noise settings demonstrate that \name~achieves superior performance over state-of-the-art baselines.

GD²: Robust Graph Learning under Label Noise via Dual-View Prediction Discrepancy
Kailai Li Jiong Lou't, Jiawei Sun', Honghong Zeng', Wen Li Chentao Wu
Yuan Luo', Wei Zhao?, Shouguo Du", Jie Li..3,4,
DDepartment of Computer Science and Engineering. Shanghai Jiao Tong University Shenzhen University of Advanced Technology
Yancheng Blockchain Research Institute
Shanghai Key Laboratory of Trusted Data Circulation and Governance and Web3
'Shanghai University of International Business and Economics Shanghai Municipal Big Data Center
(kailai 1j1994, noelsjw, zhhhhh6)@sjju, edu. cn, wen 1i..i..... sh@outlook. com, {wuct, (uoyuann0cs sjtu. edu, cn, (weizha086, shouguo. du. @outlook com, lijiecs@sjtu edu. en
Abstract
Graph Neural Networks (GNNs) achieve strong performance in node classification tasks but exhibit substantial performance degradation under label noise. Despite recent advances in noise-robust learning, a principled approach that exploits the node-neighbor interdependencies inherent in graph data for label noise detection remains underexplored. To address this gap, we propose GD², a noise-aware Graph learning framework that detects label noise by leveraging Dual-view pre- diction Discrepancies. The framework contrasts the ego-view, constructed from node-specific features, with the structure-view: derived through the aggregation neighboring representations. The resulting discrepancy captures disruptions in semantic coherence between individual node representations and the structural context, enabling effective identification of mislabeled nodes. Building upon this insight, further introduce view-specific training strategy that enhances noise detection by amplifying prediction divergence through differentiated view-specific supervision. Extensive experiments multiple datasets and noise settings demon- strate that GD² achieves superior performance over state-of -fe--o--theetrr baselines.
Introduction
Graph Neural Networks (GNNs) have recently achieved significant advancements in node classifica- tion, with extensive applicability across domains such as social network analysis (9) recommender systems (38) and biomedical research (36). Nevertheless, obtaining high-quality labeled data remains challenging in real-world scenarios, and noisy labels are inevitably present. Prior research indicates that noisy labels mislead the training of GNNs, substantially degrading predictive accuracy and generalization capability [45]. Furthermore, due to the message-passing mechanism inherent in GNNs, the negative impact of label noise exacerbated 5 28) Consequently, developing robust GNN models under label noise represents a crucial and pressing research objective.
To alleviate negative impacts associated with noisy labels, general noise-learning approaches com- monly exploit the memorization effect exhibited by neural networks [[] 42 or rely on handcrafted
"Corresponding authors: Wen Li, Jie Li.
Equaa contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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20.0
Clean Noisy
Clean Noisy
Clean
17.5
Emplrical pdf
Empirical pdf
Empirical pdr
15.0
Noisy
10.0
7.5
5.0
2.5
0.0
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.8
1.0
Normulized discrepancy 5
Normalized discrepancy 5
Normalized diserepancy 5
(a) GCN
(b) GCN + view-specific heads
(c) GD2
Figure 1: Normalized prediction discrepancy between the ego-view and structure-view the Computer dataset. (a) Standard GCN yields observable but limited separation in the discrepancy distribution between clean and noisy nodes, hindering effective noise detection. (b) GCN with a shared encoder and view-specific classifier heads produces more distinguishable discrepancy distribution. (c) GD2 enhances the distributional separability in prediction discrepancies between clean and noisy nodes, yielding well-separated distribution and facilitating noise detection.
heuristic signals [7 14] for filtering or rectifying mislabeled samples. However, these methods implicitly assume that the data are independent and identically distributed (i.i.d),, which does not hold in graph data due to interdependencies among connected nodes. Consequently, existing noise-lcarning techniques perform suboptimally when directly applied to node classification tasks [32]. Recently, several methods specifically tailored for graph data have emerged, incorporating structural informa- tion into noise-robust learning. Representative methods include graph structure refinement [)
diructure-based curriculum learning 33 35), label correction via propagation [422 and incorporation common trait among these approaches is the implicit use of semantic alignment between node features and the structural context. Such alignment captures the node-neighbor interdependencies inherent to graph data, contributing to robust representation learning and label noise mitigation. However, most existing techniques inherit noise detection mecha- nisms originally developed for i.i.d. data and do not explicitly leverage such relational patterns. The potential of interdependencies for identifying noisy labels remains underexplored. Consequently, an open question naturally arises: can the intrinsic dependencies between node features and structural context be explicitly modeled to enable effective label noise detection in graph data?
of auxiliary supervision g
To address the aforementioned research question, this paper presents GD?, noise- aware graph learning framework that explicitly leverages the semantic discrepancies between node features and structural context to detect label noise. The core component is a noise detection module based on dual-view prediction discrepancy. Specifically, node representations are decoupled into two distinct views based on information source. The ego-view constructed solely from node-specific features and captures individual semantic information. The pructure-view is derived by aggregating neighbor representations and encodes contextual semantics from local graph topology. The prediction discrepancy between the two views is exploited an intrinsic signal for identifying potential label errors. Figure illustrates the prediction discrepancy between the ego-view and structure-view under label noise. The key insight is that label noise disrupts semantic coherence between the two views, leading to divergent predictions. The ego-view, relying solely on individual features, tends to overfit spurious correlations introduced by incorrect labels, resulting in semantically misaligned representations. In contrast, the structure-view captures topological patterns that remain relatively stable under noise. Therefore, prediction divergence between the views serves indicator for identifying mislabeled nodes. This insight is further supported by theoretical analysis, which reveals that clean-labeles labeled nodes inherently exhibit bounded cross-view representation discrepancies. Building upon the above noise detection mechanism, we also introduce a view-specific training strategy, which provides differentiated supervision to each view further enhance prediction discrepancies and facilitate noise detection. The main contributions are summarized as follows:
(1) We propose novel perspective for noisy label detection in graph data, that prediction discrepancy between ego-view and structure-view can be an indicator for identifying label errors.
(2) We introduce graph learning framework named GD2, which incorporates noise detection module and a view-specific training strategy. By quantifying predictive discrepancies between views, the proposed framework effectively detects mislabeled nodes and facilitates robust lcarning.

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(3) Extensive experiments on multiple real-world graph datasets under varying noise levels demon- strate that GD consistently outperforms state-of-the-arr baselines, highlighting its effectiveness in addressing label noise in graph learning.
2 Related Work
2.1 Noisy Label Detection
Noisy label detection aims to identify and remove incorrectly labeled samples from the training data. The main challenge lies in defining a suitable metric to quantify the label quality. A widely- adopted approach leverages the memorization effect of deep neural networks [Л utilizing criteria such as training loss or prediction confidence. Representative methods include Decoupling [23], Co-teaching 13,. Co-teaching+ [42], and ProMix [4]. More advanced criteria have also been developed, such as AUM [27]. which identifies mislabeled samples by tracking the prediction margin during training. TopoFilter [37]. which isolates noisy samples based on topological properties in the representation space, and OT-Filter [10]. which selects samples from the perspective of optimal
transport theory.
Recently, some studies have extended sample selection methods to graph-structured data. For instance, TSS 39 employs class-conditional betweenness centrality based on graph topology to select nodes; UnionNet [9] aggregates labels perform sample re-weighting and label correction; and CLN- ode (35) introduces a mulli-perspective difficulty measurer for detecting label noise. Nevertheless, these methods typically inherit noise detection mechanisms originally developed for i..dd data, failing to explicitly model intrinsic dependencies between node features and structural context for effective noisy label detection.
2.2 Noise Robust Learning
Besides detecting noisy labels, another line of research focuses on developing robust training algo- rithms and models. Such methods include designing noise-resistant network architectures [17
robust loss functions [46), and regularization [34] 24). as well as training strategies [15] 20 40
In the context of Graph Neural Networks (GNNs), previous studies [3] g have demonstrated that label noise can propagate through the graph structure, significantly impairing the performance of GNNs. Several methods have mitigated this issue by refining graph structure. For instance, NRGNN (5] connects unlabeled nodes to trustworthy labeled neighbors to alleviate the effects of label noise, while RS-GNN 66] learns denoised graph structure reduce noise propagation. Other methods introduce auxiliary supervisory signals to strengthen robustness, including self-training and consistency regularization (28), information-theoreii objectives [49], and pairwise consistency modeling [8] Graph contrastive learning has also been leveraged, with representative methods including RNCGLN 50). ALEX + and CGNN 44l Label propagation approaches have likewise been explored: ERASE (2) integrates label propagation with coding rate minimization, while RºLP 4 applies propagation on reconstructed graphs to correct noisy labels. DND-NET 7 mitigates noise by decoupling message passing in GNNs.
Although these methods have improved the robustness of GNNs against noisy labels, their identifi- cation of mislabeled samples still predominantly relies on loss-based or confidence-based metrics. Different from existing approaches, propose graph learning framework that identifies noisy labels based on dual-view prediction discrepancy.
3 Preliminary
This work focuses on node classification under label noise. Consider graph G = (V,&), where V
denotes the set of nodes and & C V represents the set of edges. The graph 9 is assumed to be
undirected and without self-loops. Node features are represented by matrix X E R [Vlxd where [V] is the number of nodes and d is the feature dimension. Let Y [ denote the one-hot encoded ground-trune label matrix, and E RVC the one-hot encoded noisy label matrix, where C the number of classes. The adjacency matrix denoted by A R| where Aij = nodes v; and by are connected, and Ai 0 otherwise. The objective is to train Graph Neural Network
3

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Noise Detection
View-Specific Training
P
Clean Noisy
Le
Lm
Training set
Training set
Ego view
shared
GMM
Clean set
Clean set
P.
palla
9
Noisy set
Purified set
Pseudo- lebeling
Structure view
P,
5
Figure 2: Overview of the proposed framework GD², which consists of two core modules: noise detec- tion and view-specific training. In the noise detection module. the cross- view prediction discrepancy is quantified and modeled using a Gaussian Mixture Model (GMM) to identify label noise. For model training, pseudo-labels are assigned to confident noisy nodes refine supervision. The framework then jointly optimizes three view-specific objectives. The two modules are mutually reinforcing: the denoised training set improves model robustness, which turn sharpens the discrepancy for more effective noise detection.
(GNN) on the training set Viaan with noisy labels Y, such that accurate predictions can be made for the true labels Y the unlabeled nodes.
Graph Neural Networks (GNNs) typically follow a message- message-passing passing architecture, where node repre- sentations updated by aggregating information from neighboring nodes. At the E-th layer, the representation of node v is computed as:
h UPDATE (GG())
(GG ((h!-11) | IuE N()))))
(1)
where (w) denotes the of neighbors of node v, !G is the aggregation function, and (P is the update function. Initial representations are given by node features, i.e., (0) X, E Rdd For Graph Convolutional Networks (16), the representation matrix the f-th layer is updated as:
H o AD
where Á A + is the adjacency matrix with self-loops, I the identity matrix, D is the degree matrix of A, W(O the learnable weight matrix, and a denotes a non-linear activation function.
4 Method
This section details the proposed framework GD². A standard approach to learning under label noise typically involves two stages: first identifying mislabeled samples, and then training the model using the samples estimated to be clean. As illustrated in Figure 2 GD² follows this paradigm and consists of two core components: a noise detection module and a view-specific training module. In the noise detection module, cross-view prediction discrepancies are used to estimate the likelihood of label correctness via a Gaussian Mixture Model. In the training module, pseudo-labels are generated from mixed-view, and then distinct training objectives are designed for different views. The two components are trained in a mutually reinforcing manner: the detection module provides cleaner training set for the model, while the training process strengthens view discrepancies, further improving noise detection. The pscudo code of GD2 is presented in the Appendix
4.1 Noise Detection via Prediction Discrepancy
Identification of mislabeled nodes achieved by explicitly modeling prediction discrepancies between different views. The distinct views differ in information sources: the ego-view relies exclusively on intrinsic node features, whereas the structure-view aggregates neighborhood information. Node representations of the ego-view and structure-view. denoted Z. and Z,, respectively, first computed. Specifically, a Graph Convolutional Network (GCN)-based encoder fo with parameters is employed. Representations at the ε-th layer for the eio-view and senctture-viww denoted by H!!

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and ! are updated according to:
H 2 = ( ((())
H
AD HD
(3)
where ((e) denotes learnable weights at layer é, a represents non-linear activation function, A is the adjacency matrix without self-loops, and D is the corresponding degree matrix of A. The final representations for both views are:
Ze fo(,,I), Z, = Ax(
where X is the node feature matrix, I denotes the identity matrix.
To enhance the discrepancy between view-specific predictions and avoid mutual interference between the different training objectives (further discussed in Section 4.2.2), distinct linear classifiers are employed for each view. The ego-view prediction matrix P E RIViXC and the structure-view prediction P. RDVXCC are computed using classifiers 96, and 9o., respectively:
P. Uo1 (Ze),
P Io. (Z.).
The prediction discrepancy between the two views for node E Viain is quantified using the -o-orrm
6, 5
(6)
where p!d represents the prediction vector of node i.
To adapt flexibly across different graphs and noise scenarios, the discrepancy set D {d; Vusin is modeled using two-component Gaussian Mixture Model (GMM) via the Expectation- Maximization (EM) algorithm. Each discrepancy value ó, is mapped to posterior probability F Felean( 64), indicating the likelihood of belonging to the clean-label component with the smaller mean. threshold 5 then applied partition the training set into clean and noisy subsets:
V cleam
{i
IP Peleem (s 6;) > Virain)
V Vuoisy
Virain
Veleun
4.2
Model Training
4.2.1
Label Purification
After identifying nodes with noisy labels, pseudo-labels are generated to purify corrupted supervision. However, predictions obtained from either the ego-view or the structure-view exhibit inherent bias, as each is derived from a single source information. To mitigate this issue and improve pseudo-label reliability, a mixed-view representation is introduced. The mixed-view integrates node features with local structural context to provide more accurate semantic estimates. Formally, the mixed-view representation is computed as:
Z fxX,
where À denotes the adjacency matrix with added self-loops. Representations are updated following the standard GCN formulation [16] as described in Eq Mixed-view predictions are then obtained via the classifier !øz as Pm yo (Zm). To ensure pseudo-label quality, only high-confidence predictions are retained. Specifically, noisy nodes with prediction confidence exceeding predefined threshold yy are selected to construct the purified training set:
yuurffied = max
p! > 7, i E Vnnisy
For each node selected into V Ppriliedd the pseudo-label is determined by the class with the highest predicted probability:
l arg max Pld m E V Pariified
(10)
4.2.2 Training Objective
As training progresses, predictions from different views tend to overfit noisy labels, resulting in reduced discrepancy between views, especially for mislabeled nodes. The diminished discrepancy degrades the effectiveness of noise detection. To address this issue, view-specific training objectives introduced encourage distinct learning for each view. Specifically, the overall training objective
5

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comprises three loss terms corresponding to the ego-view, structure-view, and mixed-view each optimized on dedicated training nodes and labels.
First, the ego-view loss employs the original noisy labels Y supervise predictions over all training nodes Viriin allowing the model to closely capture potential label inconsistencies. Letting ((::)) denote the cross-entropy loss function, the ego-view loss is formulated as:
Le
E =EVam
L(P!) e Y
(11)
Varin
For the structure-view pseudo-labels Y generated from the mixed-view serve as the supervisory signals. The mixed-view integrates both node features and local structural context, producing more reliable pseudo-labels that mitigate the effect of noisy labels. Notably, nodes estimated to be mislabeled receive divergent supervision: the structure-view is trained with pseudo-labett while the ego-view relies on the original noisy labels. This asymmetry amplifies the prediction discrepancy between views, which in turn facilitates the identification of mislabeled nodes. The structure-view loss is defined as:
C. Vetean U Vpuritee
L(P! Y ELP
Σ L(P!) Y1 iEVansiee
(12)
VEVeeen
The mixed-viees view is trained using the original noisy labels Y, but restricted to the confidently identified clean nodes Velean This design aims to mitigate confirmation bias, which refers to the risk of reinforcing incorrect predictions when the model is trained unreliable pseudo-labels, The mixed- view loss is given by:
mm
Σ L(P! m )).
(13)
Velean
ie Vatn
Finally, these three losses are jointly optimized, resulting in the overall training objective:
L L. + La f.m-
(14)
During the evaluation stage, predictions P... from the mixed-viee employed the final classifi- cation outputs.
Theoretical Justification
To theoretically justify the of prediction discrepancy as an indicator of label noise, we analyze the deviation between ego-view and structure-viens representations in graph neural networks. We begin by introducing assumptions on graphs and then propose theorem that characterizes the probabilistic behavior of the discrepancy.
47 we consider a graph G. where each node has features x; E Rd and label yı. We assume that (1) The features of node i are sampled from feature distribution Fy. i.c., x; F (2) Dimensions of x; are independent to each other; (3) The features in X are bounded by positive scalar B, i.c., max,,j X[i,j] s B; (4) For node i, its neighbor's labels are independently sampled from neighbor distribution Dy,- The sampling is repeated for deg(i) times to sample the labels for deg(i) neighbors.
Assumptions on Graphs. Following previous works 22
We denote graph following these assumptions (1)-() Note that we use the subscripts in Fs, and D,,, to indicate that these two distributions are shared by all nodes with the same label node i. Define bhg == Ex-r,, [x] the expected feature of node given the ground-truth label yi. and define ,4 := Ee-D, v., x~FF. [x] the expected feature of neighbors. We analyze the embeddings obtained after a GCN operation. Following previous works 18
= {V,,, (F,, C), (D., e C)).
22
477. we drop the non- con-linearity in the analysis.
Theorem 1. Consider a graph = (V,E, (F., E C)2 (Do, E C}} that satisfies Assumptions (1)-4), For any node i E V, let h, = Wx; denote the pre-activation output of a single-layer GCN using only the node's 's own features (ego-view), where x; Fy. Let h, -W [Ma EJEN, X,) denote the corresponding structure-view representation that aggregates features from neighbors. Let

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Table I: Node classification accuracy (%, mean + std) noisy datasets. p denotes the noise rate for each setting. Best results are highlighted in bold, and second- best results are underlined.
Unifuem
Pair
Dataset
Method
2 0.2
p 0.4
p 0.6
p 0.2
p 0.3
p 0.4
GCN
85.33 + 0.45
82.68
+ 0.66
80.78 + 0.85
84.11 = 0.51
82.05 + 0.90
17.85 + 1.89
NRGNN
86.86
83.09
80.04
85.75
83.59
76.20
1.72
RTGNN
83,25
+ 1.14
82.44 + 1.63
79.94
+ 2.52
82.54 = 0.65
80.14 = 1.09
12.24 = 1.92
Computer
PI-GNN
83.25
+: 1.94
81.00 + 1,89
79.10
+: 2.24
81.42 - 2.41
79.81
1.03
75.80
2.89
TSS
86.87
2.14
83.62
1.73
82.11
1.02
83.80
1,78
82.56
1: 1.75
79.89
2.03
ERASE
86.77 + 0.93
84.84 + 0.83
83.41
+ 1.13
86.68
+ 0.75
84.60
+ 1.03
80.13 + 4.42
GD
86,91 +: 0.56
86.26
1: 0.71
84.76
+: 0.81
86.88
:: 0.55
85.75
0.64
83,16 1.75
GCN
90.10 0.72
86.38 1: 1.27
72.55
5.13
89.03 1: 0.49
87.26 1: 0.78
85.84 1: 2.21
NRGNN
89.29 +: 1,99
83.25 +: 5.20
69.64
+: 6.85
88.36 + 1.21
83,10
3.94
82.16 5.35
RTGNN
89.65 1: 1,10
87.35 1: 2.58
73.49
1: 3.38
91.66 1: 1,06
89.90 1: 1.89
87.03 6.18
Photo
PI-GNN
90.83 + 0.71
87.07 + 0.81
13.33 + 1.44
89.58 + 0.41
88.18 - 1.54
87.79 + 4.81
TSS
73.07
89.03
ERASE
91.86 + 0.47
88.00 + 0.53
75.10 + 1.57
91.41 = 0.75
87.67 + 1.47
85,59 - 2.33
GD?
92.45 + 1.30
89.72 + 0.98
74.32 + 5.85
92.83 + 1.10
91.84 + 1.00
89.00 + 1.23
GCN
91.51 1: 0.13
90.57 1 0.29
88.07 1. 0.72
91.07 1 0.27
88.54 1 0.46
80.67 2.12
NRGNN
92.07 + 0.50
91.40 + 0.46
89.37 + 1.23
89.50 - 0.14
86.44 - 1.10
75.51 + 6.00
93.23
91.91
8.44
CS
PI-GNN
92.40 0.18
91.68 + 0.34
89.57 + 0.88
91.17 = 0.76
89.75 - 0.93
82.68 5.65
TSS
89.80 - 0.52
87.23 + 1.04
82.13 1.71
87.70 + 0.94
84.69 - 2.01
75.83 + 7.20
ERASE
91.52 0.25
89.00 0.46
90.23
86.92 1.34
81.66 2.66
GD
93,43
33.43:00344 0.34
92.37 + 0.45
89.61 + 0.54
92.75 + 0,38
90.54 + 0.43
84.68 1.92
GCN
75.06
1.75
NRGNN
74.52 -
69.48 + 1.16
64.73 + 2.81
74,89 + 1.66
71.01 - 1.65
67.74 + 2.83
RIGNN
76.75 1: 0.57
75.46 + 0.70
72.35 4: 1.44
76.68 + 0.67
75.12 +: 1.93
71.56 3.47
WIKiCS
PL-GNN
74.11
1.66
71.48 1.33
69.85 +
65.05
63.40
59.28
8.92
TSS
78.23 + 0.28
77.39 + 0.66
69.9% +: 0.85
77.76 + 0.40
74.67 + 1.03
65.43 + 3.49
ERASB
79.85 + 0.62
77.27 = 0.66
74.08 + 0.76
78.86 0.52
74.43 1.52
69.74 4.07
GD2
0.36
78.21
74.47
75.88 1.68
GCN
64.65 1: 0.80
$7.86 1: 2.00
50.50 +: 1.02
66.78 +: 1.05
64.16 +: 1.04
58.34 + 2.62
NRGNN
61.85 +
59.53
49.60 1.36
62.41 0.68
60.55 0.69
53.71 1.39
RTGNN
64.85 + 0.47
60.13 + 0.98
$1.80 +: 1.31
62.28 + 0.71
$9.82 + 0.92
$1.61 + 1.68
Roman- Iiman-Fmpire
PI-GNN
63.64 = 0.48
57.49 - 1.51
47.74 2.15
62.45 0.99
57,87 1.32
50.06 1.81
TSS
58.29 + 0.35
54.18 + 0.66
47.66 + 1,10
66.35 + 0.48
63.60 + 0.52
58.52
1.04
ERASE
63.26 + 0.41
51.66 + 0.31
48.74 + 0.44
61.53 - 0.76
57,22 = 1.48
$1.81 = 2.27
66.19 + 0.69
60.26 + 0.80
51.24 1.68
68.25 + 1.01
66.22 - 0.86
62.16 1.14
GCN
36.82 0.65
35.85 + 2.16
34.95 +: 2.10
37.58 + 1.07
35.09 +: 3.06
32.99 + 2.12
NRGNN
37,90 0.26
37.05 = 0.84
35.33 1.06
37.15 1.32
36.98 0.62
36.52 0.85
RTGNN
36.65 0.01
36.62 : 0,04
34.59 -
36.59 + 0.12
34.58 + 3.64
30.87 = 3.39
Amazon-RR Amazon-Ratings
PI-GNN
37.22 0.42
35.10 0.80
33.17 2.25
36.60 - 0.49
33.35 - 1.42
31.98 - 2.73
TSS
39.56 0.55
34.73
39.65
38.99
1.46
ERASE
38.85 0.62
36.53 + 0.48
33.26 + 0.74
37.11 = 1.99
35.47 = 2.87
31.67
5.13
GD
39.80 + 0.73
37.58 + 1.10
35.72 + 1.04
39.97 = 0.55
38.76 + 0.74
38.28 = 0.90
d denote the feature dimensionality, and pl () denote the largest singular value of the weight matrix
W. Define the discrepancy between the views d; probability that o, exceeds l is bounded by
-lh h:ll2- Then, for any 0, the
deg(i) +1 2Bd
P(W) Il 1xxl12 ))
2();21) 2d22dex exp
exp
(15)
The proof provided in Appendix D Theorem shows that clean-label nodes inherently exhibit bounded representation discrepancies between the ego-view and structure-view. This behavior arises from the statistical alignment between node-specific features 14e and neighborhood semanties μ,, Furthermore, the bound strengthens with increasing node degree deg(?), implying that nodes with richer neighborhood contexts exhibit more stable discrepancy patterns. This explains the robustness of structure- -iwww representations under label noise, as neighborhood aggregation smooths out indi- vidual perturbations. In contrast, the ego-view representation a mislabeled node constructed independently of neighbor information and is therefore more susceptible to corrupted supervision. As a result, the representation deviates from the structure-view and violates the concentration behavior observed in clean-label cases.
7

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Table 2: Ablation of GD the Computer and Koman-Empire datasets under the Pair-0.4 noise.
Ablation
C.
L.
Separate classifier
Computer
Roman-Empire
GD"
Veen
Varan Pperitat
83.16 1.75
62.16 :: 1.14
GD² with du
d2
Vem
Vdeas U Vanifitt
81.89 + 1,76
60.87 + 2,52
GD w/o label purification
Vein
Veian
82.35 + 1.29
60.76 +: 1.70
Vean Vilen
Vean
81.13 +: 1.26
61.62 :: 1,48
GD² wio distinet objectives
Valen
82.69 1: 0.88
60.97 1. 2.75
Vilaa U Veuilied
Vieas U Vouiifed
82.35 +: 2.06
61.13 + 1.06
6 Experiments
6.1
Setup
Datasets and Settings. We conduct experiments on six benchmark datasets, including four ho- mophilous graphs: Computer, Photo, CS [29]. and WikiCS [25], and two heterophilous graphs: Noman-Empire and AmazonnRatinge (26]. Dataset statistics are provided in Appendix [ Following previous works [2 48), we randomly select 10% of the nodes for training. 10% for validation, and
use the remaining nodes for testing. All results are averaged over 10 runs with different random seeds, and we report both the mean and standard deviation.
Following prior studies S
28 g we synthetically corrupt labels of the training and validation
sets. We consider two types of label noise:
1) Uniform-p: Each label flipped to a randomly selected incorrect class with probability p.
2) Pair-p: Each label is flipped to a corresponding pair class with probability simulating realistic mislabeling patterns.
We set E {0.2, 0.4, 0.6] for uniform noise and p E {0.2, 0.4, for pair noise. More implemen- tation details, including model architectures and training configurations, provided in Appendix B
Baselines. We compare GD² with several representative methods designed for learning with noisy labels on graph data. The baselines include: (1) NRGNN (5), which refines the graph structure to alleviate the effects of label noise; (2) ERASE [2), which performs label denoising via label propagation; (3) RTGNN 28 and PI-GNN X which incorporate auxiliary supervision; and (4) TSS (39. which leverages graph topology for node selection under a curriculum learning framework. hyperparameters are tuned following the original publications. Additional comparisons with general noisy label learning methods are provided in Appendix C
6.2 Main Results
Table reports the node classification performance across diverse noise settings and datasets. As shown in the table, GD2 achieves the best or second-best performance across a wide range of datasets and noise settings. Compared to representative graph-specific methods such as NRGNN and ERASE. GD2 achieves substantial performance improvements, particularly under high noise rates. For example, on Computer, GD2 outperforms ERASE by more than 3.03% under pair-0.4 noise. These consistent improvements indicate that GD2 offers a general solution for robust node classification under label noise, delivering strong performance across diverse graphs and noise settings.
6.3 Ablation Study
Effect of separate classifiers. We begin by evaluating the necessity of using separate classifiers for ego-view and tirctture-veww representations. The variant GD2 with Φ1 <b employs shared classifier head for both views while keeping all other settings unchanged. As shown in Table 2 this modification results in a noticeable performance drop (-1.27% Computer and 11.9%% Coman-Emmiree, indicating that separate classifiers are crucial for preventing interference between views. The decoupled heads allow each view independently learn view-specific predictions and avoid mutual supervision contamination.
Effect of label purification. the variant GD2 w/o label purification, where E, is trained only on the clean set while the purified
To evaluate the effect of label purification, we compare GD2 with

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635
630
2625
pML2
pm066
62.5
510
(a) Computer, Uniform
(b) Computer, Pair
(c) Roman, Uniform
(d) Roman, Pair
Figure 3: Sensitivity of clean threshold т.
p-1L2
p-104
pMELS
42
price
0.6
0.3
9.6
0.5
0.8
0.2
3.6
0.5
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02
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0.
1.0
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0.0
1.0
(a) Computer, Uniform
(b) Computer, Pair
(c) Roman, Uniform
(d) Roman, Pair
Figure 4: Sensitivity of pseudo-label confidence threshold 7..
set is excluded. As reported in Table 2 this variant performs worse than GD confirming that label purification is beneficial not only for supervision but also for enhancing the prediction discrepancy signal. Although the purified set is not directly used for training the mix-view branch, plays an essential role in amplifying cross-view disagreement, thereby improving noise detection quality.
Effect of distinct training objectives. Finally, assess the impact of using distinct training objectives for the ego and structure views. The variant GD w/o distinct objectives uses the same training set for both L. and L.. with three configurations considered: (i) both views trained the full noisy set Virain. (ii) both are trained on the clean set Velean: and (iii) both are trained on the union of clean and purified nodes Velean puurifidd As shown in Table 2 all three variants exhibit performance degradation compared to GD2, with the largest drop reaching 2.03% Computer and 1.19% on Noman-Empire These results highlight the importance of assigning different supervision the views, which amplify prediction discrepancies among views.
6.4 Hyperparameter Sensitivity
Effect of clean threshold The clean threshold 7 determines the minimum agreement required between ego-view and structure-view predictions for a node to be considered clean. Figure shows the accuracy of GD2 varies from 0.1 to 0.9. Overall, increasing leads to gradual decline in performance, as stricter thresholds reduce the coverage clean samples. However, when 7 S 0.7, the degradation remains limited, suggesting that GD relatively robust moderate threshold choices. A sharp performance drop is observed at r 0.9, indicating that overly conservative filtering discards too much supervision and impairs learning. These results highlight the importance of avoiding excessively large thresholds, while also demonstrating stability under moderate settings.
Effect of pseudo-label confidence threshold ?. The pseudo-label confidence threshold yy controls the trade-off between the quantity and quality of pseudo-labels used in label purification. Figure reports the accuracy of GD as 7 varies from 0.0 to 1.0. As 7 increases, accuracy generally improves, suggesting that high-confidence pseudo-labels provide more reliable supervision and enhance model robustness. In the low-ry regime, performance exhibits greater variance and tends to degrade. In contrast, when y sufficiently large (e.g.. 7 2 0.9), accuracy becomes both higher and more stable, indicating that GD² is relatively insensitive to the threshold within the high-confidence range. Notably, setting 7 = 1.0, which disables pseudo-labeling entirely, results inferior performance compared to slightly relaxed thresholds (e.g., 7 = 0.9). This confirms that incorporating small number of highly confident pseudo-labels is more beneficial than discarding them altogether. These results highlight the importance of maintaining both precision and minimal coverage in the label purification process.

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7 Conclusion
In this paper, we propose novel graph learning framework GD2 to mitigate the detrimental effects of label noise in Graph Neural Networks (GNNs). Our key insight is leveraging the prediction discrep- ancy derived from two complementary views-the ego-view, capturing individual node semantics, and the structure-view, encoding neighborhood structural semanties. This discrepancy serves as an intrinsic signal for noisy-label detection. Furthermore, we introduce a view-specific training strategy that amplifies prediction discrepancies through differentiated supervision, enhancing the noise detection module. Extensive experiments across multiple real-world datasets under various noise conditions demonstrated that GD outperforms state-of-the-ut roise-robust GNN baselines. These results demonstrate the effectiveness modeling neichne dependencies for label noise detection and highlight the potential of graph-specific relational patterns in improving robustness. Fu- ture work includes extending this framework to dynamic and heterogeneous graphs, where structural variations and multiple relation types pose additional challenges for noise detection.
Acknowledgments and Disclosure of Funding
This work was supported in part by National Key R&D Program of China No. 2024YFBB705300, NSFC Grant 6223201 I, 62402315, and the Shanghai Science and Technology Innovation Action Plan Grant 24BC3201200.
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A Dataset Statistics
Table 3: Statistics of used graph datasets in this paper.
Dataset
# Nodes
Edges
# Classes
Features
Type
Computer
13,752
245,861
10
767
Homophily
Photo
7,650
119,081
8
745
Homophily
CS
18,333
81,894
15
6,805
Homophily
WikiCS 11,701
431,206
10
300
Homophily
Roman-Empire
22,662
32,927
18
300
Heterophily
Amazon-Ratings
24,492
93,050
5
300
Heterophily
B Implementation Details
The GNN encoder fe is implemented as Graph Convolutional Network (GCN) optionally equipped with residual connections, Batch Normalization, or Layer Normalization, depending on the specific dataset. The classifiers 96, and 9o, are implemented single-layer linear networks. We use the AdamW optimizer training. For graph data augmentations, we adopt a combination of random node feature masking and edge masking, where node features and edges are independently masked with probabilities py and Pe, respectively.
flyperparameters. select the hyperparameters through a grid search, with the search ranges detailed in Table All hyperparameters are tuned using validation sets. For baseline methods, hyperparameter tuning conducted within the ranges recommended their original publications.
Table 4: Search ranges for hyperparameters.
Hyperparameter
Search range
Traing epoch
500, 1000
Learning rate
0.001, 0.005, 0.01 64, 256, 512 1, 2, 3, 3,4,
Hidden dim
GNN Layers
Normalization
Batch Norm, Layer Norm True, False
Residual Connection
Dropout
0.2, 0.3, 0.5, 0.7
Feature masking prob.
0.0, 0.1, 0.2, 0.3, 0.4
Edge dropping prob.
0.0, 0.1, 0.2, 0.3, 0.4
Clean prob. threshold
0.1, 0.3, 0.5, 0.7, 0.9
Pseudo-label confidence threshold y
0.0, 0.5, 0.9, 0.95, 0.99, 1.0
Label Noise Generation Following prior work 8 30), label noise is simulated by corrupting
the ground-truth labels. The noise generation process is characterized using noise transition matrix Q E CCC where C denotes the number of classes. Each entry Qij Pr(gnoisy = j Strue i) represents the probability of true label being flipped noisy label j.
For Uniform-p noise, the transition matrix Q takes the following form:
C-1
Q
T-1
1
21

---

For Pair-p noise, typical transition matrix Q is defined as:
P
0
0
P
P
0
Q
1 1 P
P 1 p
p
0
Note that GD2 does not rely knowledge of the transition matrix the noise operate effectively.
We implement the proposed GD with PyTorch 2.4.0 and torch, geometric 2.6.1. All experiments are conducted on a Linux server with a NVIDIA GeForce RTX 4090 GPU with 24GB memory.
Infrastructures.
C Performance Comparison against General Noisy Label Learning Methods
We further compare GD² with representative general noisy label learning methods that originally designed for i.i.d. data rather than graph-structured data. The baselines include: (i) robust loss function approaches such SCE [31] and API. (21); (ii) small-loss based sample selection methods such as
Co-teaching [33 and JoCoR [3]; and (iii) confidence-basee sample selection and semi-supervised learning methods, exemplified by ProMix [II. These methods represent different paradigms of noise-robust learning and provide a complementary evaluation to validate the effectiveness of GD².
Table presents the comparison results. It can be observed that general noisy label learning methods, although effective on i.i.d. data, exhibit limited robustness when applied to graph- graph-structured data. In contrast, GD achieves consistently superior performance, demonstrating its effectiveness in addressing label noise by explicitly leveraging the structural information inherent in graphs. These results highlight the necessity of designing noise-robust methods tailored graph domains rather than directly transferring techniques developed for i.i.d. settings.
D Proof of Theorem
Proof. The expectation of h, is given by:
Elh.J E[ WE[x,] WMe
and the aggregated neighbor representation is:
h W
Σ
xy
EL
WM,
JEN;
Define the discrepancy:
8: h. h =
W
X
Σ X, JEN;
= =I
N
where we let:
=
Σ Xj.
W
JEN
By the sub-multppicaatiitty of matrix norms, we have:
5 < W||2 |lE.112 p(W) 11E.112-
Thus, for any / > 0,
P(8, 2 t) P
||5, 2
pl W)
22

---

Table 5: Node classification accuracy (%, mean + std) noisy datasets, p denotes the noise rate for each setting. Best results are highlighted in bold.
Uniform
Pair
Dataset
Method
p 0.2
p 0.4
p p= 0.6
p >= 0.2
p 0.3
p 0.4
SCE
86.15 = 1.80
84.41 = 0.92
79.91 + 2.10
86.05 + 0.36
83.57
+ 1.31
76.51 + 2.16
APL
78,80
77.91
76.90
74.95
Co-tesching
84.57 = 1.33
83.59 = 1.38
78.18 = 2.15
82.62 = 1.16
82.22 + 1.08
74.38 + 1.47
Computer
JeCoR
81,10 + 1.29
81.03 = 1.20
78.14 + 1.02
79.24 = 0.26
77.57 = 0.78
68.63 + 5.16
ProMix
84.66 1: 1.01
82.26
1 1.06
80.61
1: 1.52
81.60
1 0.75
80.11
1. 0.92
78.57 3.04
GD2
86.91 +: 0.56
86.26 = 0.71
84.76
:: 0.81
86.88 +: 0.55
85.75 +: 0.64
83.16 1: 1.75
SCE
91.20 + 0.64
88.86 = 0.93
73.54 +: 1.21
89.90 + 1.08
86.79 + 1.51
76.21 +: 3.54
APL
91.72 1: 1.05
89.73 1: 0.73
72.09
1: 2.05
89.80 1: 2.55
88.30 1: 1.11
83.05 1: 3.06
Co-tesching
85.60
77.11
61.98 +
86.43 +
84.67 +
78.78 +
Photo
JoCoR
88.69 = 3.36
83.33 = 4.87
68.32 = 4.67
83.30 = 3.62
81.41 = 2.96
74.49 + 2.42
ProMix
91.76 + 1.83
88.36 = 0.11
68.59 + 2.40
89.03 + 2.14
88.60 + 1.11
83.86 1: 2.39
GD2
92.45
89.72
74.32 +
92.83
91.84 + 1.00
89.00 + 1.23
SCE
92.12 = 0.29
91.25 = 0.39
88.22 + 1.38
90.10 + 0.66
87.23 + 1.53
75.89 + 2.60
APL
92.18
90.88
90.04
79.73
Co-teaching
91.66 = 0.37
90.52 = 0.48
86.38 + 1.96
90.17 = 0.89
87.26 = 0.80
73.81 + 6.66
CS
JeCoR
91.30 + 0.82
91.17 = 0.34
87.44 + 1.05
88.45 + 1.65
84.15 + 0.88
70.32 + 6.13
ProMix
92.56 1: 0.51
90.33 1: 0.59
88,91 1 1.26
90.98 1. 0.61
87.83 1. 1.13
77.31 1. 3.37
GD>
93.43 +: 0.34
92.37 - 0.45
89.61 + 0.54
92.75 + 0.38
90.54 :: 0.43
84,68 +: 1.92
SCE
72.21 = 0.63
70.68 = 0.47
61,89 + 1.94
71.22 + 0.70
68.90 + 0.85
60.48 +: 3.16
APL
71.61 1: 2.16
68.36 1: 2.84
60.82 1: 2.17
69.90 1: D.45
69.09 1: 0.73
63.21 1. 5.68
Co-teaching
76.15 -
71.69 =
60.65 +
74.45 +
71.53 -
62.23 4:
WikiCS
JoCoR
76.09 1: 1.70
74.84 1. 1.90
65.19 1: 4.33
73.50 1 0.79
68.79 1: 2.57
60.39 1 3.32
ProMix
73.74 ::: 2.29
72.52 = 2.81
68.69 +: 2.19
74.45 + 0.85
72.42 + 0.23
67.69 + 5.71
GD2
79.45
78.21
74.47 =
79.84 =
78.09 + 0.42
75.88 +
SCE
57.78 = 1.13
54.83 = 1.86
50.46 + 3.35
66.84 + 1.22
$4.14 + 0.60
$2.20 + 0.78
APL
50.67
$4.65
Co-teaching
53.92 = 0.43
52.16 = 0.46
48.53 + 0.82
61.59 + 0.63
59.13 + 0.57
$5.47 + 0.62
Roman- Emppre
JeCoR
59.52 - 0.71
55.25 = 0.75
50.41 + 1.05
66.91 + 0.22
$7.60 = 0.78
53.67 + 1.70
ProMix
53.51 1: 0.17
52.27 1 0.37
48,90 1. 0.83
61.68 1. 0.80
59.43 1. 0.88
55,50 1. 0.49
GD>
66.19 :: 0.69
60.26 = 0.80
51.24 + 1.68
68.25 + 1.01
66.22 :: 0.86
62.16 1 1.14
SCE
36.66 = 0.17
36.52 0.14
36,29 + 0.33
36.38 + 0.77
37,25 + 0.40
35.32 + 2.09
APL
38.28 1: 1.49
35.85 1 0.73
34.88 1 2.19
37.70 1 0.26
36.89 1 0.75
34.97 1 0.80
Co-teaching
38.86 -
36.12
35.02 +
38.63 + 1.64
37.71 -
35.87 +
Amazon-Ratings
JeCoR
38.15 1: 0.47
36.93
0.31
35.22 1 1.44
38.57 1 0.38
37.40 1 0.50
36.50 1 0.63
ProMix
38.55
- 1.10
37.08
1.54
35.38 + 1.74
38.89 + 1.49
37.54 + 0.84
35.33 + 1.84
GD2
39.80
37.58
1.10
35.72 = 1.04
39.97 =
38.76 -
38.28 -
We now bound ||2. First note that:
E E
E[x:]
E[xy] pe 14.-
[
We utilize Hoeffding's s inequality to bound the deviation each dimension of &, from its expectation. Let x;[k] denote the k-th coordinate of x, for k k= .,....dd. d. Then, for each fixed k. the set {x, [A] j E N())} consists of i.i.d. bounded random variables (by assumption), and by directly applying Hoeffding's 's inequality, have:
P [K E|E, 2 t1) = P
[K
1
Σ JEN
-
E
X
[K]
t1
M
JEN,
P.
(x,[M) [k]]
[[x+(A])>
Σ
E
Σ
x
24
[W
JEN;
JEN;
deg(i) + +1
< 2 eexp
2B2
(16)
We now use the following implication: if the d, norm of the deviation vector satisfies
|| E[E,l1, Vdt,.
23

---

then at least one coordinate k E {l..... d} must satisfy
[, Elg, [R]]] 2 4
Therefore, by the union bound over all d dimensions:
P [1E, B|silll2 2 vāti)
d
(15:11) - [E[E 2 t
(17)
(- deg(() +
S 2d exp
11
2B²
Now, set
we obtain the vector norm deviation bound:
va
P PIIE: [E( (2) s 2d exp (- deg(i) + 1
12
2B2d
By triangle inequality:
1| x 115. - FE + ||E(,,ll2 = |16. EES.]Il2 + lleee - 1ell2-
Hence,
PP [111112 pl (WW)
S I I1: E( ((W like Mollz)
long as p(W) like u.ll2 > Finally, we conclude:
deg(i) +1 1
(N(W)
111e 14a112 )
p(6; 2 1) 2d exp
2Bdd
((W)
E Pseudo-code
We describe the overall pipeline of GD2 in Algorithm
Limitation
One limitation of the current framework lies in its focus on static, homogeneous graphs. While the proposed discrepancy-basee noise detection mechanism demonstrates strong performance under these settings, its applicability to more complex graph structures remains unexplored. In particular, dynamic graphs introduce temporal evolution in both node features and structure patterns, which may obscure discrepancy signals introduce new sources of semantic drift. Similarly, heterogeneous graphs involve multiple node and edge types, where semantic alignment across views can be relation -laation-specfie and context-dependent. These additional layers of structural and semantic complexity pose significant challenges for robust noise detection. Future work will explore how to adapt the proposed framework to these more general graph scenarios, potentially incorporating temporal modeling techniques or discrepancy estimation to maintain effectiveness under such conditions.
24

---

Algorithm Pseudo code of GD2
Input: Node feature matrix X, adjacency matrix A, noisy labels Y, training sets Virain Parameter:
Training epochs E, clean probability threshold т, pseudo-label confidence threshold 7; GNN encoder fe. linear classifiers 9ø1: R0a
1: Initialize parameters 0, Φ1, 022
2: for epoch = E do
3: Noise Detection
4: Compute view-specific representations: Ze fo(X, 1), Z. AX
5:
Compute predictions: P. IΦ, (Ze), P - Iog (Z,)
6: Measure prediction discrepancy 6; |P -P! 1|,,
i Virain
7:
Fit GMM on { and compute clean probability IP IPelean (s (8,)
8:
Determine clean set Velean and noisy set Vnnisy using threshold T (Eq.
9:
// Label Purification
10:
Compute mixed-view prediction P.. = Iez (Jo(X
Construct Viuritted and assign pseudo-labels Y (Eq. 9 and Eq. (10)
12:
// Model Training
Compute loss terms Ces C., and Lm
14:
Joint optimization of total loss L = Le + L. + Lm Update model parameters 0, Φ1 and Φ2
16:
end for
Output: Trained encoder fo and classifiers Jo. 962
25


Reviews:
[{"review_id": "nfYNB3Jee2", "reviewer": "Reviewer_Kyqg", "summary": "The paper proposes GD2, a robust graph learning framework for noisy data. The model utilizes two distinct graph views, the ego-view and the neighbor-view, and their discrepancy, to filter out wrongly labeled data and relabel them during training to achieve robust training.", "questions": "See weaknesses.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The method is novel and is theoretically guaranteed.\n2. The empirical result is strong and gives good performance. \n3. The paper is clear in explaining the method. \n\nWeaknesses:\n\n1. It is unclear how the model can reliably distinguish clean vs noisy data at the beginning of training, when both ego- and neighbor-view predictions may be unstable. \n\n2. The experiments are conducted on a small number of benchmarks, lacking large-scale datasets [1].\n\n3. The method is only validated with GCNs; it is unknown whether the approach remains effective when applied to other widely used GNN architectures like GAT, GraphSAGE, or transformer-based models.\n\n4. The clean node threshold (τ) varies across datasets, but the paper does not offer a principled or simple strategy for choosing it automatically.\n\n[1] Lim, Derek, et al. \"Large scale learning on non-homophilous graphs: New benchmarks and strong simple methods.\" *Advances in neural information processing systems* 34 (2021): 20887-20902. datasets are too few", "was_revised": true, "final_justification": "The paper proposes GD2, a robust graph learning framework that uses dual graph views and their prediction discrepancy to filter noisy labels and progressively relabel them during training. The idea is novel, theoretically grounded, and empirically effective. The method is clearly described and supported by strong results on several benchmark datasets. However, there are a few drawbacks: first, while the rebuttal clarifies the bootstrapped nature of clean/noisy separation, the method still relies on potentially unstable early predictions. Additionally, although the evaluation is broader after the rebuttal, it remains limited in the diversity of graph types. The threshold parameter τ is shown to be moderately robust, but its selection still requires a clean validation set or heuristic tuning; an adaptive or automated mechanism would improve usability.", "rebuttal": "**Response to W1**\n\n*“It is unclear how the model can reliably distinguish clean vs noisy data at the beginning of training, when both ego- and neighbor-view predictions may be unstable.”*\n\nWe appreciate the reviewer’s concern. Our method is designed in a bootstrapped and iterative manner rather than relying on accurate clean/noisy separation at the initial stage. Specifically, as shown in the Pseudo-code in the Appendix E, GD2 updates the clean node set at every training epoch based on the discrepancy between dual-view predictions. This process allows the model to gradually refine its belief about clean samples as training progresses, leveraging the co-training-style evolution of ego-view and neighbor-view representations. Such a progressive filtering mechanism is common and effective in robust learning frameworks under uncertain supervision.\n\n**Response to W2**\n\n*“The experiments are conducted on a small number of benchmarks, lacking large-scale datasets.”*\n\nThank you for the suggestion. We have included additional experiments on the large-scale ogbn-arxiv dataset. Our method achieves consistent gains under both symmetric and asymmetric label noise settings, showing its scalability and effectiveness beyond the original benchmark datasets.\n\n|  | Uniform-0.2 | Uniform-0.4 | Pair-0.2 | Pair-0.4 |\n| --- | --- | --- | --- | --- |\n| GCN | 60.16±0.57 | 54.12±1.12 | 62.18±0.13 | 50.81±1.74 |\n| ERASE | 62.97±1.04 | 57.60±1.76 | 65.48±0.92 | 52.06±1.96 |\n| GD2 | 65.82±1.16 | 59.75±1.52 | 67.51±1.07 | 54.88±1.69 |\n\n**Response to W3**\n\n*“The method is only validated with GCNs; it is unknown whether the approach remains effective when applied to other widely used GNN architectures like GAT, GraphSAGE, or transformer-based models.”*\n\nThank you for pointing this out. We would like to clarify that GD2 is inherently architecture-agnostic and does not rely on the specifics of any GNN variant. In fact, message-passing GNNs—including GCN, GAT, GraphSAGE, and Transformer-based models—can be abstracted as consisting of two core steps:\n\n(1) Aggregation: gathering information from a node’s local neighbors or global context;\n\n(2) Update: combining the aggregated message with the node’s current embedding.\n\nOur dual-view construction leverages this decomposition:\n\n- The ego-view is computed by skipping the aggregation step, relying only on the node’s own features and performing the update step independently.\n- The structure-view is derived by removing the ego-node’s self-loop during aggregation (i.e., excluding its own embedding from the neighborhood), thus obtaining a purely structural context from neighbors.\n\nIn this way, GD2 defines two complementary perspectives via selective aggregation operations, which are supported in virtually all message-passing GNNs.\n\nTo demonstrate generalizability, we have included new experiments on Computer using GAT and SGFormer [1] as the backbone architecture (see Table below). GD2 consistently improves robustness on these architectures, confirming that our method is not confined to GCNs.\n\n|  | Uniform-0.2 | Uniform-0.4 | Pair-0.2 | Pair-0.4 |\n| --- | --- | --- | --- | --- |\n| GCN | 85.33±0.45 | 82.68±0.66 | 84.11±0.51 | 77.85±1.89 |\n| GD2-GCN | 86.91±0.56 | 86.26±0.71 | 86.88±0.55 | 83.16±1.75 |\n| GAT | 85.08±0.22 | 83.03±0.36 | 84.50±0.81 | 78.51±1.34 |\n| GD2-GAT | 86.69±0.68 | 85.94±0.40 | 86.95±0.82 | 83.91±1.50 |\n| SGFormer | 84.95±0.47 | 81.52±0.56 | 83.20±0.82 | 78.13±1.67 |\n| GD2-SGFormer | 87.21±0.93 | 85.51±0.86 | 87.04±0.19 | 82.83±1.10 |\n\n[1] SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations. NIPS’23\n\n**Response to W4**\n\n*“The clean node threshold ($\\tau$) varies across datasets, but the paper does not offer a principled or simple strategy for choosing it automatically.”*\n\nThank you for the valuable suggestion. The threshold $\\tau$ determines how strictly GD2 filters out noisy nodes based on the agreement between ego-view and structure-view predictions.\n\nAs shown in Figure 3, GD2 achieves stable and reliable performance when $\\tau≤0.7$, with only minor fluctuations. A noticeable performance drop occurs at $\\tau = 0.9$, where overly conservative filtering removes too much supervision. This indicates that the method is not overly sensitive to $\\tau$, as long as it is set within a moderate range.\n\nIn practice, $\\tau$ can be selected using a small clean validation set, by maximizing validation accuracy or minimizing disagreement with clean labels. Alternatively, this setting is closely related to pseudo-label filtering in semi-supervised learning, where model confidence is used to select high-quality training signals. A similar principle can be applied here: cross-view agreement serves as a proxy for prediction confidence, and $\\tau$ can be set to retain nodes with high agreement. This idea aligns with strategies used in recent works such as SoftMatch [1] and FreeMatch [2]. Inspired by these works, we believe designing adaptive or learnable thresholding mechanisms is a promising future direction.\n\n[1] SoftMatch: Addressing the Quantity-Quality Tradeoff in Semi-supervised Learning, ICLR’23\n\n[2] FreeMatch: Self-adaptive Thresholding for Semi-supervised Learning, ICLR’23"}, {"review_id": "97PHOObVxC", "reviewer": "Reviewer_nnqL", "summary": "In order to mitigate noises in the graph deep learning without i.i.d. node labels, the paper introduces a method to identify the nodes with nosy labels by measuring the distribution of ego-view representation and structure-view representation. The proposed framework then proposes pseudo-labels for the noisy nodes for accurate nose prediction. The paper also validates the method in theory. Finally, the authors evaluated the method on multiple datasets with different distributions and raios of noisy labels.", "questions": "1. Please clarify the narrative problems mentioned in the weakness part above.\n2. Please further conduct ablation study that only utilize the structure-view as clean representation for node label prediction in both training and inference.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper proposes a novel approach to identify nodes with noisy labels based on the distribution discrepancy between the ego-view and the structure-view.\n\n2. The paper conducted thorough experiments with both various noise ratio and noise distribution.\n\nWeakness:\n\n1. The paper should clarify how the interdependencies among connected nodes in graph affect the existing noise-agnostic works. To the best of my knowledge, NRGNN also took the neighborhood of nodes with similar labels into consideration and connected the labeled and unlabeled nodes for noise-agnostic learning.\n\n2. The notations of the papar should be reorganized. For example, ‘s’ is redefined as clean-label component in line 158 while it was the the footnote for structure-view in the notations above.\n\n3. The main assumption and theoretical justification for now seems not sound for me. First, take the experiment with p = 0.6 as an example. Emperically, for clean-labeld node with 60% noisy neighbors, I believe there would still be distribution discrepancy between the ego-view and the structure-view. In this way, it cannot be taken as an identification of nodes with noisy labels. Second, for the theoretical justification, I blieve the main suppose the authors should prove is that the the distribution discrepancy should exists and only exists in nodes with noisy labels. However in the proving procedure, the result only provides the upper bound of probability of distribution discrepancy, but does provide any direct correlation between the distribution discrepancy the whether the label of the node is noisy or not.\n\n4. Also, as the authors mention that “the structure-view captures topological patterns that remain relatively stable under noise”, why not directly utilize the structure-view as clean representation for node label prediction? \n\n5. The improvement on the results of the provided experiment seem marginal, with only less than 1% accuracy improvement. In this way, the proposed method seems not effective enough for handling the noisy labels of graph nodes.", "was_revised": true, "final_justification": "The authors addressed all my concerns.", "rebuttal": "**Response to W1**\n\n*“The paper should clarify how the interdependencies among connected nodes in graph affect the existing noise-agnostic works. To the best of my knowledge, NRGNN also took the neighborhood of nodes with similar labels into consideration and connected the labeled and unlabeled nodes for noise-agnostic learning.”*\n\nWe thank the reviewer for this helpful comment. Indeed, several prior works—such as NRGNN and related methods—have utilized local structural signals (e.g., neighborhood similarity, label propagation) to enhance robustness against noisy labels. These methods implicitly leverage interdependencies among connected nodes to smooth predictions or refine graph structure.\n\nHowever, our work differs in both purpose and formulation. Specifically, most prior approaches use interdependencies as an auxiliary tool to *mitigate* the effects of label noise—e.g., by refining edges, propagating softened labels, or enforcing similarity regularization. In contrast, our goal is to explicitly model the inconsistency between a node's own features and its structural context as a signal for detecting noise.\n\nTo this end, we construct two distinct views for each node: (1) the ego-view, reflecting prediction from a node’s own features;(2) the structure-view, reflecting prediction based on aggregated neighbors.\n\nThe cross-view discrepancy between them is not used to refine the graph or smooth labels, but to identify which nodes are likely to be mislabeled. This discrepancy serves as a dynamic and model-internal indicator during training, rather than a static preprocessing step.\n\nTherefore, while both our method and prior works acknowledge the importance of interdependencies, our contribution lies in recasting those dependencies as a core signal for noise detection itself, rather than treating them as a denoising aid.\n\n**Response to W2**\n\n*“The notations of the paper should be reorganized. For example, ‘s’ is redefined as clean-label component in line 158 while it was the footnote for structure-view in the notations above.”*\n\nThank you for pointing this out. We have carefully revised the notation and related equations to ensure that each symbol has a unique and consistent meaning throughout the paper.  All revisions will be reflected in the updated version of the paper.\n\n**Response to W3**\n\n*“The main assumption and theoretical justification for now seems not sound for me… The result only provides the upper bound of probability of distribution discrepancy, but does not provide any direct correlation between the discrepancy and label noise.”*\n\nThank you for the thoughtful critique. We believe there is a misunderstanding regarding the role of cross-view discrepancy in our framework. We clarify that our method does not rely on the binary presence or absence of discrepancy to determine whether a node is noisy. Instead, our assumption and algorithmic design are based on the distributional difference in discrepancy scores between clean-labeled and noisy-labeled nodes.\n\nConcretely, we compute a cross-view prediction discrepancy—the distance between the ego-view and structure-view predictions. Our key insight is that this discrepancy is statistically higher for noisy-labeled nodes, as their ego-view (aligned with an incorrect label) tends to disagree more with the structure-view (which captures the semantic context via neighbor aggregation). This discrepancy serves as a soft, probabilistic signal, which we then model using a Gaussian Mixture Model (GMM) to separate clean from noisy samples based on their distributional patterns.\n\nTo further illustrate this point intuitively, we provide a simple example demonstrating that even under high noise levels, nodes with incorrect labels tend to exhibit higher cross-view discrepancy. Consider a 3-class classification problem under uniform label noise with p = 0.6. Assume a node whose ground-truth class is 0, and 60% of its neighbors are truly class 0, while the remaining 40% are class 1. Due to label corruption, the observed neighbor label distribution becomes:44% class 0, 36% class 1, 20% class 2.\n\nFor the sake of simplicity and interpretability, we assume the ego-view prediction is a one-hot vector aligned with the given label, and the structure-view prediction is the distribution of observed neighbor labels.\n\nUnder these assumptions:\n\n- If the node's given label is correct (class 0), then the ego-view is $(1,0,0)$, and the structure-view is $(0.44,0.36,0.20)$, giving a discrepancy of: $||(1, 0, 0) - (0.44, 0.36, 0.20)|| \\approx 0.48.$\n- If the label is corrupted to class 1, the discrepancy becomes: $||(0, 1, 0) - (0.44, 0.36, 0.20)|| \\approx 0.64.$\n- If corrupted to class 2, the discrepancy is even larger: $||(0, 0, 1) - (0.44, 0.36, 0.20)|| \\approx 0.96.$\n\nThis example demonstrates that nodes with incorrect labels exhibit higher cross-view discrepancy, even when neighborhood noise is significant. The separation between clean and noisy nodes does not depend on the absolute value of discrepancy for any individual node, but rather on the relative distributional differences between clean and noisy groups—which the GMM is designed to exploit.\n\nRegarding the theoretical justification, we appreciate the reviewer’s concern. We clarify that the goal of our theoretical analysis is not to establish a necessary and sufficient condition that links cross-view discrepancy directly and exclusively to label correctness. Instead, the purpose is to demonstrate that, under mild assumptions, clean-labeled nodes tend to have bounded (i.e., low) cross-view discrepancy with high probability—providing a theoretical explanation for the observed distributional separability between clean and noisy samples.\n\nSpecifically, Theorem 1 in our paper derives an upper bound on the probability that a clean node exhibits high discrepancy, which formalizes the intuition that clean nodes are less likely to produce inconsistent ego- and structure-view predictions. We do not claim that noisy nodes are the *only* ones with large discrepancy, but rather that noisy nodes are more likely to lie in the high-discrepancy region, making the distributional signal exploitable for separation.\n\n**Response to W4 & Q2**\n\n*“As the authors mention that ‘the structure-view captures topological patterns that remain relatively stable under noise,’ why not directly utilize the structure-view as clean representation for node label prediction? Please further conduct ablation study that only utilize the structure-view as clean representation for node label prediction in both training and inference.”*\n\nThank you for the insightful question. While the structure-view captures topological patterns that are relatively stable under noise, using it alone would discard valuable node-specific information from the ego-view.\n\nOur final prediction model uses a mixed-view representation that combines both views, but is trained only on the filtered clean subset, where the impact of noisy labels is significantly reduced. In this setting, incorporating the ego-view adds complementary information with minimal noise interference.\n\nThe core idea of our method is to use the discrepancy between ego- and structure-view predictions to identify noisy labels. After filtering, combining both views leads to more expressive and robust representations.\n\nEmpirically, we show that structure-view alone performs worse than our mixed-view model, validating the benefit of using both.\n\n|  | Computer-Uniform-0.6 | Roman-Uniform-0.6 | Computer-Pair-0.4 | Roman-Pair-0.4 |\n| --- | --- | --- | --- | --- |\n| GD2 | 84.76±0.81 | 51.24±1.68 | 83.16±1.75 | 62.16±1.14 |\n| GD2-structure view only | 82.74±0.60 | 50.17±1.25 | 81.71±1.89 | 60.46±1.87 |\n\n**Response to W5**\n\n*“The improvement on the results of the provided experiment seem marginal, with only less than 1% accuracy improvement.”*\n\nWe respectfully disagree and would like to clarify. While some individual improvements appear small in absolute value, GD2 consistently ranks first or second across all datasets and noise settings, demonstrating strong overall robustness and competitiveness.\n\nNotably, under more challenging settings such as asymmetric pair-0.4 noise on Computer, GD2 surpasses ERASE by 3.03%, which is a substantial margin in the context of noisy node classification. Even in cases where the gains are smaller, the improvements are highly consistent and statistically stable across multiple runs, indicating better robustness and generalization.\n\nOverall, GD2 delivers reliable gains with minimal architectural complexity, validating the effectiveness of our discrepancy-based noise filtering approach."}, {"review_id": "9PYqloLH2S", "reviewer": "Reviewer_LmxF", "summary": "This paper introduces GD², a framework for addressing label noise in Graph Neural Networks for node classification. The core idea is to detect noisy labels by leveraging the prediction discrepancy between two distinct views of a node: an \"ego-view,\" constructed from the node's own features, and a \"structure-view,\" derived from the representations of its neighborhood. The framework is further enhanced by a view-specific training strategy, which uses a GMM to identify a set of clean nodes and then generates pseudo-labels for a subset of the noisy nodes. By feeding different supervisory signals (original noisy labels vs. purified pseudo-labels) to the different views, the framework amplifies the discrepancy signal.", "questions": "1.\tHow does the method perform on heterophily graphs where the assumption of neighbor similarity may be violated?\n2.\tWhat are the performance limitations of the framework under extremely high noise ratios?\n3.\tWhat is the computational complexity and runtime of the GD² framework?", "limitations": "The authors discuss the limitation that their work is restricted to static graphs.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1.\tThe paper tackles the problem of label noise, which is a significant challenge in real-world applications of GNNs. Developing methods that improve robustness is of high practical value.\n2.\tThe view-specific training strategy is clever: rather than passively observing the discrepancy between views, the framework proactively amplifies this signal. By feeding original noisy labels to the ego-view and purified labels to the structure-view, the method intentionally creates a larger divergence for mislabeled nodes.\n3.\tAs reported, the proposed GD² framework achieves state-of-the-art performance, outperforming several baselines across multiple datasets and under various noise settings.\n\nWeaknesses \n1.\tThe method's core premise is that a discrepancy between the ego-view and structure-view indicates a noisy label, which is based on the homophily assumption. In Heterophily graphs, where connected nodes are often of different classes, this assumption may be violated. For example, for fraudulent and legitimate users, a correctly labeled node in such a graph could be misidentified as noisy. More discussion on how the framework adapts to Heterophily graphs should be included.\n2.\tThe paper should further discuss the framework's limitations under extremely high noise ratios (e.g., p > 0.5). At such levels, the neighborhood information becomes unreliable, and the GMM may struggle to find a clean separation between the clean and noisy nodes. The experimental results also suggest that the method’s performance advantage over baselines may diminish under high-noise regimes.\n3.\tThe GD² framework is complex. Each epoch involves computing three distinct views, calculating discrepancies for all training nodes, fitting a GMM, and optimizing three separate loss functions. This introduces significant computational and time overhead. The authors should include an analysis of the computational complexity and runtime costs.", "was_revised": true, "final_justification": "The authors responses have addressed my concerns. Hence I have updated my confidence.", "rebuttal": "**Response to W1 & Q1**\n\n*“The method's core premise is that a discrepancy between the ego-view and structure-view indicates a noisy label, which is based on the homophily assumption. In heterophily graphs, where connected nodes are often of different classes, this assumption may be violated…”*\n\nWe thank the reviewer for highlighting this important concern. We clarify that our method does not rely on the homophily assumption (i.e., neighbors sharing the same label). Instead, the dual-view design in GD2 distinguishes information sources rather than relying on node similarity:\n\n- The ego-view captures the prediction from a node’s own features.\n- The structure-view aggregates signals from neighbors and reflects the class pattern implied by the neighborhood distribution—not necessarily the classes of neighbors.\n\nThis distinction is especially important in heterophilous graphs, where neighbors tend to belong to different classes. Prior works [1,2,3] have shown that nodes from the same class often share similar neighborhood patterns, even under heterophily. Thus, we expect that for a node with a clean label, its ego- and structure-view predictions should still be semantically aligned—i.e., they should agree on the class, despite structural label diversity.\n\nTo empirically verify this, we have conducted experiments on two heterophilous graphs (Roman-empirical and Amazon-ratings). As shown in Table 1, GD2 consistently outperforms baselines under label noise, even when neighbor-label similarity is low. This indicates the robustness of our discrepancy-based framework without relying on homophily.\n\n[1] Simple and Asymmetric Graph Contrastive Learning without Augmentations, NeurIPS 2023\n\n[2] Is Homophily a Necessity for Graph Neural Networks?, ICLR 2022\n\n[3] Decoupled Self-supervised Learning for Graphs, NeurIPS 2022\n\n**Response to W2 & Q2**\n\n*“The paper should further discuss the framework's limitations under extremely high noise ratios (e.g., p > 0.5)...”*\n\nThank you for raising this important point. We agree that when the noise ratio becomes extremely high, label supervision becomes less reliable, and the risk of polluted structural information increases. Nonetheless, we would like to clarify two key aspects of our method that preserve its effectiveness in such settings.\n\nFirst, our approach is based on a realistic and widely accepted assumption in noisy-label learning: within each true class, the number of correctly labeled nodes is greater than the number of nodes mislabeled into any single incorrect class. That is, although noisy labels exist globally, for any given ground-truth class, its clean samples are still the most concentrated compared to any other individual class. This class-wise imbalance ensures that the structure-view can retain useful semantic signals, even under significant noise.\n\nSecond, our method distinguishes clean and noisy labels based on the relative magnitude of cross-view prediction discrepancy, not on the binary presence of discrepancy. Importantly, this separation remains valid even when the neighborhood contains many noisy nodes.\n\nTo illustrate this, consider a 3-class classification task under uniform noise with p=0.6. Assume a node whose ground-truth class is 0, and 60% of its neighbors are truly class 0, while the remaining 40% are class 1. After label corruption, the observed neighbor label distribution becomes: 44% class 0, 36% class 1, 20% class 2.\n\nAssuming the ego-view predicts the given label (one-hot), and the structure-view reflects the noisy neighbor label distribution, we have:\n\n- If the node's given label is correct (class 0), then the ego-view is $(1,0,0)$, and the structure-view is $(0.44,0.36,0.20)$, giving a discrepancy of: $||(1, 0, 0) - (0.44, 0.36, 0.20)|| \\approx 0.48.$\n- If the label is corrupted to class 1, the discrepancy becomes: $||(0, 1, 0) - (0.44, 0.36, 0.20)|| \\approx 0.64.$\n- If corrupted to class 2, the discrepancy is even larger: $||(0, 0, 1) - (0.44, 0.36, 0.20)|| \\approx 0.96.$\n\nThis example demonstrates that even with p=0.6, noisy-labeled nodes consistently yield higher discrepancy scores, enabling effective separation by GMM.\n\nFinally, while our performance margins over baselines narrow under extreme noise, GD2 still consistently ranks among the top-performing methods, as shown in Table 1. This reflects a fundamental challenge shared by most robust GNNs, rather than a weakness specific to our design.\n\n**Response to W3 & Q3**\n\n*“The GD² framework is complex... The authors should include an analysis of the computational complexity and runtime costs.”*\n\nWe thank the reviewer for the suggestion. While GD² introduces dual-view inference, discrepancy modeling, and multi-view optimization, its overall computational cost remains moderate and scales linearly with graph size. We provide a detailed breakdown below, based on Algorithm 1.\n\n1. **View-specific representation (Line 4):**\n    \n    Each epoch involves two GCN forward passes: one with identity matrix $I$ (ego-view), and one with adjacency $A$ (structure-view). For $L$ layers, input feature dimension $F$, and $N=∣V∣$ nodes, the total cost is: $O\\big(2L(|E|F + NF^2)\\big)$\n    \n2. **Prediction and discrepancy (Lines 5–6):**\n    \n    Two linear classifiers produce logits in $O(NFC)$. Then, computing the $\\ell_2$ discrepancy for each training node costs $O(NC)$.\n    \n3. **GMM fitting (Line 7):**\n    \n    The discrepancy values are 1D scalars; fitting a 2-component GMM via EM costs only $O(N)$.\n    \n4. **Mixed-view inference and pseudo-labeling (Lines 10–11):**\n    \n    One additional GCN forward pass adds $O(L(|E|F + NF^2))$. Pseudo-label assignment costs at most $O(NC)$.\n    \n5. **Loss computation and update (Lines 13–15):**\n    \n    Three view-specific cross-entropy losses are computed over subsets of nodes, costing $O(NC)$, followed by standard backpropagation with cost similar to one GCN pass.\n    \n\nIn total, each epoch has complexity: $O\\big(3L(|E|F + NF^2) + NFC\\big)$.  Compared to a standard GCN with per-epoch cost $O(L(|E|F + NF^2) + NFC)$, GD2 introduces roughly 2–3× overhead due to three view-specific passes and auxiliary steps such as GMM fitting and pseudo-labeling. However, these extra components scale linearly with node count an remain lightweight in practice.\n\nTo further demonstrate practical efficiency, we report the total training time (in seconds) of GD2 against representative baselines across datasets in the table below.\n\n| Dataset | CE | ERASE | TSS | GD² |\n| --- | --- | --- | --- | --- |\n| Computer | 54.1 | 215.1 | 92.8 | 202.3 |\n| WikiCS | 30.5 | 152.5 | 55.8 | 160.3 |\n\nWe observe that GD2 has comparable runtime to ERASE, another strong noise-robust baseline, and is slower than TSS. However, GD2 significantly outperforms TSS, offering a favorable trade-off between robustness and efficiency."}, {"review_id": "jwpJmsYdQa", "reviewer": "Reviewer_aLSG", "summary": "Authors present GD2, which is a GNN training framework for node classification designed to be robust against mislabeled nodes. It uses a Gaussian Mixture Model to identify noisy samples by looking at discrepancies between individual node features and the aggregated features around the nodes. They call disagreements between these two \"views\" as the dual-view prediction discrepancy. Authors show experimental results across six datasets, and generally show improvements over existing baselines.", "questions": "Though the authors run experiments on two heterophilic graphs, I struggle to understand why GD2 would work well here. Wouldn't the model expect different labels between any ego node and its structural neighborhood?\n\nThere is quite some sensitivity to tau selection. Optimal value will also depend on the dataset. Is there some adaptive selection technique authors would recommend that might be useful on top of grid search?\n\nHow would GD2 perform when there is class imbalance? Presumably the GMM learns noise due to a healthy distribution of labels. Would it incorrectly think minority class samples are noisy?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths: the dual-view mechanism seems intuitive, and grounded in (some) theory. The experiments are well-designed, using different levels of noise to simulate mislabeled nodes, then checking to see how different models react. Some decent ablations as well to help readers understand the importance of individual components in GD2. Overall, the implementation doesn't seem too heavyweight to apply to existing GNNs as well.\n\nWeaknesses: my main reservation with this paper is that discrepancies in labels between the two views could be an outcome of heterophily in the graph. I would like to see more discussion and/or theory behind the specific gains on heterophilic graphs. Perhaps this ties in with the heterogeneous graphs, which the authors have acknowledged as one limitation. Lastly, performance gains are minor, albeit consistent. Usually <~5% relative performance gain.", "was_revised": true, "final_justification": "I was generally impressed with the paper to begin with, and would have liked to see stronger results before advocating for a 5 score. But metrics are mostly marginal, so I'd like to keep the score as a 4.", "rebuttal": "**Response to Q1**\n\n*“My main reservation with this paper is that discrepancies in labels between the two views could be an outcome of heterophily in the graph, rather than label noise... Wouldn't the model expect different labels between any ego node and its structural neighborhood?”*\n\nWe appreciate the reviewer’s thoughtful concern. We would like to clarify that our method does not rely on the homophily assumption, and is in fact designed to function under both homophilous and heterophilous graphs.\n\nThe core idea of GD2 is to compare the semantic consistency between two information sources:\n\n- The ego-view reflects the class implied by the node’s own features.\n- The structure-view reflects the class pattern inferred from its neighbors via GNN aggregation—not the actual neighbor labels themselves.\n\nEven in heterophilous graphs, nodes of the same class often share similar neighborhood distributions, even if their neighbors belong to different classes. This observation underpins many heterophily-aware GNNs and is supported by prior works [1,2,3]. Therefore, a clean-labeled node should still exhibit alignment between its ego- and structure-view predictions, while noisy nodes often show disagreement across views due to contradictory evidence.\n\nImportantly, GD2 does not penalize cross-view label disagreement per se. Instead, we use the magnitude of the prediction discrepancy as a soft indicator of semantic inconsistency. This formulation allows us to remain effective even when structural labels differ from the ego node’s label—as is typical in heterophilous graphs.\n\nTo empirically verify this, we include results on two heterophilous benchmarks: Roman-Empirical and Amazon-Ratings. As shown in Table 1, GD2 achieves consistent improvements over baselines under various noise settings, confirming that our method is robust to heterophily.\n\n[1] Simple and Asymmetric Graph Contrastive Learning without Augmentations, NeurIPS 2023\n\n[2] Is Homophily a Necessity for Graph Neural Networks?, ICLR 2022\n\n[3] Decoupled Self-supervised Learning for Graphs, NeurIPS 2022\n\n**Response to Q2**\n\n*“There is quite some sensitivity to tau selection. Optimal value will also depend on the dataset. Is there some adaptive selection technique authors would recommend that might be useful on top of grid search?”*\n\nThank you for the insightful question. We would like to clarify that GD2 exhibits stable and reliable performance when $\\tau \\leq 0.7$, with only minor fluctuations. A clear performance drop is observed only at $\\tau = 0.9$, where overly aggressive filtering removes too much supervision. These results indicate that the method is not overly sensitive to $\\tau$ as long as it is chosen within a reasonable range.\n\nTo go beyond grid search, we recommend selecting $\\tau$ using a small clean validation set, by maximizing validation accuracy or minimizing label disagreement. Additionally, this setting is closely related to pseudo-label filtering in semi-supervised learning, where model confidence is used to select reliable training samples. A similar principle can be applied here: the cross-view agreement serves as a proxy for prediction confidence, and $\\tau$ can be interpreted as a confidence threshold. This aligns with recent techniques such as SoftMatch [1] and FreeMatch [2], which dynamically select samples based on confidence-aware criteria. Inspired by these works, we believe designing adaptive or learnable thresholding mechanisms is a promising future direction.\n\n[1] SoftMatch: Addressing the Quantity-Quality Tradeoff in Semi-supervised Learning, ICLR’23\n\n[2] FreeMatch: Self-adaptive Thresholding for Semi-supervised Learning, ICLR’23\n\n**Response to Q3**\n\n*“How would GD² perform when there is class imbalance? Presumably the GMM learns noise due to a healthy distribution of labels. Would it incorrectly think minority class samples are noisy?”*\n\nWe thank the reviewer for raising this important question. We clarify that GD2 does not assume any balanced label distribution, and its noise detection mechanism is inherently class-agnostic. Specifically, the GMM is fitted over cross-view prediction discrepancy scores, which measure disagreement between ego- and structure-view predictions, rather than over class frequencies or node labels.\n\nThis design ensures that the model focuses on semantic inconsistency rather than minority status. A node from a minority class is not more likely to be marked as noisy unless its two views yield inconsistent predictions.\n\nMoreover, we note that the datasets used in our experiments—such as Computers, Photo, and WikiCS—are naturally imbalanced. The table below shows the number of samples per class in three datasets(for brevity, we display only a subset of classes):\n\n| Class | Computer | Photo | WikiCS |\n| --- | --- | --- | --- |\n| 0 | 436 | 369 | 295 |\n| 1 | 2,142 | 1,686 | 667 |\n| 2 | 1,414 | 703 | 2,153 |\n| 3 | 542 | 915 | 1,933 |\n| 4 | 5,158 | 882 | 2,679 |"}]

Author rebuttal:

Meta-review: This paper introduces a robust graph learning framework for noisy data, which measures the distribution of ego-view representation and structure-view representation. The reviewers pointed out the novelty of the proposed method and thorough experiments with both various noise ratios and noise distributions. The paper is also well-written with strong theoretical justification. 

The reviewers also pointed out some concerns, including a lack of clarification on how the interdependencies among connected nodes in the graph affect the existing noise-agnostic works, and the core premise. The authors provide extensive discussion to clarify these concerns and all the reviewers gave positive scores. I lean towards the acceptance of the papers and hope the rebuttal content can be well included in the camera-ready version.
Decision: Accept (poster)