Learn Beneficial Noise as Graph Augmentation
Authors: Siqi Huang
Yanchen Xu
Hongyuan Zhang
Xuelong Li
Venue: ICML 2025 poster (2025)
Keywords: Beneficial Noise; Graph Augmentation
Primary area: deep_learning->graph_neural_networks

Abstract: Although graph contrastive learning (GCL) has been widely investigated,  it is still a challenge to generate effective and stable graph augmentations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose **P**ositive-**i**ncentive **N**oise driven **G**raph **D**ata **A**ugmentation (PiNGDA), where positive-incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design a Gaussian auxiliary variable to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation.  Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through a trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topology and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.

Learn Beneficial Noise as Graph Augmentation
Siqi Huang 12
Yanchen Xu" 12 Hongyuan Zhang Xuelong Li²
Abstract
efforts on how to extend CL graph, which is known as Graph Contrastive Learning (GCL) (Veličković et al., 2018; Zhu et al., 2021; Peng et al., 2020; Gao et al., 2021b; Rong et al., 2020). Compared with traditional contrastive learn- ing methods, GCL. considers not only how to contrast data points but also how to generate augmentation by leveraging the topological structure (Hassani Khasahmadi, 2020; Zhu al., 2021), local features (Veličković et al., 2018; Peng al., 2020), and global context of graphs (Sun et al., 2020).
Although graph contrastive learning (GCL) has been widely investigated, it is still a challenge to generate effective and stable graph augmen- tations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose Positive-incentiv Noise driven Graph Data Augmentation (PiNGDA), where positive- incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design Gaussian auxiliary vari- able to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to esti- mate the beneficial noise via the point estimation. Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topol- ogy and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.
Despite the progress in GCL methods, graph data augmenta- tion remains a key challenge, which is substantially different from visual data. Unlike the reliable and stable visual aug- mentations (e.g.. cropping, flipping, translation) that play the core roles in visual contrastive models (He et al., 2020; Chen et al., 2020), graph topology is more complex with Non-Fuclidean structure. It results in difficulties of defining efficient and stable augmentation to retain crucial topologi- cal properties.
In early GCL models, typical graph augmentations included random modifications to edges and nodes. For example, random edge dropping (Gao al., 2021b; Rong et al., 2020) stochastically removes portion of edges, while random node dropping (Feng et al., 2020) removes nodes and their links from the graph. Such random methods increase di- versity but may disrupt inherent graph structure. More recent works propose adaptive augmentation techniques. GCA (Zhu et al., 2021) sets the probability of dropping an edge based on centrality measures of the involved nodes, aiming to better preserve graph connectivity. NCLA (Shen et al., 2023) learns adaptive graph augmentations and em- beddings using multi-head graph attention mechanism and a neighbor contrastive loss. Although providing more flex- ibility than completely random schemes, these predefined augmentation rules can still be considered as a priori as- sumptions. The heuristic methods usually lead instability, since the perturbations may introduce severe topological noise and hinder GCL pre-training and downstream tasks.
1. Introduction
With the development of Contrastive Learning (CL) in com- puter vision (Chen et al., 2020; He et al., 2020; Bachman et al., 2019; Falcon & Cho, 2020), natural language process- ing (Gao et al., 2021a; Yan et al.), and other fields(Radford et al., 2021), more and more researchers have paid great
'Equal contribution 'School of Artificial Intelligence, OPtics and ElectroNies (iOPEN), Northwestern Polytechnical University Insttitute of Artificial Intelligence (TeleAI), China Telecom 'The University of Hong Kong. Correspondence to: Hongyuan Zhang <hyzhang98@ gmail.com>, Xuelong Li <xuelong ore..
To address the challenges by learning effective graph aug- mentations, some works have explored learning-basee ap- proaches. JOAO (You et al., 2021b) proposes a optimization framework to automatically select data augmentation meth- ods for each sample. It treats augmentation selection as
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Learn Beneficial Noise as Graph Augmentation
hyperparameter optimization problem to improve GCL. Similarly, Suresh et al. proposes adversarial-GCI. (AD- GCL) (Suresh et al., 2021b), which optimizes adversarial graph augmentation in GCL to prevent redundant informa- tion capture. It designs a practical instantiation based on trainable edge-dropping graph augmentation. These meth- ods either select from predefined operations or focus on specific structural perturbations like edge modifications.
2. Related Work
2.1. Graph Contrastive Learning
Recent advancements in graph contrastive learning meth- ods (Grover & Leskovec, 2016; Hamilton et al., 2017b; Perozzi et al., 2014; Hassani & Khasahhadi, 2020) have introduced variety of data augmentation strategies, such as node dropping (You et al., 2020), edge perturbation (Zhu et al., 2020), and feature masking (Zhu et al., 2021). While effective in creating diverse graph views, these traditional techniques struggle with the inherent complexity of graph topology. Recognizing these limitations, more adaptive ap- proaches have been developed to better reflect the intrinsic properties of graph data. One notable example is GCA (Zhu et al., 2021). which proposes augmentation method that adapts both topological and semantic aspects of the graph. Recent innovations such as JOAO (You et al., 2021b) and AD-GCL (Suresh et al., 2021b) have been developed to ad- dress these challenges through more sophisticated strategies. JOAO employs an augmentation-awan aware projection head that dynamically selects augmentations during training. AD- GCL adopts adversarial approach where the model learns to optimize edge-dropping strategies in real-time, allow- ing it to adaptively modify the graph structure to enhance generalization and robustness in learned representations.
In summary, the existing learning- baaning-based graph augmenta- tions introduce topological noise to graph. In this paper, we seek a more explainable approach and focus on how to directly control the beneficial noise with a theoretical framework, i.e. Positive-ings innentiiveeeeee Noise (Pi-Noise or x- noise) (L.i, 2022) framework. --noise is defined as the beneficial noise that reduces the task complexity. We design the Pi-Noise driven Graph Data Augmentation (PiNGDA). Owing to the theory about noise, the noisy graph augmenta- tions can be easily applied to both topology and attributes. Note that the augmentations on node attributes are mainly heuristic methods, such as random permutation (Hassani & Khasahmadi, 2020) and random mask (Zhu et al., 2021). Roughly speaking. PiNGDA utilizes learnable noise genera- tors to produce beneficial noise perturbations. The contribu- tions are listed follows:
We design a Gaussian auxiliary variable related to the GCL training loss to quantify the GCL complexity, which bridges the r-noise framework and GCL. It shows us that the predefined augmentation just a point estimation of noisse, which provides a novel perspective of GCL (Section 3.3).
2.2. Methods of Learning Graph Structure
Except for GCL, graph structure learning aims at modify- ing the structure of a graph to achieve specific goals (Hu et al., 2019; Veličković et al., 2017: Kipf & Welling, 2016; Xu et al., 2018; Wu et al., 2019; Hamilton et al., 2017a). While these methods differ from the heuristic approach of edge dropping, they are still important research direction. For example, a neural network-based method (Zheng et al., 2020) automatically selects the most important nodes and edges to obtain a more compact and robust graph repre- sentation. VIB-GSL (Sun et al., 2022) employs variational inference to learn the structure of graph by maximizing the information bottleneck of its representation. In sum- mary, these methods typically require supervised informa- tion when modifying the graph structure, which differs from the unsupervised nature of GCL.
The theoretical analysis directly reveals a significant drawback of the standard GCL models. The predefined augmentations that are widely used in GCL may fail to serve as strong point estimations of x-noise. In other words, they are too unreliable to be regarded as strong priori like augmentations of vision data. We therefore propose PiNGDA to exactly minimize the π noise principle. PiNGDA leverages a m-noise generator to learn beneficial noise for topology and attributes as augmentations (Section 3.3).
2.3. The Positive Impact of Noise
Noise may not always be harmful as it has been demon- strated that random noise helps improving performance, e.g., random forest (Breiman, 2001), Dropout (Srivastava et al., 2014), noisy augmentations in contrastive learning (Verma et al., 2021; Chen et al., 2020). Verma et al. (Verma et al., 2021) proposed a method that introduces noise in the form of diverse transformations to improve contrastive learning across different domains. The paper (Lin et al.,
To ensure the differentiability of noise generation, we develop an efficient differentiable algorithm (Section 4).
By learning the noise generative model, PiNGDA im- proves GCL performance and stability compared to baselines from the extensive experiments (Section 5).
2

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Learn Beneficial Noise Graph Augmentation
Noisy node attributes
GNN
Projection
Encoder
Head
min LPINGDA
Dropping from Eu
Sharing
Sharing
p
Augmentation
generator
Distribution learning
Node attributes
GNN Encoder
Projection Head
Concat
edge feature
This figure illustrates the PÍNGDA framework, which consists of T-noise generator and contrastive learning module. The core innovation lies in its joint noise generator, which consists of two synergistic components: a topological generator for perturbing graph structures and an attribute generator for perturbing node features. contrastive loss function applied between original and noise graph representations. By jointly training the generator and encoder, PiNGDA dynamically learns optimal perturbation patterns tailored to downstream tasks.
Figure 1:
2023) proposes CNN-based hydroacoustic signal recog- nition method for ship noise classification. VPN (Zhang et al., 2023) shows that certain types of noise can benefit model. Similarly, other methods (Zhang et al., 2024; Huang et al., 2025) extended this insight to contrastive learning and vision-language alignment, respectively. EPAGCL (Xu al., 2025) demonstrates that introducing structurally effec- tive noise into graph structures enhance representation quality. In this paper, we follow the definition in (Li, 2022). Formally, the noise E, where & represents the noise set is defined as the i n-nsi if it satisfies
contrastive element is the node for simplicity, while it is straightforward to extend the analysis to graph-level GCL models as well as hybrid models, which uses both graphs and nodes for contrast. Although we only discuss the node-level GCL in Section 3 and 4, we also report the experimental results of graph tasks in Section In the succeeding sections, a graph g (V,S) consists of node set and edge set S. 0 denotes the optimal solution minimizing the loss L(V; where O represents parameters.
3.1. General Formulation of GCL
E(T,E) > + H(T)* > H)
(1)
Before the formal analysis, on given graph G (V, formulate the base GCL based on InfoNCE (van den Oord et al., 2018) as
(TT) represents the information entropy of task T and .(..)) denotes the mutual information. It informs us that the additional components should reduce task uncertainty HT) after introducing noise. From this perspective, can find that the predefined augmentations, widely used in existing GCL, may not reduce the task entropy. In this paper, we start from the above framework to learn the noisy graph augmentation with theoretical guarantee.
Epos (u: 0) epoe (w; 0) + Eneg (u: 0)
LInfONCE
Σ log WEV
|V]
pos (u; 0) and Eneg(us, 0) represent the positive and nega- tive loss associated with node u parameterized by 0, respec- tively. [V is the node number. Note that there usually temperature hyper-parameter T in Épos and Eneg. Since aim at learning π -NNoie for a specific GCL model (i.e., fixed T). we assume that a GCL model is given with fixed T and the hyperparameter T is therefore omitted.
3. -oose Driven Graph Data Augmentation
In this section, focus how apply -Nooie to GCL. As mentioned previously, it is imperative to mathematically quantif'y the difficulty of the target task T. Roughly speak- ing, we design an auxiliary Gaussian variable based on the GCL training loss and compute its information entropy to quantify the complexity of task T. We assume that the
simplify the analysis, the contrastive loss can sepa- rated into multiple node-level formulations
fpos (u:: 0)
E(u:; 0) -log Epss u: 0) + Eneg (u: 0)
(3)
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Learn Beneficial Noise as Graph Augmentation
so that LInfoNCE E ((u;0) O).
we let ((-) = exp( .) that
p(a/u) (o
(8)
3.2. A General Framework Bridge --Noise and Training Loss
where (o (1,0)+ (2;0) is defined to keep the (2:0
Given an arbitrary loss function L(V;) -77,0)=Eer Elu; 0), let 0* be the optimum that minimizes L(V: 0) over the pa- rameter space. It is clear that the quantity L(V; 0*) usually provides direct measurement of the task difficulty. In other words, smaller 0();0") implies a simpler task on V. However, it is important to point out that C(V; 0*) is neither a random variable nor a probability quantity, so it is impracticable be directly applied to computing the task entropy. To address this problem, we introduce an auxil- iary random variable a. To keep notations uncluttered, we simply substitute 0 with O. We define monotonously increasing mapping function f F + E4 such that
derivation uncluttered.
There are two probabilities remained in Eq. (7) to be dis- cussed. p(elu) is the distribution of x-noise we want to learn. A critical step in the process is to model p(ar (u, e) accurately. We define (uca(u, e; 0) and (ueg(u, E; 0) as contrastive losses with augmentation views generated by e. Then we follow the definitions of Eq. (4) and Eq. (8) to define
E(a(),,)) = (((,,, (O(,,E)
(9)
where ko(u,e) (paa(u..:00++aaamm (t. Without loss of generality, we suppose that only one augmentation is used for contrast. Clearly, the following analysis can be easily extended to the case with multiple augmentations. If the given data augmentation regarded as strongly definite noise, then augmentation can be viewed as hypothesis as follows
(por(u,e:0)
p(alu)= = (1. (((u((()))
(4)
Here ((s)) represents a Gaussian distribution. Due to the monotonous increasing property of f. a smaller contrastive loss implies higher similarity between samples and cor- responds to smaller variance of its auxiliary Gaussian distribution. It indicates a smaller entropy H (p(a)/u), i.e., a much easier task. The above definition provides us a natural scheme to define the task entropy of a given task by converting its loss E(u; 0). Formally,
p(Elu) + (E),
(10)
where (e) (E) is the Dirac delta function with translation Eo. i.e. (E) = 0 except for ε = Eo and S. deo (e)ds = 1. With this assumption, -H(T E is equivalent to
1 n / p(a) eo logp(a/ En)da L.
- -T(T)))
H(T)= Burp( ) H (p(a)u))
(11)
Eu-p(u H [ (N(O.
(5)
We can expand the density of N (o(u,,)) and substi- tute into C,
1 - C= n
1 IlggC C log ko Eo) - 1)) (12)
3.3. Rethink GCL under -Nose Framework
With the framework formulated in the previous subsection, provide new perspective for the existing GCL mod- els. We show that general GCL model with predefined augmentations is equivalent to learning parameters with m-noise. Under the n-noise framework, point estimation of
where C in the above equation represents a constant inde- pendent of learnable parameters. The detailed derivations can be found in Appendix A. To sum up, the original goal to maximize the mutual information is converted to
as the optimal parameters 8* are unknown, the optimization principle of GCL should be
1 Σ ni
max 1 (T,,(())))))))) max- O
log Kig (u, EO)
8.0
(13)
max (TTEE). 8,8
(6)
Σ log + min
epos (u, Eo; 0)
lpss (u, Eu: 0)
Eneg uu, Eu; 0):
According to the definition of (T) shown in Eq. (5), the conditional entropy is formulated as
which is the same as the standard contrastive learning paradigm.
((T())
In conclusion, the standard contrastive learning paradigm is equivalent to optimizing a contrastive learning module with point estimation of the n-noise, where the prede- fined data augmentation is the point estimation. It is easy to obtain a further conclusion: the heuristic graph augmenta- tion often fails to be a good point-estimation of 7-noise (shown in Eq. (10)), which causes the instability of GCL using heuristic graph augmentations.
=- f plalu, e)(lu,))((((l))(u)) log e)dudeda
n Σ ((alu,e)p(e log e)deda.
In this step, we use Monte Carlo method since the dataset
y can be regarded as a sample drawn from p(u). For GCL,
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Learn Beneficial Noise Graph Augmentation
3.4. Loss of r--oise Driven Data Augmentation
Algorithm Pseudo code of PiNGDA
Driven by the analysis of the previous subsection, there is natural idea to obtain stable augmentation for GCL: learning π-noise by optimizing Eq. (6), instead of randomly editing edges/nodes in heuristic way (Gao et al., 2021 Rong et al., 2020; Feng et al., 2020). It is named Pi-Noise driven Graph Data Augmentation (PINGDA). It should be emphasized that PINGDA is fully compatible with existing graph contrastive learning models.
Input: g = (V, Graph data with nodes V and edges
S, k: number of loops
Output: Node embeddings of G for epoch in range(max epochs) do
Generate topological noise gedge Generate attribute noise gattr
Get the noisy graph view Ge. Obtain node embeddings Z Enc(g), Z Enc(Ge).
Compared with the visual contrastive learning, there is stable method to generate an augmented graph with reliable topology and attributes. The instable augmentation implies that Eq. (10) fails to hold with a high probability. It results in the biased training of GCL models. In our proposed method, we denote (e(e))) as the learnable distribution with n-noise generator function parameterized by & which will be discussed in Section 4. Then H ET))) estimated by the Monte Carlo method (formulated by Eq. (7)) can be rewritten as H(T(E) 2
Compute the loss E.r by Eq. (15)
Update parameters by applying stochastic gradient as-
cent to minimize Cx by Eq. (15) and Eq. (16)
end for
node attribute noise gattr is generated using a parameterized Gaussian distribution. The whole algorithm is summarized in Algorithm 1.
4.1. Topological Noise
E Ee-nolelu)p(a log log (loggp(a,,,)ee
(14)
n
In this subsection, our goal is to model the conditional dis- tribution of topological noise p(EndBr (u), which determines edge-dropping probabilities for node u. To keep simplicity, we assume the topological noise godge follows a factored distribution over edges connected to node u.
Accordingly, the loss of PiNGDA formulated as
C. Σ Eenpo log &oss u, e; 0) + Eueg (u, E; 0)*
fpss (u, E; O)
(15)
where O represents the parameters of the contrast model. For node u. the feature embedding zu in the original graph and the augmented = generated r-noise constitutes positive sample. And the other nodes are treated as negative samples. Specifically speaking, the formulations foss and Eneg are
p (u) = II p(Eulu),
(17)
(u.b)ES
where S denotes the set of edges incident to node Each edge (u, v) may be dropped subject to
(Zu, zu)
Pr(dropping (u, v)) = p(e,lu).
(18)
Epool (u) = exp
(16)
(Zu, Zu) + exp
(Zu:200 20)
The edge-dropping probability is parameterized by a learn- able module I (u, v) that operates on node pairs. While different distribution families can be employed, we use the Bernoulli distribution as our default choice due to its natural interpretation for binary edge operations. For each edge, the preceding probability formulated
Eueg(1u) exp
T
T
where (),") is the similarity function and the cosine simi- larity is used in this paper.
Since a graph neural network usually takes two components as input, edge set and node attributes, the noise also consists of two components, topological noise gddge and attribute noise gattr, In Section 4, we will discuss how to generate the topological noise and attribute noise, respectively.
p(Ev/u) (u) Bernoulli (u, v))
(19)
where Pep (u, v) outputs the probability of edge deletion. We implement Iy as a two-layer Multi-Layer Perceptron (MLP) that processes concatenated node features.
4. Implementation Details of Topological Noise and Attribute Noise
To maintain gradient flow through discrete edge-dropping decisions, employ the Gumbel-Softmax reparameteriza- tion trick (Jang et al., 2016). This provides differentiable approximation of Bernoulli sampling:
In this section, we provide detailed explanation of the implementation of both topological and attribute noise gen- eration within our framework. We first discuss the gen- eration of topological noise eddge and then describe how
E. Gumbell-Softmaxggufee v))
(20)
5

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Learn Beneficial Noise as Graph Augmentation
This formulation enables learnable, node-specific edge dropout patterns that adapt during training while maintain- ing differentiability through the Gumbel-Softmax approxi- mation.
5.1. Experimental Settings
For every experiment of node classification, we follow the linear evaluation scheme introduced by Veličković al. (Veličković et al., 2018). Firstly, every model is trained in an unsupervised manner and then the resulting embed- dings are utilized to train and test a simple 12-regularized logistic regression classifier. For each dataset, we conducted 20 random splits of training /validation/test, and reported the averaged performance. We then calculated the average performance on each dataset based on these runs. In these experiments, we measured performance using accuracy as the evaluation metric. For graph classfication, all methods are trained with the corresponding self sulf-vupe objective and then evaluated with a linear classifier. We follow the conventional 10-Fold evaluation. All our experiments are performed 10 times with different random seeds and we report mean and standard deviation of the corresponding test metric for each dataset. We use accuracy to measure the performance.
4.2. Attribute Noise
In this subsection, detail the process of generating at- tribute noise gater_ The objective is to introduce noise to the node attributes in a way that is both effective for model training and differentiable. We model the attribute noise gattr as a Gaussian distribution conditioned on the node attributes u,
P u) = (,, E).
(21)
where j is the learnable mean vector and E is the learnable covariance matrix of the distribution. These parameters are learned by an MLP that takes the node attributes u as input. Similarly, we employ the reparameterization trick (Kingma, 2013) to ensure that the model is differentiable. Similar to (Kingma, 2013), we assume the Gaussian noise on at- tribute, which is discussed in Section 4.2, is uncorrelated, i.e., Σ- diag where E Rd. The assumption can drastically decrease the parameters from d2 to d. Using the reparameterization trick, the attribute noise can be generated
5.2. Baselines
For node classification, we compare PiNGDA with state- of-the-art methods for node classification. These meth- ods include two supervised graph neural networks (GNNs), namely GCN (Kipf & Welling, 2016) and GAT' (Veličković et al., 2017). Additionally, we compare PiNGDA with self self-supervised GCL methods, which are DGI (Veličković et al., 2018), GMI (Peng et al., 2020). GCA (Zhu al., 2021), BGRL (Thakoor al., 2021), GREET (Liu et al., 2023), SGRL (He et al., 2024), GRACEIS (Liu et al., 2024), GOUDA (Zhuo et al., 2024), GASSL (Yang et al., 2021) and two learnable method AD-GCL (Suresh et al., 2021a) and JOAO (You et al., 2021a). These methods represent the current state-of-the-ar art in the field of semi-supervised node classification, and we compare the performance of PiNGDA against them evaluate its effectiveness. For all baselines, implement them based their official codes and conduct hyperparameter search according to the original paper.
by
attr p EE,
(22)
where ~ (0, is a standard normal random vari- able. This reparameterization ensures that the sampling process is differentiable, enabling backpropagation of gradi- ents through the noise term during training.
We then add the noise the attributes to obtain the perturbed attributes. By introducing noise into the node attributes in this way, we effectively perturb the node features.
5. Experiments
In this section, we conduct experiments to evaluate our model by answering the following questions.
Q1: Does our proposed PiNGDA on graph outperform existing baseline methods?
5.3. Performance on Graph Tasks (Q1)
5.3.1. 1. NODE CLASSIFICATION RESULTT
Q2: Is the n-noise we trained more useful than random noise? How does each component affect model perfor- mance?
In Table 1, we present the node classification accuracy re- sults of various methods across seven benchmark datasets. The bold numbers indicate the best performance and un- derlined numbers represent the second-bighes accuracy for each dataset. We applied two types of augmentation to our method: learning the beneficial noise both the topology and attributes through a trainable noise generator. A de- tailed analysis of these components will be provided in the following ablation study.
Q3: How does our method perform in terms of time and space efficiency?
Q4: How does the ronoie look like?
We begin with a brief introduction of experimental settings, followed by a detailed presentation of the experimental results and their analysis.
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Learn Beneficial Noise Graph Augmentation
Table I: Node classification accuracy on seven datasets. The bold numbers represent the best results and the second highest results are underlined. OOM indicates the Out-Of- Memoory exception on a 24GB GPU. *JOAO marked with an asterisk clarify that it does not learn augmentation parameters directly. It adaptively selects augmentations based on a Liilaariy-driver policy.
Methods
Learnable
Cora
CiteSeer
PubMed
Wiki-CS
Amazon-Photo
Coauthor-Phy
ogbn-arxiv
Rank
GCN
X
84,22 + 1,14
71.59 + 0.75
85.19 = 0.21
80.27 = 0.55
92.55 0.25
95.75 + 0.05
69.42 + 0.06
GAT
83.74 0.50
72.11 0.36
84.79 0.28
80.41 # 0.58
92.48 0.21
95.40 0.08
OOM
DGI
X
83.25 # 0.77
72.01 + 0.83
85.12 = 0.18
79.34 # 0.42
89.01 = 0.98
0OM
OOM
7.2
GMI
X
83.60 = 1.06
69.11
1.07
84.12 0.37
79.99 0.51
90.13 1.39
0OM
OOM
GCA
x
85.20 = 0.21
71.76 - 0.24
87.07 +: 0.25
81.26 + 0.11
93.19 = 0.24
94,96 + 0.25
69.23 + 0.01
3.4
BGRL
X
83.80 + 0.68
71.51
0.65
85.60 + 0.17
81.38 + 0.14
93.19 0.43
95.54 4 0.06
68.60 0.23
4.2
GREET
x
80.47 = 0.55
72.28 0.59
86.07 = 0.53
79.92 = 0.28
93.61 = 0.35
96.05 + 0.12
0OM
4.3
SGRL
X
83.63 + 0.49
71.89 + 0.25
86,34 0.16
81.28 + 0.16
92.97 = 0.32
95.64 0,10
68.03 +: 0.04
4.3
GRACEIS
84.57 + 0.41
71.40 -: 0.53
0.37
79.33 4: 0.27
94.28 0.43
65.97 0.20
GOUDA
x
82.25 # 0.54
70.25 + 1.24
85,82 0.71
89.61 = 1.17
94.54
GASSL
81.82 = 0.79
69.51
84.91 = 0.57
92.14 0.23
94.93
AD-GCL
83.88 + 0.25
68.74 0.53
84.23 +: 0.21
80.57 + 0.27
91.92 + 0.37
95.63 + 0.10
68.45 +: 0.11
6
JOAO
82.77 = 0.71
72.09 0.17
83.83 0.32
80,43 = 0.27
78.23 = 2.63
94.30 +: 0.38
68.66 -: 0.09
6.8
Ours
86.25 + 0.25
72.44 1: 0.14
87.34 0.08
82.07 + 0.10
93.29 + 0.17
95.81 0.06
68.72 0.04
1.4
The results show that our method maintains high accuracy across diverse graphs. Moreover, our method exhibits lower variance, demonstrating greater stability in its performance. When compared other methods that employ learnable components, method stands out. Notably, while AD- GCL is also learnable method, it focuses only on learning the topology of the graph, which limits its effectiveness in many datasets. In contrast, our method leverages both the topology and attribute information, leading to more comprehensive and robust representation learning. As a result, our method consistently outperforms AD-GCL on most datasets, showcasing the advantages of augmenting both graph topology and node features.
5.3.2. GRAPH CLASSIFICATION RESULTS
In Table 2, we evaluate the performance of various graph classification methods across five datasets. We compare with four unsuperviseal/sedf-ung susperrrsesssseei learning basclines, which include randomly initialized untrained GIN (RU- GIN) (Xu al., 2018), InfoGraph (Sun et al., 2020), GraphCL (You et al., 2020) and AD-GCL (Suresh et al., 2021a). They generally outperform in graph-level tasks. For all baselines, we report their performance based on AD- GCL (Suresh et al., a). Our method achieves top or near-top performance on all datasets, demonstrating its ro- bustness and ability to generalize across various tasks, Our method and AD-GCL (both learnable methods) perform bet- than the other methods across most datasets. However, Ours demonstrates superior generalization, particularly ex- celling on MUTAG and RDT-B, whereas AD-GCL performs slightly better on NCI1 and PROTEINS. Despite these slight differences, Ours achieves a balanced and consistent perfor- mance, providing strong evidence of its capability to handle diverse graph classification tasks effectively.
On the large-scale ogbn-arxiv dataset, several methods en- counter out-of-memory issues. While the supervised method GCN achieve the best results, our method performs almost equally well, with very small margin difference. This in- dicates that our approach highly competitive when graph large.
3. HETEROGENEOUS GRAPII RESULTS
Table 2: Classification accuracy on graph classification datasets. The bold numbers represent the best results and the second highest results are underlined.
In this section, evaluate the performance of our method on node classification tasks using three heterogeneous graph datasets: Texas, Cornell, and Wisconsin (Pei et al., 2020). As summarized Table 4, our approach consistently sur- passes other methods on the Texas and Cornell datasets, achieving the best classification outcomes. This demon- strates the effectiveness of our model in capturing and leveraging the structural diversity inherent in heterogeneous graphs. On the Wisconsin dataset, our method delivers com- petitive results, ranking closely behind the top pop-erffommin
Methods
NCII
MUTAG
PROTEINS
DD
RDT-B
RU-GIN
62.98_0.11
87.6110339
69:03:0.33
74.22-0.30
58.97100.33
InfoGiaph
68.13-0.59
87.71+1.77
72.57+40.6
75.23-00.9
78.79-2.14
GraphCL
68.51=0.555
1..29
12.86:1.011
74.70.0.70
82.63-10.99
AD&GCII
69.67-0.51
1.020+103
73.51+0.46
75.10-00.99
85.52-0.79
OURS
69.35
89.71.10.33
73.2110.40
75.51.10.57
83.99110.34
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Learn Beneficial Noise Graph Augmentation
Table 3: Ablation study on the impact of feature and edge augmentation methods. In this table, the red values represent the highest classification accuracy for each dataset in each row, while the cells with a background indicate the highest performance in each column.
Edge
Cora
PubMed
Wiki-CS
Feature
Without Aug.
Random
Learnable
Without Aug.
Random
Learnable
Without Aug.
Random
Learnable
Without Aug.
82.59 0.66
0.99
0.54 84.28
85.11 0.19
86.61
81.05 0.23
80.99
Random
83.12 # 0.82
85.84 0.44
85.99 :: 0.29
84.97 = 0.14
86,89 = 0.13
87.07 + 0.25
80.12 = 0.49
81.61 # 0.19
82.03 = 0.07
Learnable
83.36 + 0.54
85,83 0.37
86.25 0.25
85,37 0.07
87.04 0.20
87.34 0.08
80.13 + 0.18
81.51 + 0.14
82.17 0.15
Table 4: Classification accuracy on three heterogeneous datasets. The bold numbers represent the best results and the second highest results are underlined.
structure yields a greater improvement than augmenting the node features. Compared other datasets, WikiCS has relatively higher number of average edges. The learnable augmentation method may not effectively enhance model performance when modifying the edge structure. Moreover, the node features in WikiCS have relatively low dimen- sionality. indicates that edges may be more important than features in WikiCS. As result, modifying features without adjusting edges might lead to suboptimal perfor- mance. Overall, in cases where random augmentation is applied, it can sometimes cause excessive disruption to the graph structure, especially on datasets where the edge rela- tionships are more crucial to the performance. Therefore, our learnable augmentation method offers a more adaptive and data-aware alternative in preserving the underlying data distribution while improving performance.
Methods
Texas
Cornell
Wisconsin
GCN
4.46
48.44 4.82
58.01
GAT
56.19
2.16
47.62 4.06
55.12
DGI
57.55
2.94
47.89 + 2.05
47.56 + 5,56
GMI
48.98
3.60
41.09 + 5.24
51.24 :: 3.93
GCA
58.57 2.10
47.45 1: 0.88
52.04 :: 3,34
BGRL
54.88 3.35
35.15 4 10.43
48.59 1: 3.77
GREET
62.79 2.57
51.90 1 2.47
63.11 0.74
SGRL
60.00 0.27
50.07 + 0.33
56.92 + 0.24
GRACEIS
61.90
48.57 + 1.95
59.10 :: 0.96
AD-OCL
60.82 2.49
49.52 1: 2.93
$7.01 :: 2.70
JOAD
62.43 2.96
51.02
1: 0.96
60.90 1: 0.87
Ours
65.31 1.29
53.06
1.05
61.99 1. 1,36
approach. These findings highlight the strong generalization ability of our method across diverse heterogeneous graph structures.
Table 5: Performance comparison of GRACE and SpLGCL before and after applying the proposed PiNGDA augmenta- tion across benchmark datasets.
5.4. Ablation Study (Q2)
5.4.1. EFFECT OF AUGMENTATION STRATEGIES
Methods
Cora
CiteSoer
PubMid
Amazon-Photo
Crauther-PHy
GRACE
83.43 0.32
70.93 0.21
85.90 0.24
93.13 0.17
95.74 0,06
In this ablation study, We assess the influence of various augmentation strategies on classification accuracy across multiple datasets, comparing three approaches: no augmen- tation, random augmentation, and learnable augmentation. The results are detailed in the Table 3. Specifically, "without augmentation" refers using the original data without any additional operations. "Random augmentation" involves randomly dropping nodes or edges according certain ra- tio, while "learnable augmentation" leverages our proposed learnable method, which allows for adaptive manipulation of node features and edge structures.
-ENGDA
84.28 0.24
71.47 0.30
86.79 0.27
93.10 0.18
95.81 0.65
Sp"OCI
82:45 + 0.35
65.54 =2 0.51
B4.26 t: 0.29
93.05 0:33
95.73 0.04
+PINGDA
K3.89 0.48
67.21 0.63
84.73 0.23
95.11
95.74 0,04
5.4.2. GENERALIZATION TO OTHER GCL MODELS
To evaluate the generalizability of our proposed noise aug- mentation method, we conducted an ablation study by ex- tending it to other GCL. frameworks. Specifically, we se- lected a classical GCL method (GRACE (Zhu et al., 2020)) and a more recent approach (Sp*GCL (Bo et al., 2023)) to validate the robustness and effectiveness of our approach when applied to diverse contrastive methods. As shown in Table 5, our method consistently improves performance across various datasets when integrated into both models. This highlights the generalizability and robustness of our method when incorporated into various contrastive learning frameworks.
Overall, we observe that learnable augmentation consis- tently outperforms random augmentation, and random aug- mentation in turn performs better than the augmentation approach. This pattern holds across most datasets, with both augmentation strategies improving performance in compar- ison to using the original data. However, the effects of augmenting edge and feature structures vary across datasets. For instance, on Cora and PubMed, augmenting the edge
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Learn Beneficial Noise Graph Augmentation
PulMidd
Amtzzae-Phuie
21
233
10000
15000
3300
11905
94
0000
2902
28000
6000
1030
ADgCL
2500
D0A
10000
GRogees
103K
10go
1000
XIND
330
7030
Trant
Figure 2: Comparison in terms of training time of one epoch, and memory costs between different graph representation learning methods. On Amazon-Phan Photo, the model is trained with a batch size of 256 due to the memory limit.
Cora
CiteSeer
PubMed
WikiCS
Figure 3: Visualization of noise in graph data. Nodes are selected from the graph which are colored according to their labels, edges are colored to differentiate between intra-class (solid gray) and inter-class (dashed red) relationships. The node layout is determined by their connectivity relationships. The width of the edges corresponds to the learned weights.
5.5. Efficiency Analysis (Q3)
lines. The width of the edges in the figure corresponds to the learned weights, which are indicative of the strength of the connections between nodes. It highlights the trend of our method towards removing inter-class edges while main- taining intra-class connections. By focusing on the removal of inter-class edges and preserving intra-class edges, method ensures that the most relevant class- specific infor- mation is retained. It leads to more reliable augmentations.
Figure 2 reports the time and memory efficiency of our learnable method compared to other methods across mul- tiple datasets. Compared with some GCL methods, our method has an advantage in occupying less memory. Mean- while, terms of runtime, our method is not significantly different from other methods. While some more complex methods may marginally outperform
approach in terms of computational cost, they come at poor performance accuracy. On the other hand, our learnable augmentation method offers an optimal trade-off between accuracy and computational efficiency.
6. Conclusion
In this paper, we propose Pi-Noise driven Graph Data Aug- mentation (PiNGDA), novel method for graph data aug- mentation in graph contrastive learning (GCL). PiNGDA leverages the concept of instttveinneentie noise to mitigate the instability commonly observed in traditional augmen- tation methods by learning adaptive noise. Furthermore, we introduce the notion of task entropy for classical GCL, showing that standard GCL can be viewed as an approxima- tion under the optimization framework of positive-incentiv noise. By employing noise generator that learns beneficial noise, PiNGDA achieves performance improvements across various graph tasks. Additionally, future work may explore alternative strategies for incorporating positive-incentin noise with diverse noise distributions.
5.6. Topological Noise Visualization (Q4)
Although our method introduces noise to both edges and node attributes, we only visualize the topological (edge- based) component here. This because node attributes are typically digh-dimensional and lack an inherent spatial structure, making them difficult to visualize intuitively. In Figure 3, visualize the effects of topological noise graph through edge weights. Specifically, nodes are selected from the full graph and different classes are represented us- ing distinct colors. The node layout is determined by their connectivity relationships. Edges connecting nodes of the same class are shown solid gray lines, while edges link- ing nodes of different classes are displayed dashed red
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Learn Beneficial Noise Graph Augmentation
Impact Statement
He, D., Shan, L., Zhao, J., Zhang, H., Wang, Z., and Zhang, W. Exploitation of latent mechanism in graph contrastive learning: Representation scattering. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024.
This paper presents work whose goal to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
He. K., Fan, H., Wu, Y.. Xie, S., and Girshick, R. Mo- mentum contrast for unsupervised visual representation learning, 2020.
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Appendix
A. Derivation of Eq. (12)
can expand the density of (00 Kig (u, =) and substitute into L,
L = Σ log C + log ke(u, 5o)
1 2
(23)
where the details can be found in Appendix
pla En) CV niolu, En) expl- a² x,
(24)
1 logp(a/u, Eo) log C (og Koo kko En).
a²
Substituting into C, we can simplify as
c Σ / p(alu,Eo) (log C+ log ko(uu, a²
no((u, da
eo) ko(u,
Σ llo C + (o)
a² p(p(aau, s0)doa
(25)
2
Σ log + log (0 - )
where C' in the above equation represents constant independent of learnable parameters. In the final step, use the fact that J a p(alu, co)da ke(u, (u) =o
B. More Experimental Details
B.1. Datasets
We use seven benchmark datasets semi-supervised node classification, including Cora, Citeseer, Pubmed (Sen et al., 2008), Wiki-CS (Memyei & Cangea, 2020), maazoon-Phote Coauthor- CS (Shchur al., 2019) and ogbn-arxit (Hu et al., 2020). The detailed statisties of the datasets are summarized in Table 6. For all datasets, randomly split the datasets, where 10%, 10%. and the rest 80% of nodes are selected for the training, validation, and test set, respectively.
We evaluate our proposed framework in the semi-supervised learning setting on graph classification on the benchmark TUDataset (Morris et al., 2020). The detailed statistics of the datasets are summarized in Table
Table 6: Statistics of datasets used in node classification experiments.
Dataset
Nodes
Edges
Features
Classes
Cora
2,708
5,429
1,433
7
Citeseer
3,327
4,732
3.703
PubMed
19,717
44,338
500
3
Wiki-CS
11,701
216,123
300
10
Amazon-Photo
7,650
119,081
745
8
Coauthor-C'S
18.333
81.894
6,805
15
ogbn-arxiv
169,343
1,166,243
128
40
B.2. Implementation Details
Our experiments are conducted on an NVIDIA 4090 GPU (24 GB memory) for most datasets and on an NVIDIA A100 GPU (40 GB memory) for OGB-arxin For our proposed method, we employ a two-layer GCN network with PReLU activation, where the hidden layer dimension is set to 512, and the final embedding dimension is 256. Additionally, we utilize a projection head, consisting a 256-dimensional fully connected layer with ReLU activation, followed by a 256-dimensional
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Learn Beneficial Noise Graph Augmentation
Table 7: Statistics of datasets used in graph classification experiments.
Dataset
Graphs
Avg. Nodes
Avg. Edges
Classes
NCI1
4110
29.87
32.3
MUTAG
188
39.06
72.82
PROTEINS
1113
39.06
72.82
DD
1178
284.32
715.66
RDT-B
2000
429.6
497.75
linear layer. Edge noise generator uses an MLP to process node features and then applies Gumbel-Softtax sampling method. Feature noise generator uses two MLPs estimate the mean and variance of feature noise and then uses the reparameterization trick.
B.3. A blation Study on Graph Classification
Table 8: Ablation study on the impact of feature and edge augmentation methods. In this table, the red values represent the highest classification accuracy for each dataset in each row, while the cells with background indicate the highest performance in each column.
Edge
PROTEINS
Fenture
Without Aug.
Random
Learnable
Without Aug.
Random
Learnable
Withont Aug.
Random
Learnable
Without Aug.
72.49 0.90
71.56 + 0.41
73.16 = 0.77
75.24 + 0.21
73.07 = 0.52
75.53 +: 0.76
68.59 = 0.75
67.40 1.24
68.83 0.69
Random
72.38 0.46
72.38 1. 0.79
72.49 4 0.58
75.06 J. 0.88
74.23 0.82
74.80 J: 0.46
69.05 0.74
68.54 1.02
68.84 0.65
Learnable
1.24
72.15
75.16
74.83 0.46 75.70
0.62
1.22
69.35 0.63
We also explore the impact of different augmentation on graph classification performance across three datasets: PROTEINS, DD, and NCII. Overall, the effectiveness of augmentation strategies varies across datasets, largely due to the differing semantic roles that node attributes play each graph. In some cases, neither random nor learnable perturbations alone can fully capture the optimal augmentation pattern. Nevertheless, our results show that the combination of learnable feature and edge augmentations consistently yields strong and stable performance across all datasets. This demonstrates the robustness and generalizability of our augmentation framework, especially in adapting diverse graph structures and attribute types.
B.4. Hyperparameter Analysis
Datasets
epoch
Ir
wd
Cora
500
5e-4
le-4
0.3
CiteSeer
500
5c-4 lc-4
0.3
PubMed
1000
le-3 le-4 0.3
WikiCS
1500
5e-4 le-4 0.3
Amazon-Photo
2000
le-2 1e-4 0.3
Coauthor-Phy
2000
le-2 le-4 0.5
ogbn-arxiv
500
le-3 le-4 0.3
Table Hyper-parameter that vary for different datasets.
Some hyper-parameters of the experiment vary on different datasets, which is shown in Table 9. For the learnable noise generators, we use separate optimizers with learning rates of 0.0001 for edges and 0.001 for features, and apply a weight decay of 0.0001 to both. Specifically, we carry out grid search for the parameears on the following search space:
Number of training epochs: (500, 1000, 1500, 2000, 3000}.
Learning rate for training: (1e - 2, 1e - 3, 5e - 4}
Weight decay for training: {le 3, 4)
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Learn Beneficial Noise Graph Augmentation
Random Edge dropping rates Pe2: {0.1, 0.3, 0.4, 0.5, 0.6} Random Feature masking rates Pfi,Pr2: (0.1, 0.3, 0.5)
Temperature {0.3, 0.4,
For each dataset, set of hyper-parameters is chosen to obtain the best average accuracy. Figures and show the results
Cara
PrisMee
WiGES
Temperature
Temperaiur
'eompertture
Temperature
Figure The effect of the temperature
Car
CliSar
PrisMaa
Wiki'
BL25
3125
34
121
Liddee
Hiddde
Figure 5: The effect of the hidden dim.
of node classification with variable temperature 7 and hidden dim. We can observe that our PiNGDA is not very sensitive to temperature and hidden dim. For small graphs, smaller temperature leads to better performance.
15


Reviews:
[{"review_id": "bZBNvcx7Dh", "reviewer": "Reviewer_PRCX", "summary": "This work introduces the PiNGDA method, designed to enhance graph data augmentation through the incorporation of beneficial noise. The paper also introduces the concept of task entropy, offering a fresh lens through which to comprehend the objective function of contrastive learning. Practical results demonstrate that PiNGDA leads to performance gains, thereby confirming its efficacy.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Reviewer PRCX**\n\nWe greatly thank you for the detailed and valuable comments. Please find our responses to the comments as follows:\n\n>**W1:** The depth of the discussion of the experimental results can be further improved, such as the explanation of certain experimental phenomena and the possible differences between different datasets. For example, in the Table 2, the learnable methods seem not to perform as well as the other two datasets.\n\n**Reply:** Regarding the observation that learnable augmentation performs worse than random augmentation on the WikiCS dataset, we believe this may be due to the following reasons.  Compared to other datasets, WikiCS has a relatively **higher number of average edges**. The learnable augmentation method may not effectively enhance model performance when modifying the edge structure. Moreover, the **node features** in WikiCS have relatively **low dimensionality**. It indicates that edges may be more important than features in WikiCS. As a result, modifying features without adjusting edges might lead to suboptimal performance. However, if the learnable edge augmentation cooperates learnable feature augmentation, it may yield better results as can be found in the last column of **Table 2**. We will include a more detailed analysis in the paper to further investigate the differences across datasets. Thank you again for your insightful feedback!\n\n>**W2:** The mathematical derivation in the method section can be more detailed to enhance readability and understanding. For example, the random variable alpha is a bit confusing. Why is this variable necessary? And why do you assume the probability distribution showed in equation 4? It will be very helpful if they are explained clearly.\n\n**Reply:** Thank you for your comments. In our paper, the random variable $\\alpha$ is introduced to indirectly **measure the difficulty of the task**, closely tied to the concept of **task entropy**. We adjust the variance of the auxiliary Gaussian distribution, which directly influences the calculation of task entropy. \n\n>**Q1:** How is your method different from AD-GCL[1]? AD-GCL uses an adversarial method to enhance contrastive learning of graphs. It also uses a learnable method to drop edges which is quite similar as your method. Please clearly explain the key differences in the design of the two methods.\n\n**Reply:** Our method differs from AD-GCL primarily in its augmentation strategy and focus. From the aspect of motivation,  AD-GCL applies **adversarial graph augmentation** to minimize information from the original data which tries to maximize the loss, our approach enables the model to learn the augmentation simplify the representation learning.  From the aspect of augmentation, AD-GCL mainly targets **graph structure**, whereas our method considers **both graph structure and node attributes**, leading to a more comprehensive augmentation. This advantage is reflected in our superior results in node classification, as shown in **Table 1**.\n\n>**Q2:** There are two main components proposed by PiNGDA, however the visualization part only shows the edge noise, how does the node attribute noise look like? The authors should provide more detailed explanation on the part.\n\n**Reply:** Thank you for your insightful suggestion. From a contrastive learning perspective, methods like SimCLR and BYOL commonly use **Gaussian noise** as an augmentation, making it a natural choice for adaptation to **non-vision data (tabular data)**. This is also an advantage of our method which serves as a **unified framework** for both **graph** and **tabular node features**. Regarding visualization, node attributes are typically **high-dimensional**, making them difficult to represent intuitively. Even if converted into a matrix or heatmap, unlike in vision tasks, there is **no inherent spatial relationship between adjacent values**, which could lead to misleading interpretations. We appreciate your valuable feedback and will add further explanations to clarify this point.", "claims_and_evidence": "This work asserts that its method addresses the stability issues associated with traditional methods. According to experimental findings, the proposed method excels in various tasks, including node classification and graph classification, demonstrating its efficacy. Additionally, ablation studies provide insight into the individual contributions of each module.", "methods_and_evaluation_criteria": "This paper introduces a novel graph contrastive learning data augmentation technique along with an innovative framework aimed at resolving issues with existing approaches. By employing a learnable augmentation strategy, the framework enhances the model's capabilities while maintaining the integrity of graph structure information. To ensure fairness and comparability in experimental results, the evaluation criteria adhere to traditional GCL methods, utilizing standard contrastive learning loss functions and widely accepted evaluation metrics.", "theoretical_claims": "In Section 3 of this paper, the key theoretical assertions are meticulously validated through rigorous mathematical proofs. The authors clearly articulate their underlying assumptions, derive conclusions logically, and maintain coherence in the entire derivation sequence.", "experimental_designs_or_analyses": "The experimental design of this paper is well-conceived, encompassing various benchmark datasets to fortify the reliability of the experimental outcomes. It employs widely-acknowledged baseline methods for comparative analysis. Furthermore, ablation studies are included to dissect the individual impacts of different modules.", "relation_to_broader_scientific_literature": "The paper proposes method about graph contrastive learning. Prior studies, such as DGI and GraphCL have demonstrated the effectiveness of contrastive objectives in learning graph representations, mainly using augmentations such as node/edge dropping. Newer methods such as GCA have introduced adaptable augmentation strategies. This paper extends these ideas by incorporating learnable noise into the contrastive framework, thereby enhancing representation robustness while maintaining theoretical consistency.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths:\n1）The paper is clearly expressed, allowing readers to easily understand the research content. In addition, the experimental section provides sufficient comparative analysis. The paper conducts experiments on multiple datasets and compares the performance of different methods, such an experimental design can help verify the robustness and applicability of the method.\n2） The paper also provides a detailed analysis in the ablation experiment section to further verify the effectiveness of the method. It analyzes the impact of different components in the method on the final performance through detailed ablation experiments. This can help understand which parts contribute the most to the final result. \n3） The authors visualize the changes in edge weights to make the abstract “noise” expression more intuitive. This helps us understand how the model adjusts the graph structure, optimizes information propagation, improving the interpretability of the method.\n\nWeaknesses:\n1) The depth of the discussion of the experimental results can be further improved, such as the explanation of certain experimental phenomena and the possible differences between different datasets. For example, in the Table 2, the learnable methods seem not to perform as well as the other two datasets.\n2) The mathematical derivation in the method section can be more detailed to enhance readability and understanding. For example, the random variable alpha is a bit confusing. Why is this variable necessary? And why do you assume the probability distribution showed in equation 4? It will be very helpful if they are explained clearly.", "other_comments_or_suggestions": "See the weaknesses.", "questions_for_authors": "1) How is your method different from AD-GCL[1]? AD-GCL uses an adversarial method to enhance contrastive learning of graphs. It also uses a learnable method to drop edges which is quite similar as your method. Please clearly explain the key differences in the design of the two methods.\n2) There are two main components proposed by PiNGDA, however the visualization part only shows the edge noise, how does the node attribute noise look like? The authors should provide more detailed explanation on the part. \n[1]Suresh, S., Li, P., Hao, C., and Neville, J. Adversarial graph augmentation to improve graph contrastive learning, 2021", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9ZcyG3gD6Y", "reviewer": "Reviewer_65ie", "summary": "This paper proposes a graph contrastive learning (GCL) methods, namely PINGDA, with a novel learnable graph augmentation. The learnable augmentation follows a new information theory framework, namely positive-incentive noise. The authors propose to view all augmentations as “noise” and thus design a new algorithm to add beneficial noise to both graph topology and node attributes. The experiments are run on several graph tasks, including node classification and graph classification.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Reviewer 65ie**\n\nWe greatly thank you for the detailed and valuable comments. Please find our responses to the comments as follows:\n\n>**W1:** The introduction of positive-incentive noise and the discussions with the existing papers of noise are not enough, especially in the main paper.\n\n**Reply:** Thank you for your valuable suggestion. Due to space limitations, we only provide a simple and brief discussion in the main paper.  We will consider expanding this discussion in the supplementary material or refining the main text to provide a clearer comparison. \n\n>**W2:** Figure 1 can be further improved. It is hard to distinguish how to simultaneously generate augmentations on both graph topology and node features. Meanwhile, $\\mathcal{N}(0,I)$ in the figure is inconsistent with the notations appearing in the main paper.\n\n**Reply:** Thank you for your valuable feedback.  We will refine the figure to enhance clarity. As for the notation inconsistency, we apologize for any confusion. In **Appendix [B]**, we explicitly describe the reparameterization trick used in our method, where the covariance matrix is defined as $\\Sigma = \\text{diag}(\\sigma^2)$, ensuring a diagonal structure. Here, $\\sigma\\sim \\mathcal{N}(0, I)$, aligning with the notations in the figure. \n\n>**W3&4:** In Table 2, the best results should be further highlighted. The current version is not intuitive. The caption of Table 4 is quite confusing. The authors fail to clarify that the datasets are heterogeneous graphs in the caption.\n\n**Reply:** Thank you for your helpful suggestions. We will update Table 2 to better highlight the best results for improved clarity and we will revise the caption of Table 4 to clearly specify that the datasets are heterogeneous graphs.\n\n>**Q1:** Why do the authors assume that the topological noise is a Bernoulli distribution?\n\n**Reply:** Thank you for your question. We assume that the **topological noise follows a Bernoulli distribution** because the simplest way to model edge perturbation is to learn whether an edge should be kept or removed, which naturally aligns with a **0/1 binary decision process**. This makes Bernoulli distribution a **straightforward and effective choice** for modeling edge retention or deletion in graph structures.\n\n>**Q2:** I cannot completely understand the meaning of Figure 3. How are the nodes visualized? t-SNE? Why does it only contain dozens of nodes? As we all know, there are thousands of nodes in a graph. The authors should clarify this in the rebuttal and the main paper.\n\n**Reply:** Sorry for the lack of clarity in Figure 3. To improve visualization, the nodes shown in the figure are **a subset selected from thousands of nodes** for a case study. This selection helps make the visualization more interpretable. The node distribution in the figure is based on their **connectivity relationships**, rather than a dimensionality reduction method like t-SNE. We will clarify this in the main paper. Thank you for your valuable feedback.\n\n>**Q3:** What’s the additional computational and space complexity? Will it lead to a significant burden on both computation and memory?\n\n**Reply:** Thank you for your insightful question. The **computational and space complexity** of noise learning depends on the design of the noise network. In the two noise generation modules, since each edge and each node feature is calculated by MLP, the computational complexity of the noise module is $\\mathcal{O}(\\mathcal{E} \\cdot d) + \\mathcal{O}(N \\cdot d)$, where N is the number of nodes, $\\mathcal{E}$ is the number of edges in the graph, and d is the dimension of the node feature. To minimize the burden, we have carefully **simplified the network structure**, such as reducing the number of hidden layers. The memory overhead as shown in Figure 2, is not significant. While our method introduces some additional computational costs, it provides clear performance improvements, making the trade-off worthwhile. The detailed table can be found in the response to **Reviewer J7B2**. We appreciate your feedback and will clarify this further in the paper.", "claims_and_evidence": "Yes, the theoretical claims are well verified by the experiments. In most cases, the proposed PINGDA achieves the best results. In some cases, the method also achieves sub-optimal results. I notice that the stds are usually smaller than other GCL methods, which seems to prove that the proposed idea of using noise makes sense.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria make sense for the problem. The experiments contain both node classification and graph classification. The datasets also contain both heterogeneous and homogeneous graphs.", "theoretical_claims": "I checked most of the mathematical derivations. It seems that the formulations are roughly correct.", "experimental_designs_or_analyses": "I checked the experimental design and analyses. The results can well support the claims and conclusions.", "relation_to_broader_scientific_literature": "The paper provides a new perspective for stable graph augmentation, the theory is well grounded by information bottleneck.  It is also an interesting advantage compared with the existing GCL methods, such as GCA and JOAO.", "essential_references_not_discussed": "none", "other_strengths_and_weaknesses": "Strengths:\n\n1. The paper proposes an interesting and new perspective for graph augmentation in GCL. The idea of viewing graph augmentation as noise seems new as far as I know. It can therefore unify the augmentation on graph topology and node attributes, which is an advantage compared with the existing GCL models with learnable augmentations. \n2. PINGDA also focuses on how to augment node attributes while most existing GCL models focus on how to modify the graph and only utilize the simple perturbations on attribute augmentations. \n3. The experimental results seem promising. The learnable augmentations seem to well support the theoretical analysis. The experiments contain node classification and graph classification. The datasets consist of both homogeneous graphs and heterogeneous graphs. I noticed that the standard derivations are smaller in most cases, which validates the effectiveness of the learnable augmentation. \n\n\nWeaknesses:\n\n1. The introduction of positive-incentive noise and the discussions with the existing papers of noise are not enough, especially in the main paper.\n2. Figure 1 can be further improved. It is hard to distinguish how to simultaneously generate augmentations on both graph topology and node features. Meanwhile, $\\mathcal{N}(0, \\mathcal{I})$ in the figure is inconsistent with the notations appearing in the main paper. \n3. In Table 2, the best results should be further highlighted. The current version is not intuitive. \n4. The caption of Table 4 is quite confusing. The authors fail to clarify that the datasets are heterogeneous graphs in the caption.", "other_comments_or_suggestions": "See above.", "questions_for_authors": "1. Why do the authors assume that the topological noise is a Bernoulli distribution? \n2. I cannot completely understand the meaning of Figure 3. How are the nodes visualized? t-SNE? Why does it only contain dozens of nodes? As we all know, there are thousands of nodes in a graph. The authors should clarify this in the rebuttal and the main paper. \n3. What’s the additional computational and space complexity? Will it lead to a significant burden on both computation and memory?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ahkGF1c9mB", "reviewer": "Reviewer_LdjD", "summary": "This paper proposes a novel method called PiNGDA for addressing the instability of traditional heuristic augmentation techniques in graph contrastive learning (GCL). The authors introduce the concept of π-noise, which is beneficial noise that reduces task complexity, and design a trainable noise generator to produce optimal perturbations in both graph topology and node attributes. Experimental results on graph benchmarks demonstrate superior performance compared to existing methods.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Reviewer LdjD**\n\nWe greatly thank you for the detailed and valuable comments. Please find our responses to the comments as follows:\n\n>**W1:** Innovation of application of $\\pi$-noise to GCL.\n\n**Reply:** Although $\\pi$-noise has been explored in other fields, its adaptation for graph data and integration within the GCL framework offers a unique perspective. The core challenge of π-noise—**how to define task entropy—remains highly difficult**, especially for **graph data**. This is not merely incremental work, but rather a fundamental challenge, which forms the core contribution of our research. Our work achieves **unified augmentations on both graph topology and node features within a theoretical framework**, which prior GCL methods have not been able to accomplish. This novel application allows us to leverage noise in a way that improves the quality of graph representations. \n\n>**W2:** Lacks detailed experimental settings.\n\n**Reply:**  Thank you for your suggestion. Our experiments are conducted on an NVIDIA 4090 GPU (24 GB memory) for most datasets and on an NVIDIA A100 GPU (40 GB memory) for OGB-arxiv. For our proposed method, we employ a two-layer GCN network with PReLU activation, where the hidden layer dimension is set to 512, and the final embedding dimension is 256. Additionally, we utilize a projection head, consisting of a 256-dimensional fully connected layer with ReLU activation, followed by a 256-dimensional linear layer. Edge noise generator uses an MLP to process node features and then applies Gumbel-Softmax sampling method. Feature noise generator uses two MLPs to estimate the mean and variance of feature noise and then uses the reparameterization trick. We appreciate your feedback and will ensure these details are clearly presented in the revised version.\n\n>**W3:** Compared to AD-GCL, PiNGDA does not show advantages in terms of time and space efficiency.\n\n**Reply:** Our method indeed introduces some additional computational overhead because we have two augmentation modules—one for graph structure and one for node features. This results in a slight increase in memory and time consumption. However, as shown in the table, this increase is not substantial, and more importantly, our method achieves significantly better performance, demonstrating its effectiveness.\n|Methods | Cora Mem.(M)|Time(s)|Acc(%) | PubMed Mem.(M)|Time(s)|Acc(%)|WikiCS Mem.(M)|Time(s)|Acc(%)|Amazon-Photo Mem.(M)|Time(s)|Acc(%)|\n|-|-|-|-|-|-|-|-|-|-|-|-|-|\n|AD-GCL(aug on graph only) |986|0.03|83.88|13632|0.22|84.23|9836|0.20|80.57|4768|0.14|91.92|\n|Ours(aug on graph & fea)|1070|0.04|86.25|15108|0.44|87.34|9704|0.21|82.07|4072|0.13|93.29|\n|Δ|84|0.01|+2.8%|1476|0.22|+3.7%|-132|0.01|+1.9%| -696|-0.01|+1.5%|\n\n\n>**C1&2&3:**  \n\n**Reply:** Thank you for your helpful suggestions. We will restructure Section 3 to improve readability by separating the discussion of existing research. Additionally, we will correct minor grammatical issues. To enhance reproducibility, we will also provide more details on the experimental settings. We appreciate your valuable feedback and will make the necessary revisions.\n\n>**Q:** How does PiNGDA compare to other baselines that also focus on adaptive or learnable graph augmentations, such as those mentioned in the \"Essential References Not Discussed\" section?\n\n**Reply:** \n\n| Method| CORA|CiteSeer| PubMed | Amazon-Photo| Coauthor-Phy|\n|-|-|-|-|-|-|\n| **GOUDA** | 82.25 ± 0.54| 70.25 ± 1.24| 85.82 ± 0.71| 89.61 ± 1.17| 94.54 ± 0.59 |\n| **GASSL** | 81.82 ± 0.79| 69.51 ± 0.84| 84.91 ± 0.57| 92.14 ± 0.23| 94.93 ± 0.21|\n| **Ours**  | **86.25 ± 0.25** | **72.44 ± 0.14** | **87.34 ± 0.08** | **93.29 ± 0.17** | **95.81 ± 0.06** |\n\nSince the official code for Paper 1 was not available, we replicated the results from the supplementary materials submitted with Papers 2 and 3 from OpenReview. The performance difference between the reported results and our replication could be due to the absence of specific hyperparameters in the papers. We base our results on our own replication.\n\nAlso, as suggested by **Review J7B2**, we also added PiNGDA to different GCL backbones and achieved good results. \n|| Cora| CiteSeer|PubMed| Amazon-Photo | Coauthor-Phy |\n|-|-|-|-|-|-|\n| **GRACE**| 83.43 ± 0.32 | 70.93 ± 0.21 | 85.90 ± 0.24 | 93.13 ± 0.17 | 95.74 ± 0.06 |\n| **GRACE+PiNGDA**  | **84.28 ± 0.24**| **71.47 ± 0.20**| **86.79 ± 0.27** | **93.19 ± 0.18**| **95.81 ± 0.05**|\n| **Sp²GCL**| 82.45 ± 0.35 | 65.54 ± 0.51 | 84.26 ± 0.29 | 93.05 ± 0.23 | 95.73 ± 0.04 |\n| **Sp²GCL+PiNGDA** | **83.89 ± 0.48**|**67.21 ± 0.63**| **84.73 ± 0.23** | **93.11 ± 0.14**| **95.74 ± 0.04**|\n \nOur method consistently outperforms existing approaches across all datasets, achieving significant improvements in accuracy. This demonstrates the effectiveness of our adaptive graph augmentation strategy, which better captures the underlying structure of the data and enhances model generalization.", "claims_and_evidence": "The authors claim that learning beneficial noise through a π-noise framework can provide a more reliable and stable augmentation strategy. This claim is supported by theoretical analysis and extensive experiments across multiple datasets.", "methods_and_evaluation_criteria": "The proposed PiNGDA consists of a π-noise generator and a contrastive learning module. The noise generator produces topological and attribute noise using a Gaussian auxiliary variable and reparameterization tricks to ensure differentiability. The model is evaluated using node classification accuracy and graph classification accuracy across several datasets.", "theoretical_claims": "The authors theoretically analyze the relationship between π-noise and the training loss in GCL. They show that predefined augmentations in existing GCL models can be considered as point estimations of π-noise, which may not always be reliable. By learning π-noise directly, PiNGDA provides a more robust approach to graph augmentation.", "experimental_designs_or_analyses": "Yes, I have checked the soundness of the experimental designs (including the compared methods and experimental setups) and analyses.", "relation_to_broader_scientific_literature": "1) The authors provide a novel perspective on GCL by analyzing it through the lens of the π-Noise framework. They elucidate why traditional random noise augmentation methods lead to unstable performance, which offers a fresh direction for future research in GCL.\n\n2) The proposed model demonstrates extensive applicability, achieving superior performance in both node classification and graph classification tasks.", "essential_references_not_discussed": "1) Spectral Feature Augmentation for Graph Contrastive Learning and Beyond, in AAAI 23\n\n2) Unified Graph Augmentations for Generalized Contrastive Learning on Graphs, in NeurIPS 24\n\n3) Graph Adversarial Self-Supervised Learning, in NeurIPS 21", "other_strengths_and_weaknesses": "**Strengths**\n\nThe ablation studies provide valuable insights into the impact of different augmentation strategies.\n\n\n**Weaknesses** \n\n1) The π-noise framework itself is not entirely novel, as it is based on existing research. The innovation lies in its application to GCL.\n\n 2)  The paper lacks detailed descriptions of some experimental settings, such as hardware environment and encoder choices, which may hinder reproducibility.\n  \n3) Compared to AD-GCL, PiNGDA does not show advantages in terms of time and space efficiency.", "other_comments_or_suggestions": "1) The organization of the paper could be improved. For example, separating the discussion of existing research in Section 3 would enhance readability.\n\n2) Minor grammatical issues, such as the lowercase \"where\" in line 19, should be corrected.\n\n  3)  The authors should provide more details on the experiments to ensure reproducibility.", "questions_for_authors": "How does PiNGDA compare to other baselines that also focus on adaptive or learnable graph augmentations, such as those mentioned in the \"Essential References Not Discussed\" section?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pSnqf4fHQO", "reviewer": "Reviewer_smN2", "summary": "This paper proposes a graph data augmentation method based on beneficial noise. The noise generator learns the optimal perturbation of graph structure and node features to solve the problem of insufficient stability of traditional data augmentation strategies in graph contrastive learning. Experimental verification shows that PiNGDA outperforms baseline methods in tasks.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Reviewer smN2**\n\nWe greatly thank you for the detailed and valuable comments. Please find our responses to the comments as follows:\n\n>**W1&Q1:** The theoretical analysis in Section 3.3 is interesting, but the definition of task entropy are unclear.The theoretical analysis in Section 3.3 is intriguing. However, I am unclear about the definition and role of task entropy. Could you provide a more detailed explanation or an example to clarify its significance?\n\n**Reply:** In our framework, **task entropy is used to measure the difficulty of a task**. The key idea is that adding noise can help simplify the task, which is quantitatively measured by the task complexity, making it easier for the model to learn meaningful representations. This aligns with our theoretical analysis, where learned beneficial noise can lead to better performance. We hope this explanation can answer your question and we would like to further clarify it if the concern is still well-addressed.\n\n>**W2&Q2:** The paper does not detail the hyperparameters used in the experiment, such as learning rate batch size, etc., which will affect the reproducibility of the research. While the experimental setup is well-documented, the hyperparameter settings are not explicitly detailed. Could you provide more information on these aspects, either in the main text or in supplementary materials?\n\n**Reply:** Thank you for your helpful suggestions. The hyperparameters were selected within the following ranges: For smaller datasets, we do not apply batch processing, for large datasets, we set the batch size of 256. The number of epochs varies from 500 to 2000 depending on the dataset. The learning rate is set between 0.0005 and 0.01, while the weight decay is kept constant at 0.0001 across all datasets. The feature dropout rates range from 0.0 to 0.3, and the edge dropout rates  vary between 0.1 and 0.4. The temperature is typically set to 0.3 for most datasets, with an exception for Coauthor-Phy, where it is set to 0.5. This is a simple description, the detailed version will be added later.\n\n>**Q3:** The computational efficiency in Figure 2 does not show much advantage of PiNGDA. Can you explain why this is the case and provide analyze of the complexity?\n\n**Reply:** The computational efficiency of PiNGDA may not appear significantly advantageous in Figure 2 because our method involves adding noise to all data points, which introduces additional computations. In the two noise generation modules, since each edge and each node feature is calculated by MLP, the computational complexity of the noise module is $\\mathcal{O}(\\mathcal{E} \\cdot d) + \\mathcal{O}(N \\cdot d)$, where N is the number of nodes, $\\mathcal{E}$ is the number of edges in the graph, and d is the dimension of the node feature. However, this process is crucial for improving the robustness and generalization of the model. To provide a more comprehensive comparison, we have included detailed memory-performance  analyses in the tables. Please refer to response to **Reviewer J7B2**.", "claims_and_evidence": "The paper presents experimental results to support its main claims. The authors verified the method's effectiveness on node classification and graph classification datasets. Additionally, an ablation study on the key noise generation module was conducted, enhancing understanding of the key module's contribution. Thus, the proposed conclusions are somewhat powerful and credible.", "methods_and_evaluation_criteria": "This paper presents a new augmentation method for graph contrastive learning. The proposed approach effectively tackles the recognized issues by integrating learnable augmentations into the contrastive learning framework. In contrast to traditional augmentation techniques like node and edge dropping, this method enriches representation learning through the introduction of beneficial noise.\n\nThe chosen evaluation criteria, which consist of standard benchmarks for node classification and graph classification, are appropriate for assessing the effectiveness and generalization ability of the proposed method. The employment of multiple evaluation metrics guarantees a comprehensive analysis of the model's performance.", "theoretical_claims": "The main theoretical assertions proposed in the paper have been proved mathematically. The author lists the assumptions and derives the conclusion. The derivation process is presented clearly.", "experimental_designs_or_analyses": "The experimental settings are reasonable. The inclusion of ablation studies further strengthens the analysis by isolating the contributions of different components.", "relation_to_broader_scientific_literature": "Previous graph contrastive augmentation methods included edge dropping and node dropping. Later GCL methods were developed based on these by introducing learnable dropping techniques.  This paper further expands on these approaches. It incorporates beneficial noise into contrastive learning, integrates these techniques into a unified framework, and proposes a new method.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n1. The main conclusion of the theoretical part is convincing. \n2. The experiments are somehow abundant, covering both node classification and graph classification tasks.\n3. The inclusion of ablation studies provides evidence for the effectiveness of different components of the method. \n\nWeaknesses:\n\n1. The theoretical analysis in Section 3.3 is interesting, but the definition of task entropy are unclear. \n2. The paper does not detail the hyperparameters used in the experiment, such as learning rate batch size, etc., which will affect the reproducibility of the research.", "other_comments_or_suggestions": "Please refer to the strengths and weaknesses.", "questions_for_authors": "1. The theoretical analysis in Section 3.3 is intriguing. However, I am unclear about the definition and role of task entropy. Could you provide a more detailed explanation or an example to clarify its significance?\n2. While the experimental setup is well-documented, the hyperparameter settings are not explicitly detailed. Could you provide more information on these aspects, either in the main text or in supplementary materials?\n3. The computational efficiency in Figure 2 does not show much advantage of PiNGDA. Can you explain why this is the case and provide analyze of the complexity?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "q129Q0EpkH", "reviewer": "Reviewer_J7B2", "summary": "This paper proposes a framework named Positive-incentive Noise driven Graph Data Augmentation (PiNGDA). It theoretically analyzes the drawbacks of the existing data augmentation in GCL and leverages a π-noise generator to learn beneficial noise as the augmentations for GCL. Meanwhile, they also design a differentiable algorithm to efficiently generate the noise. From the experimental results, PiNGDA achieves the highest performance compared to the current baselines.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Reviewer J7B2**\n\nWe greatly thank you for the detailed and valuable comments. Please find our responses to the comments as follows:\n\n>**W1&2&3&4:** The relationships between the proposed model and the learnable methods are not discussed in Section 1. The graph contrastive learning task should be introduced in more detail in Section 1. The connections and differences between PINGDA and some current GCL models based on learnable strategies should be discussed in details. In contributions, the authors should clarify the merits of the proposed model from the Pi-Noise perspective.\n\n**Reply:** Thank you for your valuable suggestions. Due to space limitations, we did not provide an in-depth discussion of these aspects in Section 1.  We will provide a more comprehensive introduction to the graph contrastive learning task in the revised version. Additionally, we will provide a more detailed introduction to the graph contrastive learning task to improve clarity and comprehensiveness. For the specific differences  with AD-GCL, please refer to the response to **Reviewer PRCX**.\n\n>**W5:** The authors could add the ablation study such as extending the proposed noise augmentations to more current GCL models.\n\n**Reply:** We have included the requested ablation study by extending our proposed noise augmentations to more GCL models. Specifically, we selected both a classical GCL model (GRACE [1]) and a more recent approach (Sp²GCL [2]) to demonstrate the effectiveness of our method. The results are summarized in the table below:\n\n|               | Cora         | CiteSeer     | PubMed       | Amazon-Photo | Coauthor-Phy |\n| ------------- | ------------ | ------------ | ------------ | ------------ | ------------ |\n| GRACE         | 83.43 ± 0.32 | 70.93 ± 0.21 | 85.90 ± 0.24 | 93.13 ± 0.17 | 95.74 ± 0.06 |\n| GRACE+PiNGDA  | 84.28 ± 0.24 | 71.47 ± 0.20 | 86.79 ± 0.27 | 93.19 ± 0.18 | 95.81 ± 0.05 |\n| Sp²GCL        | 82.45 ± 0.35 | 65.54 ± 0.51 | 84.26 ± 0.29 | 93.05 ± 0.23 | 95.73 ± 0.04 |\n| Sp²GCL+PiNGDA | 83.89 ± 0.48 | 67.21 ± 0.63 | 84.73 ± 0.23 | 93.11 ± 0.14 | 95.74 ± 0.04 |\n\nThese results highlight the impact of our augmentation approach across different GCL models.\n\n[1]Zhu, Yanqiao, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. \"Deep graph contrastive representation learning.\" *arXiv preprint arXiv:2006.04131* (2020).\n\n[2]Bo, Deyu, Yuan Fang, Yang Liu, and Chuan Shi. \"Graph contrastive learning with stable and scalable spectral encoding.\" *Advances in Neural Information Processing Systems* 36 (2023): 45516-45532.\n\n>**W6:** Apart from the Memory-Times experiments, Memory-Performance or FLOPs-Performance should be introduced to validate efficiency.\n\n**Reply:** The detailed tables are shown below. The results show how our method compares to existing baselines in terms of both computational cost and accuracy improvements. A negative value in ΔFLOPs or ΔMem. indicates **a reduction of our method** in computational cost or memory usage, while a positive value in ΔAcc% reflects our accuracy improvement over the respective method.\n\n| Methods | Cora ΔFLOPs (G) | ΔAcc% | PubMedΔFLOPs (G) | ΔAcc% | WikiCSΔFLOPs (G) | ΔAcc% | Amazon-Photo ΔFLOPs (G) | ΔAcc% |\n|-|-|-|-|-|-|-|-|-|\n| DGI| -3.27| +3.60 | -4.93| +2.61 | -0.50| +3.44 | -3.83| +4.81 |\n| GMI| -1.99| +3.17 | -5.06| +3.83 | -1.77| +2.60 | -2.93| +3.51 |\n| GCA | -0.71| +1.23 | -5.18| +0.31 | -3.04| +1.00 | -2.01| +0.11 |\n| BGRL| +0.33| +2.92 | +2.46| +2.03 | +1.45| +0.85 | +0.95| +0.11 |\n| GREET| -4.79| +7.18| -16.59| +1.48 | +0.72| +2.69 | -16.60| -0.34 |\n| GRACEIS | +0.53| +1.99 | +3.91| +3.30 | +2.33| +3.45 | +1.50| +2.22 |\n\n| Methods | Cora ΔMem. | ΔAcc(%) | PubMed ΔMem. | ΔAcc(%) | WikiCS ΔMem. | ΔAcc(%) | Amazon-Photo ΔMem. | ΔAcc(%) |\n|-|-|-|-|-|-|-|-|-|\n| DGI| -63.30%| +3.61%| -29.50%| +2.61%| -15.90%| +3.44%| -51.70%| +4.81%  |\n| GMI| -66.50%| +3.17%| -54.40%| +3.83%  | -36.70%| +2.60%  | -60.80%| +3.50%  |\n| GCA| -17.60%| +1.23%| -36.90%| +0.31%  | -51.20%| +0.99%| -58.60%| +0.11%|\n| GREET| -24.20%| +7.19%  | -61.10%| +1.48%  | -53.40%| +2.70%  | -55.50%| -0.34%  |\n| AD-GCL| +25.1%| +2.83%  | +12.6%| +3.69%  | +9.3%| +1.86%  | -14.60%| +1.49%  |\n\nOur results demonstrate that while some methods, such as GRACEIS and AD-GCL, achieve efficiency gains by significantly reducing FLOPs and memory usage, our approach **strikes a balance between efficiency and performance**.\n\n>**W7:** There are some typos. For example, in line 19, “. Where” should be “, where”. In Figure 3, it lacks explanations about the dashed line between two nodes.\n\n**Reply:** Thank you for your careful review. We will correct the typos. Regarding the dashed lines in Figure 3, they represent connections between nodes of different classes. We apologize for the unclear representation and will revise the figure or improve the explanation to ensure better clarity. We appreciate your valuable feedback and will make the necessary improvements.", "claims_and_evidence": "Yes. The authors design theoretical analyses of the proposed model and extensive experiments validate performance.", "methods_and_evaluation_criteria": "Yes. The proposed PiNGDA can quantify to learn the beneficial graph augmentations not random drop some nodes.", "theoretical_claims": "Yes. I have checked the theoretical proofs in Section 3 and Appendix A. They are correct.", "experimental_designs_or_analyses": "Yes. I have checked the experimental details in Section 5 and Appendix D. The results can validate performance.", "relation_to_broader_scientific_literature": "In this paper, the authors theoretically analyze the drawbacks of the existing data augmentations and propose a novel PiNGDA to differentiable learn the beneficial graph augmentations.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "## Strengths:\n1) The authors propose an interesting framework to directly learn the beneficial noise augmentations. After all, the noise generally is regarded as the harmful signal.\n2) The theoretical analysis is logical, and the paper is well-organized to follow.\n\n## Weaknesses:\n1) The relationships between the proposed model and the learnable methods are not discussed in Section 1.\n2) The graph contrastive learning task should be introduced in more detail in Section 1.\n3) In contributions, the authors should clarify the merits of the proposed model from the Pi-Noise perspective.\n4) The connections and differences between PINGDA and some current GCL models based on learnable strategies should be discussed in details.\n5) The authors could add the ablation study such as extending the proposed noise augmentations to more current GCL models.\n6) Apart from the Memory-Times experiments, Memory-Performance or FLOPs-Performance should be introduced to validate efficiency.\n7) There are some typos. For example, in line 19, “. Where” should be “, where”. In Figure 3, it lacks explanations about the dashed line between two nodes.", "other_comments_or_suggestions": "No.", "questions_for_authors": "I hope the authors can state the generalization of the proposed model. For example, does it improve the performance on other new GCL models or graph tasks? (Please see Weakness 6)", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ls6ARCaegU", "reviewer": "Reviewer_iJqw", "summary": "The paper proposes a graph contrastive learning method called Positive-incentive Noise driven Graph Data Augmentation (PiNGDA), which makes the model learn to generate perturbations that benefit the training. Comprehensive experiments are conducted to evaluate the performance of the method.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Reviewer iJqw**\n\nWe greatly thank you for the detailed and valuable comments. Please find our responses to the comments as follows:\n\n>**W1&W2:** As is mentioned in 'Experimental Designs or Analyses', the detailed hyperparameter of the training is not listed. Moreover, as is mentioned in Figure 2, the model can be trained with a batch size to decrease memory burden, which is not discussed in Table 1, where some methods report OOM on some datasets.\n\n**Reply:** Thank you for your valuable feedback. We will add detailed hyperparameter settings to improve clarity and reproducibility. Regarding batch size and memory efficiency, all **GCL methods were trained using the same batch size** to ensure a **fair comparison**. For smaller datasets, we do not apply batch processing, for large datasets, we set the batch size of 256. Our experiments are conducted on an NVIDIA 4090 GPU (24 GB memory) for most datasets and on an NVIDIA A100 GPU (40 GB memory) for OGB-arxiv. However, we recognize that this was not explicitly stated in Table 1. We will update Table 1 with a clarification that all methods follow the same batch size setting and discuss the impact of batch size adjustments on memory consumption. We appreciate your insightful comments and will revise the paper accordingly.\n\n>**Q1:** JOAO is mentioned as 'learnable' in Table 1. However, to the best of my knowledge, JOAO randomly selects augmentation methods, which are all randomly applied. The projection head of each augmentation method differs.\n\n**Reply:** Thank you for your insightful comment. While **JOAO does not learn augmentations directly**, it does **adaptively select** augmentation strategies based on a similarity-based policy. Referring to it as \"learnable\" in Table 1 may not be the most accurate description. Instead, \"adaptable\" better captures its mechanism. We will revise it in the paper and provide a clearer explanation of this distinction.\n\n>**Q2:** The further discussion of 2.3 is placed in Appendix C after the detailed discussion of 3.3 and 4.2, which is kind of disordered.\n\n**Reply:** We appreciate your feedback regarding the structure of the paper.  We will reorganize the content to ensure a more intuitive and coherent presentation. Thank you for your valuable suggestion!\n\n>**Q3:** The performance of the method on Wiki-CS in Table 2 is different from that in Table 1, why? The difference also appears between Table 7 and Table 3.\n\n**Reply:** Thank you for your question. The differences in performance  arise because Table 1 and Table 3 report the best results, while in the ablation study, we re-run the experiments to ensure a **fair comparison** across different settings. The results in the ablation study reflect newly obtained experimental outcomes under controlled conditions. \n\n>**Q4:** The results of the ablation study are kind of hard to read. Maybe the average value of columns and rows can be added to better show the trend of difference between w/o Aug., Random, and Learnable.\n\n**Reply:** Thank you for your helpful suggestions. We will update Table 2 to better highlight the best results for improved clarity.\n\n>**Q5:** Can the attribute noise also be visualized?\n\n**Reply:** Thank you for your insightful suggestion. Similar to our response to  Reviewer PRCX, visualizing **attribute noise** is challenging because **node representations are high-dimensional** and lack the structured spatial relationships found in visual data. Even if represented as a **matrix or heatmap**, the absence of spatial correlations between adjacent values could lead to **misleading interpretations**.", "claims_and_evidence": "Yes.\n\nThe claims of the effectiveness and efficiency of the method are supported by experiments. \nThe theoretical claim that \"the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation\" is proved with mathematical derivation based on information theory.", "methods_and_evaluation_criteria": "Yes.\n\nThe performance of the proposed PiNGDA, as a GCL method, is evaluated in several aspects, including node classification, graph classification, node classification on heterogenous graphs, efficiency, visualization, and ablation study.", "theoretical_claims": "Yes. \n\nAn auxiliary variable is introduced to prove the theoretical claim (Eq. (13)). The proof is correct and rigorous.", "experimental_designs_or_analyses": "All the experimental designs and analyses are checked. Comprehensive experiments are conducted to evaluate the proposed method's performance.\n\nHowever, the detailed hyperparameter of the training is not listed. \n\nMoreover, as is mentioned in the caption of Figure 2, the model can be trained with a batch size to decrease memory burden, which is not discussed in Table. 1, where some methods report OOM on some datasets.", "relation_to_broader_scientific_literature": "The paper proposes a novel method that learns to generate augmented views, other than the adversarial method (AD-GCL). With a similar computational and time burden to AD-GCL, the proposed method achieves better performance than AD-GCL on most node classification and graph classification tasks, including higher accuracy and lower standards, indicating its effectiveness and stability.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "S1: According to the results of experiments, the effectiveness and stability of the method are validated comprehensively.\n\nS2: According to the visualization, the proposed method tends to remove inter-class edges while maintaining intra-class edges, which is a common strategy applied in supervised learning.\n\nW1&W2: As is mentioned in 'Experimental Designs or Analyses', the detailed hyperparameter of the training is not listed. Moreover, as is mentioned in Figure 2, the model can be trained with a batch size to decrease memory burden, which is not discussed in Table 1, where some methods report OOM on some datasets.", "other_comments_or_suggestions": "No.", "questions_for_authors": "Major questions: Please see weaknesses.\n\nHere are some tiny questions:\n\n1. JOAO is mentioned as 'learnable' in Table 1. However, to the best of my knowledge, JOAO randomly selects augmentation methods, which are all randomly applied. The projection head of each augmentation method differs.\n\n2. The further discussion of 2.3 is placed in Appendix C after the detailed discussion of 3.3 and 4.2, which is kind of disordered.\n\n3. The performance of the method on Wiki-CS in Table 2 is different from that in Table 1, why? The difference also appears between Table 7 and Table 3.\n\n4. The results of the ablation study are kind of hard to read. Maybe the average value of columns and rows can be added to better show the trend of difference between w/o Aug., Random, and Learnable.\n\n5. Can the attribute noise also be visualized?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: Thank you for submitting your work to ICML 2025, and for your efforts in the rebuttal phase to clarify the reviewers' concerns. 
However, the current version fails to provide a theoretical and experimental comparison with some methods. The lack of detailed experimental settings may also hinder reproducibility. Additionally, the authors should include a deeper analysis of the experimental results. After reading the reviewers' comments and the authors' responses, I believe the authors can effectively address these issues in the camera-ready version. Since all the reviewers affirmed the novelty of the authors' work, I therefore recommend acceptance of the paper.
Decision: Accept (poster)