DropEdge not Foolproof: Effective Augmentation Method for Signed Graph Neural Networks
Authors: Zeyu Zhang
Lu Li
Shuyan Wan
Sijie Wang
Zhiyi Wang
Zhiyuan Lu
Dong Hao
Wanli.Li
Venue: NeurIPS 2024 poster (2024)
Keywords: Graph Neural Networks
Signed Graph Neural Networks
Graph Data Augmentation
Stability
Generalization Guarantees
Primary area: graph_neural_networks
TL;DR: A novel signed graph augmentation method

Abstract: Signed graphs can model friendly or antagonistic relations where edges are annotated with a positive or negative sign. The main downstream task in signed graph analysis is $\textit{link sign prediction}$. Signed Graph Neural Networks (SGNNs) have been widely used for signed graph representation learning. While significant progress has been made in SGNNs research, two issues (i.e., graph sparsity and unbalanced triangles) persist in the current SGNN models. We aim to alleviate these issues through data augmentation ($\textit{DA}$) techniques which have demonstrated effectiveness in improving the performance of graph neural networks. However, most graph augmentation methods are primarily aimed at graph-level and node-level tasks (e.g., graph classification and node classification) and cannot be directly applied to signed graphs due to the lack of side information (e.g., node features and label information) in available real-world signed graph datasets. Random $\textit{DropEdge} $is one of the few $\textit{DA}$ methods that can be directly used for signed graph data augmentation, but its effectiveness is still unknown. In this paper, we first provide the generalization bound for the SGNN model and demonstrate from both experimental and theoretical perspectives that the random $\textit{DropEdge}$ cannot improve the performance of link sign prediction. Therefore, we propose a novel signed graph augmentation method, $\underline{S}$igned $\underline{G}$raph $\underline{A}$ugmentation framework (SGA). Specifically, SGA first integrates a structure augmentation module to detect candidate edges solely based on network information. Furthermore, SGA incorporates a novel strategy to select beneficial candidates. Finally, SGA introduces a novel data augmentation perspective to enhance the training process of SGNNs. Experiment results on six real-world datasets demonstrate that SGA effectively boosts the performance of diverse SGNN models, achieving improvements of up to 32.3\% in F1-micro for SGCN on the Slashdot dataset in the link sign prediction task.

DropEdge not Foolproof: Effective Augmentation Method for Signed Graph Neural Networks
Zeyu Zhang 1., Lu Li², Shuyan Wan', Sijie Wang
Zhiyi Wang". Zhiyuan Lu", Dong Hao Wanli Li
Engineering Research Center of Intelligent Technology for Agriculture, Ministry of Education
"College of Informatics, Huazhong Agricultural University, Wuhan, China The University of Auckland, 'University of Electronic Science and Technology of China zhangzeyudmail hzau. edu. cn, 1u123@vebmail aazzu.eedu en, wanshuyanzzz0163. com, @wan3870auck1 anduni ac nz, 1492487431@qq com, 19537647600qq com, haodongduestc. edu, cn, wwt.llllwwmmmm hzau. edu. cn
Abstract
Signed graphs can model friendly antagonistic relations where edges anno- tated with a positive or negative sign. Signed Graph Neural Networks (SGNNs) have been widely used for signed graph representation learning. While signifi- cant progress has been made SGNNs research, two issues (i.e., graph sparsity and unbalanced triangles) persist in the current SGNN models. We aim allevi- ate these issues through data augmentation (DA) techniques which have demon- strated effectiveness in improving the performance of graph neural networks. However, most graph augmentation methods are primarily aimed at graph-level and node-level tasks (e.g., graph classification and node classification) and can- not be directly applied to signed graphs due to the lack of side information (e.g.. node features and label information) available real-world signed graph datasets. Random DropEdge is one of the few DA methods that can be directly used for signed graph data augmentation, but its effectiveness is still unknown. paper, we are the first to provide the generalization error bound for the SGNN model and demonstrate from both experimental and theoretical perspectives that the random DropEdge cannot improve the performance of link sign prediction. Therefore, we propose a novel Signed Graph Augmentation framework (SGA) tailored for SGNNs. Specifically, SGA first integrates a structure augmentation module to detect candidate edges solely based on network information. Further- more, SGA incorporates novel strategy to select beneficial candidates. Finally, SGA introduces a novel data augmentation perspective to enhance the training process of SGNNs. Experiment results on six real-world datasets demonstrate that SGA effectively boosts the performance of diverse SGNN models, achieving improvements of up 26.2% in F1-micro for SGCN the Slashdot dataset in the link sign prediction task. Code and data are available at https::/githubb.cmm com//lex- Alex- Zeyu/SGA.
this
Introduction
As social networks continue to gain widespread popularity, they foster a multitude of interactions
among individuals, which are later documented within social graphs [1, 2]. While many of these social interactions denote positive connections, such as liking, trust, and friendship, there are also
Coorespondingg Author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

---

instances of negative interactions, encompassing feelings of hatred, distrust, and more. For exam- ple, Slashdot [3]. tech-related news website, allows users tag other users as either 'friends' or "foes'. Graphs that incorporate positive and negative interactions or links are commonly termed signed graphs [4, 5]. In recent years, there has been growing interest among researchers in ex- ploring network representation within the context of signed graphs [6-8]. Most of these methods are combined with Graph Neural Networks (GNNs) [9. 10), and are therefore collectively referred to as Signed Graph Neural Networks (SGNNs) [11, 7, 12, 13J. This endeavor focuses on acquiring low-dimensional representations of nodes, with the ultimate goal of facilitating subsequent network analysis tasks, especially link sign prediction.
Despite increasing interest in SGNNS in recent years, two issues remain unresolved. First, real-world signed graph datasets are exceptionally sparse (see Table from Ap- pendix H). The sparsity of signed graphs makes down- stream tasks challenging. As shown Issue 1 (from Fig- ure 1), without additional structure information side in- formation, predicting the edge sign between nodes v; and vn in the test set is difficult. However, this changes with the introduction of extra edges (ex) through data augmen- tation. Second, according the analysis in [14], SGNNs cannot learn proper representations for nodes from unbal- anced triangles. The intuitive understanding is follows: as shown in Issue 2(c) (from Figure 1), there is a nega- tive relationship between node V; and node Uy in one- hop path, while through a two-hop path via node Uk. it becomes positive relationship. In other words, the rela- tionship between node o; and node 2y is uncertain, which complicates the task of SGNNs in learning representa- tions for these three nodes. Furthermore, we notice that the proportion of unbalanced triangles considerable (see Table 3).
Origral Grop
[i
[
Auprented Gropl
Trioegies
Untolaneed Thlonges
Ioree
Iorue 2
Green and red lines represent positive and negative edges, resp. Solid lines represent edges in the training set, while dashed lines represent edges in the test set.
Figure 1:
One promising approach to alleviate the aforementioned issues in SGNNs is data augmentation (DA) which has been well studied in computer vision [15-18] and nat- ural language processing [19-21]. Recently, significant advancements have been made in graph augmentation [22-24], including node perturbation [25, 26), edge per- turbation [27]. and subgraph sampling [28]. However, current graph augmentation methods cannot be directly applied to signed graphs for the following reasons: 1) Some methods [22, 23] require side information (e.g.. node features and labels), which are often absent in real- world signed graph datasets that contain only structural information. 2) Random structural perturbation-bun based en- hancement methods [27, 8, 29] cannot improve SGNN performance. As shown in Figure 2, random EdgeDrop cannot stably improve SGCN performance. For more ex- perimental results on data augmentation methods based on random structural perturbations, please refer to the Ap- pendix A. In addition, models and deriving the generalization error bound of the SGCN. Based on this analysis, we further demonstrate that randomly deleting edges increases the generalization error bound of SGNN, and therefore it is not an effective enhancement method for SGNN (see Section 4). In summary, it is necessary to design a new DA method specifically for SGNNs.
Bissio
Sadsll
0.75
0.70
455
450
Eage Delttion Ralio
Figure 2: Effectiveness of random EdgeDrop (SGCN [11] backbone model) on link sign prediction perfor- mance with six real-world signed graph datasets.
take first step in developing deeper theoretical understanding of SGNN
Overall, the designed signed graph augmentation method should address the two common obstacles encountered by popular SGNN models:
1. Exploring new structural information using only network information.
2. Alleviate the negative impact of unbalanced triangles on SGNNs.

---

To address the aforementioned obstacles, we propose a novel Signed Graph Augmentation frame- work, SGA. For the first obstacle, we use a classic SGNN model, such as SGCN [11] discover candidate samples. The nodes of a signed graph are first projected into the embedding space. In the embedding space, following the principles of the extended structural balance theory [30], we interpret the relationships between closely proximate nodes as potential positive edges, whereas the relationships between more distant nodes are considered as potential negative edges. The newly added edges are treated candidate samples (i.e., edges). To overcome the second obstacle, ap- proach it from two perspectives. Foremost, we attempt to reduce the number of existing unbalanced triangles. The candidate samples yield two outcomes: creating new edges or modifying the sign of existing edges. These operations do not reduce the number of training samples, which is consistent with the results of the theoretical analysis (see Sect. 4). Instead of directly incorporating the can- didate samples into the training set, we analyze them beforehand. Only candidate samples that do not introduce new unbalanced triangles are retained. Next, aim to reduce the training weight of edges that helong to unbalanced triangles. To achieve this, we introduce a new perspective on data augmentation, namely edge difficulty scores (see Def. 3.3). Based on this, we design curriculum learning training strategy tailored for SGNNs, aiming to decrease the training weight of edges with high difficulty scores and increase the training weight of edges with low difficulty scores.
To evaluate the effectiveness of SGA, we perform extensive experiments on six worldworld datasets, L.c Bitcoin-alpha, Bitcoin-otc, Epinions, Slashdot, Wiki-elec, and Wiki-RfA. We verify that our proposed SGA framework can improve the performance of the baseline models. The results of the experiment show that SGA improves the accuracy of the prediction of link signs of five base models, including two unsigned GNN models (GCN [9] and GAT' [31]) and three signed GNN models (SGCN [1 J, SiGAT [32] and GS-GNN [13]) (see Table 1 and Table 6). SGA boosts up to 14.8% in terms of AUC for SGCN on Wiki-RfA, 26.2% in terms of F1-binary, 32.3% in terms of Fl-micro, and 24.7% in terms of Fl-maero for SGCN on Slashdot in link sign prediction, at best. These experiment results demonstrate the effectiveness of SGA.
Limitations. Our data augmentation method utilizes the conclusions from SGNN representation limitation based on balance theory [14]. However, it is well known that balance theory cannot model all signed graph formation patterns, discussed in the paper [13]. Therefore, for real- world datasets that do not strongly conform to balance theory, our data augmentation may be less effective. Additionally, we have only validated our method on the primary downstream task of link sign prediction in signed graphs. Some works [33, 34] consider the clustering task for signed graphs, but these primarily use synthetic datasets and there are real-world datasets available yet, which is why we have not conducted tests on them.
Overall, our contributions are summarized as follows:
We are the first to provide the generalization error bound for the SGNN model. Based on this, we theoretically demonstrate the random DropEdge method, which is suitable for node classification and graph classification, is not applicable edge-level task (i.e., link sigm prediction).
We propose a novel signed graph augmentation framework that alleviates the two issues (i.e., sparsity and unbalanced triangles) widely existing in SGNNs.
Extensive experiments on six real-world datasets with five backbone models demonstrate the effectiveness of our framework.
2 Problem Statement
signed graph is defined as G = (V,E+,E-) where (ui,..., } represents the set of nodes, and + and 8- denote the positive and negative edges, respectively. Each edge eij E g+ U E- connecting two nodes and ey can be either positive or negative, but not both, meaning that E+ EE = 2. We use (ee,) E -} to denote the sign of ezy. The structure of & is represented by the adjacency matrix A E | where each entry Aij E {1, - -, signifies the sign of the edge eij- It's important to note that, unlike unsigned graph datasets, signed graphs typically do not provide node features, meaning there is no feature vector I; associated with each node U,,
Positive and negative neighbors of U; are denoted as V = {o; Ag > 0} and = {uz Aij < 0}, respectively. Let N,- = N, UN, be the set of neighbors of node us- Og represents the set of
3

---

Generate candidates
Select beneficial candidates
Introduce new features for for-ugg Derain
Predict labels
True labels
Train Danann
Candidate samples
Updated Direis
Difficuity scores of edges
Figure 3: The overall process of SGA. Green lines represent positive edges and red lines represent negative edges.
triangles in the signed graph, i.e., O3 = (for, Ug, AnA + 0}. A triangle (2t, Vj vk is called balanced if Ask-AAAAss > O, and is called unbalanced otherwise.
Problem Definition: Diain refers to the of train samples (edges) and Dies refers the set of test samples. When only given Dunin, our purpose is to design a graph augmentation strategy vb (Dunin) (Dini F), where Dimin refers augmented train edge set and F refers to the newly generated edge features (i.e., edge difficulty score).
3 Proposed Method
The overall framework of SGA is shown in Figure 3, which aims to augment training samples (i.e., edges) from a structure perspective (edge manipulation) mainly encompasses three key elements: 1) generating new training candidate samples, 2) selecting beneficial candidate samples, and 3) introducing a new feature (i.e., edge difficulty score) for training samples. For the specific procedural details of each part, please refer to Appendix C.
side information (edge feature). SGA
3.1 Generating Candidate Training Samples
Real-world signed graph datasets are extremely sparse (see Table 2) with many uncovered edges. In this part, we attempt uncover the potential relationships between nodes. We first use a SGNN model, e.g., SGCN [11], as the encoder to project nodes from topological space to embedding space. Here, the node representations are updated by aggregating information from different types of neigh- bors as follows:
For the first aggregation layer f = 1:
( = (Wrro(1)) [At (o (loe
(I)
g (woea()) 000) H0ol
For the aggregation layer l
Hoos(() =o (Worostt) A 1ooate-1) A
@)
Hmsa(() =a (wwnet(() + Hmeatt-1), A
where (F)s(E) (f) represents the positive (negative) segment of representation matrix at the Eth layer. A+ 4+(A)) represents the row normalized matrix of the positive (negative) part of the adja- cency matrix A. WPos(() (Wnen(()) denotes learnable parameters of the positive (negative) part, and (.)) the activation funetion ReLU. [-] is the concatenation operation. After conducting message- passing for L layers, the final node representation matrix is Z HLL) [HPoo(L), Hmee(L)]. For node vt, the node embedding is 2,. As we wish to classify whether pair of nodes has positive, negative, or no edge berween them. We train multinomial logistic regression classifier (MI.) (as in [1]]). The training loss is as follows:

---

exp (IZ,, 2,] (a(mss)
e (OMLLC)
1
Σ
log
(3)
train
-ee(+.-23 23 exp (1Z:: 23) OMLG)
(Mo0yin(013))) )) Pasin
MLG refers to the parameter of the MI.G classifier. Using this classifier, for any nodes Ui, U/j can calculate the probability of forming a positive or negative edge between any two nodes, denoted as Pres and Pr We set up four probability threshold mlyperparameters, namely the probability threshold for adding positive edges (Eada). the probability threshold for adding negative edges (Fada), the probability threshold for deleting positive edges (Cde) and the probability threshold for deleting negative edges de Subsequently, we employ the following strategy to generate candidate training samples:
Vo,,es E V. Vf Prep Codd V Preff Sada- then Doum add U [(vi, Vy a(e))))
Ver,e E V. (vi, U5 (ess)) Dusin, Aij > 0, Preig cd then dain U {(u,, Uy (e:;)))
v, E V. if (vt, Uy, ((es)) E Doin, Asy- < 0, Praty
< Cet. then Deminte {(v, Uy, o(,,))
Deand rain_add and Deand drain_del refer to the candidate training set for adding edges and the candidate training set for deleting edges.
3.2 Selecting Beneficial Candidate Training Samples
After obtaining candidates, we do not merge them into the training set directly. Instead, we select the beneficial portions based on some rules. According [14], it proves SGNNs cannot learn proper representations from unbalanced triangles (see Figure 1). The intuitive insight from this conclusion for signed graph augmentation is that beneficial candidates should not lead new unbalanced tri- angles. Therefore, after generating candidate training set Deand add and Dean del- we need to discern which operations are beneficial or not. Considering that removing edges will not introduce new unbalanced triangles, it can be directly applied to the training set. However, adding edges may po- tentially introduce unbalanced triangles, so it needs be analyzed whether it should be applied to the training set. The specific criteria are as follows:
v (w,, ug. E Deand craindde: Drsin \ ((Vs, ((s.,)
V
Diand if (vi, (1,, ((eo))
Drins and Vee
Ns n N₁.
(a(e;) a(eax) * (ej+)) then Diain U [(vi, uy o ((s)))).
According to the above steps, we have merged the Deand.
add and Deand
dain into the training set Dusin-
3.3 Introducing New Feature for Training Samples
In this part, we attempt to alleviate the negative impact of unbalanced triangles SGNNs from another perspective by augmenting a new feature for training samples (i.e., edges). namely edge difficulty score. Intuitively, edges belonging to unbalanced triangles have higher difficulty scores, while those belonging to balanced triangles have lower difficulty scores. Based on the difficulty scores, we design a curriculum learning- based training plan, aiming to reduce the training weights of edges with high difficulty scores, thereby mitigating the negative impact of unbalanced triangles on SGNNs.
We provide a definition of global and local balance degree:
Definition 3.1. The Global Balance Degree [35] of signed graph is defined by:
10
D2
(4)
[Os]
where O3 represents the set of triangles, O represents the set of balanced triangles. |- the set cardinal number. Definition 3.2 (Local Balance Degree). For edge Ciy, the local balance degree is defined by:
represents
Da(en) = O0 (ex) 10 (e.,) 0 (eg) 00 (e:))
(5)
5

---

where Oj (ey)) (Og (ety) represents the set of balanced (unbalanced) triangles containing edge eij- |- represents the set cardinal number.
From Def. 3.2, we can observe that the edge's local balance degree is related to the count of balanced and unbalanced triangles that include this edge. Based on this, we can define the edge difficulty score:
Definition 3.3 (Edge Difficulty Score). For edge Cij. the difficulty score defined by:
Score(esy) 1 Dz(es)
where Dy((i)) denotes the local balance degree of edge Vij-
Upon quantifying the difficulty scores for each edge within the training set, a curriculum-bars -bsse training approach is applied to enhance the performance of the SGNN model. This curriculum is fashioned following the principles outlined in [36], which enables the creation of structured pro- gression from easy to difficult. The process entails initially sorting the training set & in ascending order based on their respective difficulty scores. Subsequently, a pacing function g(() is used to al- locate these edges to distinct training epochs, transitioning from casier to more challenging samples, where t signifies the t-th epoch. use linear pacing function shown below:
s(() = min L, Ao + (1 Ao) T)
Ao denotes the initial proportion of the easiest examples available, and T indicates the training epoch which gt) reaches value 1. The process of SGA is detailed in Appendix D.
4 Generalization Bound of SGNN
In this section, we are going to prove the generalization eтror bound for SGNN. Our results show that the generalization performance of the model affected by the number of edges. A larger number of edges in the training set usually generalizes better, which means that dropout cannot always contribute improving the model's generalization ability in many situations. For the basic setup and assumptions, please see the Appendix E.
Main Result. Under link prediction task, we denote Ad learning algorithm trained on dataset D. According to Algorithm 2, we can set AD a of ži "),w)); w)), the generalization gap is defined as the difference between training error and test error:
8 ggen EA(R (ADrraun) R(AD...))
(8)
1
8 gge
I VT
[.,0
-.
(9)
74
Theorem (Generalization Gap of SGNN).
8 gen S 20 22,0,M3(0 + tmaja a
(10)
n4.
Here B refers to the infinite norm of the matrix Z 0 refers to paradigm of initial weight matrix |[wsssel-- R() is the eитоr function and is the loss function. The generalization ability mainly influenced by scale of the graph(the number of nodes and edges) and the norm of weights matrix. In the main result, is the number of iterations in training, ela is the learning rate, az, Oy,, M are constants determined by the non-linear activation function, function g and function f respectively.
5 Experiments
In this section, we commence by assessing the enhancements brought about by SGA in comparison to diverse backbone models for the link sign prediction task. We will answer the following questions:
Q1: Can SGA improve the performance of backbone models? Does SGA effectively alleviate issues related to graph sparsity and the presence of unbalanced triangles?

---

Table 1: Link sign prediction results (average + standard deviation) with AUC (%) and F1 F1-binary
(%) on six benchmark datasets.
Ppiniom
Metheds
AUC
Fi
AUC
Fl.
ALC
FL
F1-binzyy
ADC
Fl.bisary
MFC
Fl-binary
16.61077
733320
+9GA
651222
767439
07
168
688:2033
506200
51.24:17
62.--98
6691008
77.54406
635-209
74.72099
698-1
01151
-1.35
13.7%
1.2%5
500
1.5%
603222
613199
0822113
16
531217
6811118
51:2118
74:767
5674231
66-21114
518
71.3244.6
+SGA
63.0245
869825
71.7814
90.0334
614333
808:66
55.2821
586::19
58,58200
72.43499
5344:06
09.923377
(mpoos.
4.5
37.5%
5.1
4.7%
15
18.7%
7.85
4.4%
7.0% 1
8.6%
3.8
3,256
SOUN [11]
15.320
994512
123
086244
5U5
01
0133233
10.2331
S1
653:22
TIREET
+SGA
80.020
82.13503
0..
724304
9222300
65
45.021.0
774809
87.000777
15.:006
65.5
Oappess
7.5%
2.5%
3.4 1
2.5%
12.9%
19%
12.6% 1
26.2%
10.3%
69% 1
14.8%
18.2%
S6dM (22)
4555200
68.32100
065:02
1013003
5522001
$4.52001
85253011
9032350
$111001
+SEA
818289
96 71
511300
89 111
911111
$60
404
(mppons
3.39
0.7
21%
0.19
2.43
01%
13.1
1
01511
18.1
ISGNNN
11111
03
188304
883161
56
907211
596205
910000111
(Ippors)
0.18
099
Table 2: Density of original graph and after augmentation.
Dataset
Bitcoin-alpha
Bitcoin-ote
Epinions
Slashdot
Wiki-elec
Wiki-RFA
Original
1.45e-3
8.92e-4 9.26ic4
4.81e-5
7.55e-5
1889--3 3.41e-3
1.29e-3
+SGA
1.59c-3
7.29c-5
1.16c-4
1.81e-3
Q2: Does each part of the SGA framework play positive role?
Q3: Is the proposed method sensitive to hyper-parameters? How do key hyper-paramette impact the method performance?
For an introduction and statistical information on the datasets, please refer to the Appendix H. For details on baselines and experimental settings, please also see the Appendix I.
5.1 Performance Evaluation (Q1)
To comprehensively evaluate the performance of our proposed SGA, we contrast with several baseline configurations that exclude SGA integration on link sign prediction. For a detailed view, AUC and Fl-binary score results are presented in Table 1. Further, F1-macro and F1-micro can be referenced in Appendix J. For each model, the mean AUC and Fl-binary scores, along with their respective standard deviations, are documented. These metries are derived from five independent runs on each dataset, utilizing distinct, non-overlapping splits: 80% of the edges are used for train- ing, while the residual 20% serve as the test set. Additionally, the table elucidates the percentage improvement in these metrics attributable to the integration of SGA, relative to the baseline models without SGA. The results provide several insights:
Our investigations affirm that the SGA framework serves as an effective method in aug- menting the performance of both signed and unsigned graph neural networks.
For unsigned GNN models (GCN, GAT), the SGA method can effectively enhance the predictive performance (Some metries show an improvement of over 10%.), possibly be- cause both signed GNN and unsigned GNN models are based on a similar peessag--asssngg mechanism.
Concerning the signed GNN models (SGCN, SiGAT, GS-GNN), observed that SGA significantly enhances SGCN SiGAT compared to GS-GNN. The reason for this might be that SGA primarily focuses on mitigating the impact of unbalanced triangles on the model's predictive performance. Both SGCN and SiGAT are designed based on balance theory, making them more susceptible to the influence of unbalanced triangles, whereas GS-GNN is not, and therefore, it is less affected by unbalanced triangles. This indirectly reflects that SGA indeed alleviates the negative impact caused by unbalanced triangles to some extent.
Next, we will verify whether SGA effectively addresses the two issues in signed graph representa- tion learning based on SGNN. Regarding the dataset density, we conducted a statistical analysis, as shown in Table 2. From the statistical results, it can be observed that after augmentation through the SGA method, the density of all six real-world datasets has increased, indicating certain improve- ment in data sparsity issues.
7

---

Table 3: The balance degree of original datasets and after augmentation. BT refers to balanced triangle, UT refers unbalanced triangle, BD refers to balance degree (see Def. 3.1).
Original RUT
+SGA
Dataset
(1))
FUT
(D((%)
Bilcoin alpha
52,126
6,971
$8.20
63.535
5,060
92.58
Bitcoin-otc
73,460
9.292
89.04
72,105
9,289
88.60
Epinions
6,286,577
516,723
92.40
6,162,877
391,707
94.02
Slasbdot
709,417
64,190
91.70
676,378
45,268
93.72
92,934
242,691
29.579
Wiki-Re RÉA
603.753
195,532
75.54
494,458
84,840
85.38
SGCN
SGON-SGA
SGCN
SGAN
Wrong Prediction
Correct Prediction
Wrong Prediction
Correct Prediction
Case
Case
Figure 4: Case Study of SGA. Note that green lines denote positive edges and red lines denote negative edges.
Regarding unbalanced triangles, we conduct a statistical analysis, as shown in Table 3. The calcula- tion of balance degree is based on Definition 3.1. From the statistical results, it can be seen that in most cases, SGA indeed reduces the number of unbalanced triangles, improving the balance degree of real-world datasets.
In addition to the statistical results, we also validated the effectiveness of SGA through the case study illustrated in Figure 4. Both of these two cases from Bitcoin-alpha dataset. Case verifies that SGA, by exploring latent structures, assists SGCN in correctly predicting the sign of edge (5144,130+ 1130,147) that originally mispredicted. Case 2 indicates that SGA, by changing the signs of edges (667,12) in existing structures, reduces the impact of unbalanced triangles, allowing the model achieve correct prediction results (667,1536).
5.2 Ablation Study (Q2)
In this section, we explore how different parts of SGA, contribute its overall effectiveness. We do this by testing the SGCN [11] under various settings:
SGCN: Here, we use the SGCN its basic form. works directly on the original graph data without any additional techniques or modifications.
+SA (Structure Augmentation, refer to Sec. 3.1 and Sec. 3.2): SGCN operates on augmented datasets. This augmentation involves the addition removal of edges from the initial graph.
+TP (Training Plan, refer to Sec. 3.3): SGCN runs on the original graph but with modified training paradigm. Adopting curriculum learning approach, we rank edges by their difficulty. The model is then progressively exposed these edges, transitioning from simpler to more challenging ones as training epochs progress.
A.GAA(Combinn both the structural augmentation and the tailored training plan) The SGCN runs augmented graph using curriculum learning training plan.
Our thorough ablation study, detailed in Table 4 and conducted across six benchmark datasets, re- veals several insights:
Importance of Structural Augmentation: This strategy proves crucial for improving model performance. In almost all cases, using only structural augmentation leads to bet- ter results than the baseline model, which is trained on the unmodified graph without any specific training strategy.
8

---

Table 4: The ablation study results of using different components of SGA.
Dataset
Meene
SOCN
-IP
-SGA
AUC
75.1102
75:122
8.
Fi-binary
90.5008
RUK104
91:11:2
92.44-07
Bitcoan-algla
F1-micro
8344113
88810.7
846621
62.11:1
AUC
194113
907422
197110
Blicnin-oke
Fi-binary
F1-micro
92.3412
86.719
902412
94.54077
9133177
863422
90.5-0044
94.61-03
AUC
656114
BS1TO
751111
Epinions
Fi-binary
839:120
90.54144
944116
801144
67.433
0.21009
Fl-macro
680422
72.5126
691
AUC
6101116
070113
637103
L8
Stasddot
67.1433
R53+15
673410
15
F1-maero
$4.4224
61.
554406
AUC
00131
780103
711123
814119
$44009
8151277
Fl micro
73.11117
01010
7341330
8.6
Fl mocro
66.112
70.
668.10
74210.3
65X427
75.6107
15.618
Wikd RIA
Fi-binary
F1-micco
6322437
720441
149419
T13422
7866116
70.1
78.6
N5.5
F1-macro
58.7424
717E13
64.42111
72.1::666
Effect of the Training Plan Alone: Implementing just the training plan, without other modifications, yields smaller performance improvement compared to using structural augmentation alone.
Combined Advantages of Training Plan and Data Augmentation: Combining the train- ing plan with structural augmentation often enhances the benefits of each approach, yield- ing the largest performance gain on most of the datasets.
5.3 Parameter Sensitivity Analysis (Q3)
In this subsection, we perform sensitiv- ity analysis focusing on six hyper-parameters: ddll 'ddl + add (these denote the proba- bility thresholds for adding or removing pos- itive/negative edges); T represents the num- ber of intervals during the training process where more challenging edges are incremen- tally added to the training set; and A desig- nates the initial fraction of the easiest exam- ples. Performance metrics for the SGCN model within the SGA framework, AUC across various hyper-paramett rations, is illustrated in Figures 5. F1-binary, F1-macro and F1-micro scores are illustrated in Appendix K.
measured by configu-
Figure Performance SGCN: AUC scores (with standard deviation) across six benchmark datasets, evaluated under variations in parameters Coat dest add Cadd T and Ag-
The figures reveal divergent patterns in AUC and Fl scores based on hyperparameter adjustments, with SGCN showing more significant variations the Slashdot dataset compared to others. On broader scale, the AUC is fairly consistent with changes to t and Cadd- Notably, as des or ct rise, there's tendency for the AUC to augment. Interestingly, AUC initially increases and then experiences a slight dip as A rises. Regarding the Fl score, it is less sensitive to changes in é enda T, and An except for the case of the Slashdot dataset. In general, an increase in Get and et boosts
+ the Fl score. However, for del the optimal value can differ across datasets, typically lying between 0.1 and 0.4.
Conclusion
In this paper, we introduce the Signed Graph Augmentation framework (SGA), novel approach designed to address two prominent issues in existing signed graph neural networks, namely, data

---

sparsity and unbalanced triangles. This framework has three main components: generating candi- date training samples, selecting beneficial candidate training samples, and introducing a new feature (edge difficulty score) for training samples. Based on this new feature, we have designed cur- riculum learning framework tailored for SGNNs. Through extensive experiments on benchmark datasets, our SGA framework proves its effectiveness in boosting various models.
Acknowledgments
This work supported by the Fundamental Research Funds for the Central Universities, China [Project 2662023XXQD003, 2662023XXQD002). We express our gratitude to Xingyu Ji and Jiale Liu, undergraduate students from the Class of 2022 at the Information College of Huazhong Agricul- tural University, for their assistance in conducting additional experiments during the rebuttal phase. We thank the nigh-performance computing platform at the National Key Laboratory of Crop Genetic Improvement in Huazhong Agricultural University.
References
[1] Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Predicting positive and negative links in online social networks. In Proceedings of the 19th international conference on World wide web, pages 641-650) 2010.
[2] Srijan Kumar, William Hamilton, Jure Leskovec, and Dan Jurafsky. Community interaction and conflict on the web. In Proceedings of the 2018 world wide web conference, pages 933- 943, 2018.
[3] Jure Leskovec, Kevin J Lang, Anirban Dasgupta, and Michael W Mahoney. Community struc- ture in large networks: Natural cluster sizes and the absence large well-defined clusters. Internet Mathematics, 6(1):29-123, 2009.
[4] Tyler Derr. Network analysis with negative links. In Proceedings of the 13th international conference web search and data mining, pages 917-918, 2020.
[5] Jiliang Tang, Yi Chang, Charu Aggarwal, and Huan Liu. A survey of signed network mining in social media. ACM Computing Surveys (CSUR), 49(3):1-37, 2016.
[6] Suhang Wang, Jiliang Tang, Charu Aggarwal, Yi Chang, and Huan Liu. Signed network em- bedding in social media. In Proceedings of the 2017 SIAM international conference on data mining, pages 327-335. SIAM, 2017.
[7] Yu Li, Yuan Tian, Jiawei Zhang, and Yi Chang. Learning signed network embedding via graph attention. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 4772-4779, 2020.
[8] Lin Shu, Erxin Du, Yaomin Chang, Chuan Chen, Zibin Zheng, Xingxing Xing, and Shaofeng Shen. Sgel: Contrastive representation learning for signed graphs. In Proceedings of the 30th ACM International Conference on Information & Knowledge Management, pages 167 1671-1680, 2021.
[9] Thomas N Kipf and Max Welling, Semi supersuper classification with graph convolutional networks. arXiv preprint S0ti::6609002000 02w.0,09777.. 2016.
[10] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, tukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017.
[11] Tyler Dem,, Yao Ma, and Jiliang Tang. Signed graph convolutional networks. 2018 IEEE International Conference on Data Mining (ICDM), pages 929-934. IEFE, 2018.
[12] Junjie Huang, Huawei Shen, Liang Hou, and Xueqi Cheng. Sdgnn: Learning node representa- tion for signed directed networks. arXiv preprint arXiv:2101.023300 2021.
10

---

[13] Haoxin Liu, Ziwei Zhang, Peng Cui, Yafeng Zhang, Qiang Cui, Jiashuo Liu, and Wenwu Zhu. Signed graph neural network with latent groups. In Proceedings of the 27th ACM SIGKDD Conference Knowledge Discovery & Data Mining, pages 1066-1075, 2021.
[14] Zeyu Zhang, Jiamou Liu, Xianda Zheng, Yifei Wang, Penggian Han, Yupan Wang, Kaiqi Zhao, and Zijian Zhang. Rsgnn: A model-agnostic approach for enhancing the robustness of signed graph neural networks. In Proceedings of the ACM Web Conference 2023, pages 60-70, 2023.
[15] Terrance Vries and Graham W Taylor. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv: 04552, 2017.
[16] Daniel Ho, Eric Liang, Xi Chen, Ion Stoica, and Pieter Abbeel. Population based augmen- tation: Efficient learning of augmentation policy schedules. International conference on machine learming, pages 2731-2741. PMLR, 2019.
[17] Zifan Song, Xiao Gong, Guosheng Hu, and Cairong Zhao. Deep perturbation learning: En- hancing the network performance via image perturbations. In International Conference on Machine Learning, pages 32273-32287. PMLR, 2023.
[18] Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning visual features by contrasting cluster assignments. Advances in Neural Information Processing Systems, 33:9912-9924, 2020.
[19] Mengzhou Xia, Xiang Kong, Antonios Anastasopoulos, and Graham Neubig. Generalized data augmentation for low-resource translation. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 5786-5796, 2019.
[20] Gözde Gül Şahin and Mark Steedman. Data augmentation via dependency tree morphing for low-resource languages. arXiv preprint wxxiv:1903.094505 2019.
[21] Alexander Richard Fabbri, Simeng Han, Haoyuan Li, Haoran Li, Marjan Ghazvininejad, Shafiq Joty, Dragomir Radev, and Yashar Mehdad. Improving zero and few-shot abstrac- tive summarization with intermediate fine-tuning and data augmentation. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 704-717, 2021.
[22] Tong Zhao, Yozen Liu, Leonardo Neves, Oliver Woodford, Meng Jiang, and Neil Shah. Data augmentation for graph neural networks. In Proceedings of the aaai conference on artificial intelligence, volume 35, pages 11015-11023, 2021.
[23] Xiaotian Han, Zhimeng Jiang, Ninghao Liu, and Xia Hu. G-mixup: Graph data augmentation for graph classification. In International Conference on Machine Learning, pages 8230-8248. PMLR, 2022.
[24] Songtao Liu, Rex Ying, Hanze Dong, Lanqing Li, Tingyang Xu, Yu Rong. Peilin Zhao, Jun- zhou Huang, and Dinghao Wu. Local augmentation for graph neural networks. In International Conference on Machine Learning, pages 14054-1407 PMLR, 2022.
[25] Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. Graph contrastive learning with augmentations. Advances in Neural Information Processing Systems, 33:5812-5823,, 2020.
[26] Wenbing Huang, Tong Zhang, Yu Rong, and Junzhou Huang. Adaptive sampling towards fast graph representation learning. Advances in neural information processing systems, 31, 2018.
[27] Yu Rong, Wenbing Huang, Tingyang Xu, and Junzhou Huang. Dropedge: Towards deep graph convolutional networks on node classification. In International Conference on Learning Representations, 2019.
[28] Yiwei Wang, Wei Wang, Yuxuan Liang, Yujun Cai, and Bryan Hooi. Grapherop: Subgraph cropping for graph classification. arXiv preprint arXiv:2009. 10564, 2020.
[29] Zeyu Zhang, Jiamou Liu, Kaiqi Zhao, Song Yang, Xianda Zheng, and Yifei Wang. Contrastive learning for signed bipartite graphs. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1629-1638, 2023.
11

---

[30] Marek Cygan, Marcin Pilipezuk, Michat Pilipczuk, and Jakub Onufry Wojtaszezyk. Sitting closer to friends than enemies, revisited. In International Symposium on Mathematical Foun- dations of Computer Science, pages 296-307. Sprinnrr, 2012.
[31] Petar Velickovic, William Fedus, William L. Hamilton, Pietro Liò, Yoshua Bengio, and De- von Hjelm. Deep graph infomax. ICLR (Poster), 2(3):4, 2019.
[32] Junjie Huang, Huawei Shen, Liang Hou, and Xueqi Cheng. Signed graph attention networks. In International Conference on Artificial Neural Networks, pages 566-577. 1166-577..piii Springer, 2019.
[33] Yixuan He, Gesine Reinert, Songchao Wang, and Mihai Cucuringu. Sssnet: Semi-supervised signed network clustering. In Proceedings of the 2022 SIAM International Conference on Data Mining (SDM), pages 244-252. SIAM, 2022.
[34] Pedro Mercado, Francesco Tudisco, and Matthias Hein. Spectral clustering of signed graphs via matrix power means. In International Conference on Machine Learning, pages 4526-4536. PMLR, 2019.
[35] Samin Aref and Mark Wilson. Measuring partial balance in signed networks. Journal of Complex Networks, 6(4):566-595, 2018.
[36] Xiaowen Wei, Xiuwen Gong, Yibing Zhan, Bo Du, Yong Luo, and Wenbin Hu. Clnode: Curriculum learning for node classification. In Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pages 670-678, 2023.
[37] Yiqi Chen, Tieyun Qian, Huan Liu, and Ke Sun. bridge" enhanced signed directed net- work embedding. In Proceedings of the 27th acm international conference on information and knowledge management, pages 773-782, 2018
[38] Hongwei Wang, Fuzheng Zhang, Min Hou, Xing Xie, Minyi Guo, and Qi Liu. Shine: Signed heterogeneous information network embedding for sentiment link prediction. In Proceedings of the eleventh ACM international conference on web search and data mining, pages 592-600, 2018.
[39] Lu Li, Jiale Liu, Xingyu Ji, Maojun Wang, and Zeyu Zhang, Se-sgformer: A self-explainable signed graph transformer for link sign prediction. arXiv preprint arXiv:2408.08754, 2024.
[40] Fang He, Jinhai Deng, Ruizhan Xue, Maojun Wang, and Zeyu Zhang. Mitigating degree bias in signed graph neural networks, arXiv preprini arXiv:2408.0m 085008 2024.
[41] Jiliang Tang, Charu Aggarwal, and Huan Liu. Node classification in signed social networks, In Proceedings of the 2016 SIAM international conference on data mining, pages 54-62. SIAM, 2016.
[42] Jinhong Jung, Woojeong Jin, Lee Sael, and U Kang. Personalized ranking in signed networks using signed random walk with restart. In 2016 IEEE 16th International Conference on Data Mining (ICDM), pages 973-978. IEEE, 2016
[43] Francesco Bonchi, Edoardo Galimberti, Aristides Gionis, Bruno Ordozgoiti, and Giancarlo Ruffo. Discovering polarized communities signed networks. Proceedings of the 28th acm international conference on information and knowledge management, pages 961-970, 2019.
[44] Shuhan Yuan, Xintao Wu, and Yang Xiang. Sne: signed network embedding. In Pacific-Asia conference on knowledge discovery and data mining, pages 183-195. Springer, 2017.
[45] Junghwan Kim, Haekyu Park, Ji-Eun I Lee, and U Kang. Side: representation learning in signed directed networks. In Proceedings of the 2018 World Wide Web Conference, pages 509-518, 2018
[46] Jinhong Jung, Jaemin Yoo, and U Kang. Signed graph diffusion network. arXiv preprint axX1v:2012.14191, 2020.
12

---

[47] Amin Javari, Tyler Derr, Pouya Esmailian, Jiliang Tang, and Kevin Cheann Chang, Rose: Role-based signed network embedding. In Proceedings of The Web Conference 2020, pages 2782-2788, 2020.
[48] Petar Veličkovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. arXiv preprint (tt.::1710.0000) 2017.
[49] Hyeonjin Park, Seunghun Lee, Sihyeon Kim, Jinyoung Park, Jisu Jeong. Kyung-Min Kim, Jung-Woo Ha, and Hyunwoo Kim. Metropolis-hasting data augmentation for graph neural networks. Advances in Neural Information Processing Systems, 34:19010-19900
2021.
[50] Hongyi Ling, Zhimeng Jiang, Meng Liu, Shuiwang Ji, and Na Zou. Graph mixup with soft alignments. In International Conference on Machine Learning, pages 21335 21349. PMLR, 2023.
[51] Lu Lin, Jinghui Chen, and Hongning Wang. Spectral augmentation for self-supervised learning on graphs. In The Eleventh International Conference on Learning Representations.
[52] Yutong Xia, Runpeng Yu, Yuxuan Liang, Xavier Bresson, Xinchao Wang, and Roger Zimmer- mann. Through the dual-prism: A spectral perspective on graph data augmentation for graph classification. arXiv preprint arXiv:2401.09955 2024.
[53] Kaize Ding, Zhe Xu, Hanghang Tong, and Huan Liu. Data augmentation for deep graph learning: A survey, ACM SIGKDD Explorations Newsletter. 24(2):61-77, 2022.
[54] Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. Graph contrastive learning with adaptive augmentation. In Proceedings of the Web Conference 2021, pages 2069- 2080, 2021.
[55] Yuning You, Tianlong Chen, Yang Shen, and Zhangyang Wang. Graph contrastive learning automated. In International Conference Machine Learning, pages 12121-12132. PMLR, 2021.
[56] Dongsheng Luo, Wei Cheng, Wenchao Yu, Bo Zong, Jingchao Ni, Haifeng Chen, and Xiang Zhang. Learning drop: Robust graph neural network via topological denoising. In Pro- ceedings of the 14th ACM International Conference on Web Search and Data Mining, pages 779-787, 2021.
[57] Zhe Xu, Boxin Du, and Hanghang Tong. Graph sanitation with application to node classifica- tion. In Proceedings of the ACM Web Conference 2022, pages 1136-1147, 2022.
[58] Cheng Zheng, Bo Zong, Wei Cheng, Dongjin Song, Jingchao Ni, Wenchao Yu, Haifeng Chen, and Wei Wang. Robust graph representation learning via neural sparsification. In International Conference Machine Learning, pages 11458-11 11 11468. PMLR, 2020.
[59] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXi:: 2017.
[60] Vikas Verma, Meng Qu, Kenji Kawaguchi, Alex Lamb, Yoshua Bengio, Juho Kannala, and Jian Tang. Graphmix: Improved training of gnns for sumi-supervised learning. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 10024-10032, 2021.
[61] Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. Deep graph con- trastive representation learning. arXiv preprint mxxiv:2006.0413. 2020.
[62] Tianxiang Zhao, Xiang Zhang, and Suhang Wang. Graphsmote: Imbalanced node classifi- cation on graphs with graph neural networks. In Proceedings of the 14th ACM international conference on web search and data mining, pages 833-841, 2021.
[63] Johannes Gasteiger, Stefan Weißeenberger, and Stephan Günnemann. Diffusion improves graph learning. Advances in neural information processing systems, 32, 2019.
[64] Xianchen Zhou and Hongxia Wang. The generalization error of graph convolutional networks may enlarge with more layers. Neurocomputing, 424:97-106, 2021.
13

---

[65] Srijan Kumar, Francesca Spezzano, VS Subrahmanian, and Christos Faloutsos. Edge weight prediction in weighted signed networks. In 2016 IEEE 16th International Conference Data Mining (ICDM), pages 221-230. IEFE, 2016.
[66] Srijan Kumar, Bryan Hooi, Disha Makhija, Mohit Kumar, Christos Faloutsos, and VS Subrah- manian. Rev2: Fraudulent user prediction in rating platforms. In Proceedings of the Eleventh ACM International Conference Web Search and Data Mining, pages 333- 133-341. ACM, 2018.
[67] Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Signed networks in social media. In Proceedings of the SIGCHI conference on human humanfactors in computing systems, pages 1361- 1370, 2010.
[68] Robert West, Hristo Paskov, Jure Leskovec, and Christopher Potts. Exploiting social net- work structure for person-to-perse sentiment analysis. Transactions of the Association for Computational Linguisties, 2:297-310, 2014.
[69] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems, 32, 2019.
[70] Matthias Fey and Jan E. Lenssen. Fast graph representation learning with PyTorch Geometric. In ICLR Workshop on Representation Learning on Graphs and Manifolds, 2019.
[71] Junjie Huang, Huawei Shen, Qi Cao, Shuchang Tao, and Xueqi Cheng. Signed bipartite graph neural networks. In Proceedings of the 30th ACM International Conference on Information & Knowledge Management, pages 740-749, 2021.
14

---

088
080
0.1
660
8.38
610 623
-.00
020
6.31
130
Figure 6: Effectiveness of data augmentation through random structural perturbations (SGCN [1I] backbone model) on link sign prediction performance. (a) Randomly increasing or decreasing positive edges. (b) Randomly increasing or decreasing negative edges. (c) Randomly flipping the
sign of edges.
A Experimental results of data augmentation through random structural perturbations
We employ three different random methods (random addition/removal of positive edges, random addition/removal of negative edges, and random sign-flipping of cxisting edges) were tested with the classic SGNN model, SGCN [11]. As is Shown in Figure 6, The results indicate that these random methods do not enhance SGCN performance, suggesting that data augmentation methods used in signed graph contrastive learning models [8, 29] do not readily extend general SGNNs not using a contrastive learning paradigm.
B Related Work
this section, we will introduce two aspects related to this paper: signed graph neural networks and graph data augmentation.
B.1 Signed Graph Neural Networks
Due to the widespread popularity social media ,signed networks have become ubiquitous There- fore, the network representation of signed graphs has gained significant attention 38, 29, 14, 39, 40]. Existing research has predominantly concentrated on tasks related to link sign prediction, while overlooking other crucial tasks like node classification [41], node ranking [42], and community de- tection [43]. Some signed graph embedding techniques, such as SNE [44], SIDE [45], SGDN [46], and ROSE [47], utilize random walks and linear probability methods to capture the positive and negative relationships within graphs. These techniques consider complex interactions hetween nodes when processing graph data, but they may not be sufficient capture deep-seated relationships in signed graphs. With the further exploration of signed graphs, neural networks have also been ap- plied to signed graph representation learning recent years. There are some SGNN models based on GCN F9r example,th the first Signed Graph Neural Network (SGNN), SGCN [11], generalizes GCN signed graphs by utilizing balance theory to correctly aggregate and propagate the informa- tion across layers of signed GCN model. Another noteworthy GCN- approach is GS-GN GS-GNN, which moves beyond the traditional balance theory by categorizing nodes into multiple groups Ad- ditionally, there are SGNN models based on GAT [48] such as SiGAT [32], SNEA [7], SDGNN (12), and SGCL. which further enhance the ability to identify the varying levels of importance of nodes in the graph by introducing attention mechanisms. Unlike the above methods dedicated developing more advanced SGNN models, we introduce plugin to enhance the performance of SGNNs.
B.2 Graph Data Augmentation
With the rapid development of graph neural networks, there has been a growing interest and de- mand for graph data augmentation techniques. To address issues such as data sparsity and noise
15

---

Draie
Doond
12
SGNN
candidate train
Encoder
Cos
samples
Train Set truin
Embedding Space
probability forming the positive edge negative edge
Candidate samples
Figure 7: Generating candidate training samples
Creditaa eottecelggroc
Cuodater Anurndgr
APeal
Chonee
Merge
beneficial
into Frem
edges
Candidate samples
Keep The Candidate Sample
Drop The Candidate Sample
Delete The Negative Edges ss
Delete The Positive
Updated
Edges 6610 6610
Deratn
Figure 8: Selecting beneficial candidate training samples
in graphs, many research studies have focused on enhancing graph data augmentation techniques [49, 23, 24, 50-52]. According survey of graph data augmentation [53], graph augmentation methods can be classified into three types, i.c., feature-wise [24, 54, 55], structure-wise [56-58] and label-wise [59, 60]. Feature-wise augmentation methods primarily involve modifying, creating, or merging new features to enhance graph data. For examplc,LAGNN [24] operates by using genera- tive model that takes into account the localized neighborhood information of target node enrich the node's 's features. Other feature-wis wise methods [61, 25] generate augmented node features by ran- dom shuffling. Structure- wise augmentation methods target at modifying edges and nodes (e.g., randomly adding or deleting edges) to simulate different graph structures. GAUG [22] employs neural edge predictors that can effectively encode class-homophilic structure promote intra-class edges and demote inter-class edges in a given graph structure. GraphSMOTE [62] inserts nodes to enrich the minority classes. Graph diffusion method (GDC [63]) can generate an augmented graph by providing global views of the underlying structure. Label-wise augmentation methods aim at aug- menting the limited labeled training data.especially cases where labeled data scarce in graph data G-Mixup [23] augment graphs for graph classification by interpolating the generator (i.e., graphon) of different classes of graphs.Note that these existing data augmentation methods rely on additional information such node features and labels. However, the absence of key information such as node features and labels signed graphs limits the applicability traditional data aug- mentation techniques to SGNN. Therefore, is necessary to develop data augmentation strategies tailored for signed graphs.
C Detailed Design of SGA
Figure 7, and show the details of the three steps of the SGA framework.
D SGA Algorithm Details
The SGA Algorithm is shown in Algorithm 1.
16

---

Training
Difficulty scores of edges order by
22,6
Easy edges
Harder edges subset
Whole edgres
Calculate scores
subseet
set
66,8
:0.5
33,4
Curriculum training
Caa
012
112
edges
C4.5
C0.10
:0.5
33,5
Czn
62.6
f
SCNN
e4,5
:0.5
63,6
Predict labels
True labels
Grose Entropy Loss
12
Update Drrain
Difficulty Measurer
Training Scheduler
Figure 9: Introducing new feature for training samples
Algorithm 1: SGA Algorithm
1: Input: A signed graph training edge set Dinr, SGCN and SGNN f', pacing function g(t), C & Caw Sest
2: Output: SGNN parameters y
3: Initialize SGCN parameter 95, SGNN 8r,, Digh Diah
4: Pre-train the f on Dunnn Generation Candidate Training Samples
5: vs, VUy
6: Calculate Prety and Prazy using.
7: if (Pregg "ada ar Pragg > Saa) then
8: Dinnsss Dimte ([V2) Uy (leg)))
9:
end
10:
if ((r.)). Dram Ae 0 and Preiz eda then
11:
Dank Dand U ([0s a(cg)))
12:
end if
13:
[Ue, Uy, ((es)) E Dran Aig < and Preyy <d then
14: Dimns Den ((Ws, o(ey))
15: end
16:
end for
Selecting Beneficial Candidate Training Samples all o),,)))(())))) E Dimiua do
18: Den +- Dem ) [(e,, d(r,))
19:
20: for all (vs, ((ss)) Dead. do
21: if (ve, ((.ee)) $ Dean then
22:
for un No NN do
23:
(a(a(e))) ((Ex) ((exx)) > then Duna Danin U [(Vi, Uy, o(ees)
24:
25:
end for end if
26:
27:
28:
end
Introducing Nov Feature for Training Samples
29: for (vz, R.. (le4y)) Dwan du
30: Caleulate Score(esy) using Eq.
31: end for
32: Sart Dirain according to difficulty ascending urder
33: Let
34: while Stopping condition not met do
35:
g(t)
36:
E, + Dean (U...., A. [Deanl]
37:
Use f' predict the labels (E,)
38:
Calculate cross-cntropy loss on (a (E.), (8:))
39:
Back-propagation on for minimizing &
40:
41:
end while
42:
return p,
17

---

E
Theory Analysis
E.1
Basic Setup
Before the proof begins, the framework of the SGNN for edge prediction is given Algorithm 2. A network first performs feature aggregation, where each node learns the representations of its neighboring nodes, and subsequently uses the feature representations of several pairs of nodes as inputs classifier for predicting the nature of the edges connecting these two nodes. Before the proof begins, we show the framework of the SGNN for edge prediction below.
Algorithm 2: Simplified SGNN Framework
Input: the adjacency matrix A E R MM of graph 9, number of aggregation layers L, weight matrix w 2: Output: Label prediction of edge Ho=A
// Feature Aggregation
I,- for 1 fi-1=p(Hi, m) = = MyEN aggregate(y, v.) + aggregate v2)
4:
end for
6: Z = Hr.
// Classifier
(exy) f (26, w)
Upgrade parameters hased on loss function
return Aij
A network first performs feature aggregation, where each node learns the representations of its neighboring nodes, and subsequently uses the feature representations of several pairs of nodes as inputs to a classifier for predicting the edges connecting these two nodes. Here, 2g,2g denote the i-th and j-th rows respectively, in matrix Z and Å.ş is the predicted label of edge eij. These vectors cor- respond to the node representations learned through graph filters in traditional GNNs. But actually SGNN does not have representations for each node, and this is done here to more clearly represent the variables that affect the generalization performance during the proof process next.
E.2 Assumptions
I-Lipschitz Continuous and Smooth Loss Function: A function ʃ X - R is -Lisschht continuous if for all x. y E X. [f(x) [(y) & an y|1- A function f X IR ax-Lipschitz
smooth if for all æ. E X, ( < 0r2 a2||x-yl]| where I' represents the differential function of f, and ||-|| represents the 2-norm.
Similarly, for functions of three variables, a function f X + R a -ipsschit continuous
if for all x, x,y,² E X. If (I,, 2), - f (I,, My, 2) S v (a; - =x,) + (y. yz)² A func- tion
X + R is -rg-Lipsehitz smooth if for all v, E X, |s' yi, f' Vj =)] s 02 V (a,- -
x,,² )² + (y - 3. We assume that the loss function I.). f() g(). satisfies the Lipschitz
condition.
Actually, in simple terms, Lipschitz continuity portrays how smooth the function is, ensuring that the function does not have too steep a slope or abrupt changes: in the event of a small change in the input value, the change in the output value is also limited to certain range.
In practice, regularization, normalization, gradient trimming, and other methods of keeping the model stable actually limit the drastic changes in the function, which means that the assumption easily satisfied.
Training set and Test set: Training data is usually easier to obtain than test data. In the link prediction task, training set contains more edges and can simulate the data distribution in real scenarios, while the test set is used to validate the performance of the model in real applications. also taken into account that if the number of edges the test set too high, it may cause the evaluation results to be skewed towards the distribution of the training set, which does not accurately
18

---

reflect the generalization ability of the model. So we assume that the training set has more edges than the test set.
F Proof of Theorem 1
In this section, we will present the entire proof of our main result about the generalization gap bound. Similar as proof of theorem 1 [[[64], Theorem IJ. we have:
8gen
EA [R (ADmuin) RR (ADsccll
Σ
T. (A Ais)
1
Σ
I (Ape: Aps)
nt
Poyr
cit eijEe Lee
(II)
(8)
Σ C2g
(Acs:As) -T (Apor Ara)
The loss function we use is based link sign prediction, where 7m is the number of edges in training set and test set respectively. Step (a) is the application of our assumption. In learning process, the number of edges in test set always lower than in training set. Therefore, we get Equation (11). Then using absolute value inequality, we have:
Σ (Ag, A1s) I. (Apq: Apg)
(Aiis.AA)) - L (Aig. Apq) + f/ (z((AAn (AAij, (A)))AApa) I (Apg. Apa)
(12)
a
Ai Aij - App + + Ais - Apg
Step (b) uses the Lipshitz-continuity of loss function I. 7 AA. Next, we consider the first item. As Aij Apg E -1,-1,0), signifies the original sign and the predicted sign of the edge eij. obviously get the upper bound: max |Ag =2.
For the last item, according to the process link prediction:
Å. (eis)) f(z,, 2j, w)
(13)
Continuing to use the Lipschitz-oontiuitty of the function f(), we get:
Σ at Any Apul
Eig.Epp
S ooy
Σ (z11,23) 23,,,, w) - 22p
- Zgg w)
(6)
$ Sa/Milui
Σ
V - =2)) + (2) - -2))
(14)
Σ
/ +27+2
G1 1pg
S 22a,MMM0
exy.ppg
Here, Step (c) is extension of the Lipschitz-condition for multivariate functions. Similar to aý and of, M is constant determined only by the function SQ) itself. We will subsequently prove the existence of the constant M in the proof of Lemma 1.
19

---

In Equation (14), 20 refers to the infinite norm of the matrix Z. We set 2, the i-th row of
matrix Z, which can be represented as 2, Z 1- Here I = [0, .... 12 ... . vector with position being and the other positions being O. The Last step followed the definition that
[
|| = max (21 F2,
Bringing Equation (12) and (14) into Equation (11), we get the following result:
EA [|| (AD R (AD IlI S 2a V2a M | |0
(15)
14
Next will prove an upper bound for ||t/|| based on the SGD algorithm.
W++1 We 17 V
loss
VL
VS
We V
(16)
Vw
< w/
gor f
|0
This gives the iterative formula for After t iterations, obtain upper bound of weight matrix ||w/]|:
|wull S
[[aasee] tma ||
(17)
Bringing Equation (17) into Equation (15), let 3 = || and = | |l. we get the final result:
Egen S 20 + 2200MM + tna
(18)
T4t
G Proof of Lemma 1
For the ternary function [x,, y, with bounded 2o, if the function satisfies the Lipschitz- condition for 2, it can be obtained:
If (11,31, U1, - f (x2, U2, 20)1 S M |z0 V (x) - x²)² + (3) y22)
(19)
For a succinct represetatio in the next proof, we define D(
x2
) ( -x2
+ 111-92
31
1/2
To prove our conclusion, we first construct the auxiliary function G:
G G(I, U, Ar, Av)
(20)
(s x Ax, y + Au.2) + & (1, v.
By the definition of G(x,,,, Ax, An), we have:
G(o1,81, ATI, Agi) G(x2, 12, z, Ar2, Azz)
| + ATI, Ayi, 2) (12 + AZ2. y22 + Ay2, 2) + f(r, f v2, v2,2)) 2)]
Ls
z V
D( I1 + Azi
x2 Ar
D( σ1 22
y1 Avi
+ Ay2
y2
(21)
Using special case of Cauchy Schwarz's inequality, have:
20

---

D
+ Ar
22 + A
S D
22
) ) D(
y1
9/2
)
(22)
y1 + Ay
U2 + Ay2
A1
Ar2
Ay
Ay2
Given
that
2 is
bounded
and the obvious conclusion
D(
21
222
S
y1
y/2
V
D
#ı + Ari
#2 + Ar
).
y/
Ay
1/2 Ay2
G( V1, 2, Ari Avi) G( V2: 2, A22 Ay2)
(23)
S K (m1 x2)² + (y1 y2)) (Az1 Ar²)² + (Ay1 Ay2)
Here K is constant ultimately determined by function f. Based on Equation (23), next we construct a differential of the following form:
f(r1, 21,
f(22, V2.
2
2
[z] [0118112) f (f((fff
V1, 2) + f y2, x2,
(24)
= 21, 0) - G( 92, 2, 0, 91)
As what we defined in Equation (20) and (23), Az Z2 21. Ay2 Y22 11 Az2 Applying Equation (23) to Equation (24):
Ay 0.
(x1, y1, 21, - f (x2, 1/2 V2K|aly (m1 x22²² (y1 v2)
(25)
Let M /2K, we managed to proof the existence of M Equation (14).
H Datasets
We conduct experiments on six real-world datasets, i.e., Bitcoin-OTC, Bitcoin-Alpha, Wiki-elec, Wiki-RfA, Epinions, and Slashdot. The main statisties of each dataset are summarized in Table 5. In the following, we explain the important characteristics of the datasets briefly.
Bitcoin-OTC2 [65, 66) and Bitcoin-Alpha' two datasets extracted from bitcoin trading plat- forms. Because Bitcoin accounts are anonymous, individuals assign trust or distrust tags to others enhance security.
Wiki-elec* [67, 1] a voting network which users can choose trust or distrust to other users in administer elections. Wiki-RfA [68] is more recent version of Wiki-elec.
Epinions [67] is consumer review site with trust and distrust relationships between users.
Slashdot [67] is a technology-related news website in which users can tag each other as friends (trust) enemies (distrust).
Following the experimental settings in [11], we randomly split the edges into a training set and testing set with ratio of 8: 2. We run with different train-test splits for 5 times to get the average scores and standard deviation.
hhtp://wwww.btccoi-otcc
http://wwww.bc-appha.coomm
hhtps://wwwwwikipcciia wikipedia.or..oo "htt://www.eppnions com
"ttp://wwwwslsshhoo.comm com
21

---

Table 5: The statistics of datasets.
Dataset
# Nodes
# Links
# Pos edges
# Neg edges
Density
Bitcoin-OTC
5,881
35,592
32,029
3,563
1.03e-3
Bitcoin-Alpha
3,783
24,186
22,650
1,536
1.69c-3
Wiki-elec
7,115
103,689
81,345
22,344
2.05c-3
Wiki-RfA
11,017
170,335
133,330
37,005
1.40e-3
Epinions
131,580
840,799
717,129
123,670
4.86e-5
Slashdot
82,140
549.202
425,072
124.130
8.14e-5
I Baselines and Experiment Setting
We used five popular graph representation learning models the backbones, including both un- signed GNN models and signed GNN models.
We employ two classical GNN models (i.e., GCN [9] and GAT [3I]. These methods are designed for unsigned graphs; thus, as mentioned before, we consider all edges as positive edges to learn node embeddings in the experiments.
Unsigned GNN:
Signed Graph Neural Networks: SGCN [11] and SiGAT [32] respectively generalize GCN [9] and GAT [31] to signed graphs based on message mechanism. In addition, they integrate the balance theory, GS-GNN [13] adopts a more general assumption (than balance theory) that nodes can be divided into multiple latent groups. We use these signed graph neural networks as baselines to explore whether SGA can enhance their performance.
We implement our SGA using PyTorch [69] and employ PyTorch Geometric [70] as its complemen- tary graph library. The graph encoder, responsible for augmenting the graph, consists of 2-layer SGCN with an embedding dimension of 64. This encoder is optimized using the Adam optimizer, set with learning rate of 0.01 over 300 epochs. For SiGAT, we randomly standardized the em- bedding dimension of the node to 20 as recommended in [32]. For the remaining embedding- -basdd methods, it was set to 64, which matches the dimensionality used in GS-GNN [13]. For the baseline methods, we adhere to the parameter configurations recommended in their originating papers. Specifically, for unsigned baseline models like GCN and GAT, we employ the Adam optimizer, with learning rate of 1c-2, weight decay of 5c-4, and span the training over 500 epochs. For signed baseline models, SGCN is trained with an initial learning rate le-2 and run for 300 epochs, SiGAT is trained with initial learning rate of 5e-3 and run for 1500 epochs, and GSGNN is trained with an initial learning rate of le-2 and run for 3000 epochs. The experiments were performed on a Linux machine with eight 24GB NVIDIA GeForce RTX 3090 GPUs.
Our primary evaluation task is link sign prediction. We evaluated performance using AUC, F1- binary, Fl-macro, and Fl-micro metrics, consistent with established norms in related literature [71, 13). imperative to note that for all these evaluation metrics, a higher score directly translates to better model performance.
J More Link sign prediction results
Table 6: Link sign prediction results (average + standard deviation) with F1-micro (%) and F1-
macro (%) on six benchmark datasets.
Danses
Bicon dgha
Bhoole 0oG
Epiniors Fismino
Stadddee
Willede dec
WET
Mathule
Floman
Plamaro
Flsmano
Fl-maem
Fl-miemo
Flemano
Flamian
Fl-magm
Flamien
Fl-marm
369219
450300
S777114
401123
78.52244
60.12:.2
52.2:79
65.42:05
64091.1
(mppes)
795237
$38:33
58.2292
58.1134
5696
36.25
738
9.58
21.5%
24.5%
218
15555
4,6%
106
SGUN
854513
021211
86TETM
1201113
8391220
OKBE29
503231
S06214
711117
6C111
633117
SKTEZA
+SDA
$1.2810
676303
905204
77.34666
969513
15
720210
68.1203
806508
7438803
7864609
12.12.0
(apeos)
4.6%
8.8
4.5%
75%
378
11.2%
32.3%
24.7%
10.2% 1
12.3%
24.5%
25% 1
SHOU 31
313304
12.EE13
8072303
1272301
730231
852202
+5TA
442281
3111
222202
7601111
919202
31.2204
632200
145200
714205
847403
760202
(mpens)
0.95
7.8%
7.7%
0.2%
1.9%
0.9 1
212
0.5%
3.1%
0.4% 1
2.19%
05 GSNNNN [15]
9.5003
221230
134173
0171110
$1.E11
ALSETO
83312011
75
$1.1003
750EL1
+95A
947202
746:09
930203
81.5066
92,0202
S16-104
1211210
454203
75
747200
(Impon)
0.76
3.891
011
675.1
0.45
2.65
0.19
0.5%1
22

---

K Parameter Sensitivity Analysis with F1 scores
332
86A
165
200
6.20
020
335
Figure 10: Performance of SGCN: F1-binary scores (with standard deviation) across six benchmark datasets, evaluated under variations in parameters del dets Endd Edda T and λg.
0.59
6790
683
2480
1401
02
0
305
6.60
0.8
0.8
6.200
6.90
6595
0.0
Figure 11: Performance of SGCN: FI-macro scores (with standard deviation) across six benchmark + datasets, evaluated under variations in parameters del delt add Edd T and Ag
0.5
0.00
0.5
0.2
$101
1390
0.71
2000
030
8.72
0.75
4790
310
Mrdertng
15
335
Figure 12: Performance SGCN: F1-micro scores (with standard deviation) across six benchmark datasets, evaluated under variations in parameters E Edtts Endd Eadas T and Ag.
23

---

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

---

Justification:
The main theoretical result is Theorem 1. For the complete proof, please refer Appendix G and
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theo- rems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be comple- mented by formal proofs provided appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclu- sions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: Please refer to the code link provided in the abstract section and the experi- ment setting in the Experiments section.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is a dataset and/or model, the authors should describe the steps taken make their results reproducible verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, other means that are appropriate the research performed.
While NeurIPS does not require releasing code, the conference does require all sub- missions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily new algorithm, the paper should make it clear how to reproduce that algorithm.
(b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results way produce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which thors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models. it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers have some path reproducing verifying the results.
5. Open access to data and code
25

---

Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: [Yes]
Justification:
Please refer to the code link provided the abstract section.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https: (https://nipp) //ipp..c///cc/////////
for more details.
While we encourage the release code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (c.g., for a new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https: //nips... ///ipsccc///// public/guider Swweeeeeeeeeeeemeeeeeeeee onPolicy) for more details.
cc/
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental Setting/Details
Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Question:
Answer: [Yes]
Justification:
Please refer to the Baselines and Experiment Setting.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment Statistical Significance
Question:
Does the paper report error bars suitably and correctly defined or other appropri- ate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: We average improvement ratio represent the statistical significance and calculate the results with average and standard deviation. (Please refer to Table 1)
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
26

---

The method for calculating the error bars should be explained (closed form formula, call a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should prefer- ably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not show in tables or figures symmetric error bars that would yield results that are out of range (c.g. negative emror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: Please refer the Baselines and Experiment Setting part.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g.. preliminary or failed experiments that didn't t make it into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https: httpp::/nnett httpp::////eriiss.pee http:
Answer:
Baselines and Experiment Setting
Justification: Please refer to the code link provided in the abstract section.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification:
Please refer to the introduction part.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact spe- cific groups), privacy considerations, and security considerations.
27

---

The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitiga- tion strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have high risk for misuse (e.g., pretrained language models, image generators, scraped datasets)?
Question:
Answer: [NA]
Justification:
This paper poses such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have a high risk for misuse or dual-use should be released with necessary safeguards allow for controlled use of the model, for example by re- quiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided relcasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification:
We have given proper citations or URLs to those existing datasets and codes 1451 of baselines.
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use the pack- age should be provided. For popular datasets, paperswi www.wwwtthhhee...cee cww datastts has curated licenses for some datasets. Their licensing guide can help determine the li- cense of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
28

---

If this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documenta- tion provided alongside the assets?
Answer: [NA]
Justification: This paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moodl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the per include the full text instructions given to participants and sereenshots, applicable, well as details about compensation (if any)?
Answer: [NA]
Justification:
This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contri- bution of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According the NeurIPS Code of Ethies, workers involved in data collection, cura- tion, or other labor should be paid at least the minimum wage the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does involve crowdsourcing research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equiva- lent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
29


Reviews:
[{"review_id": "PYgsJaN8QK", "reviewer": "Reviewer_wfoh", "summary": "This paper proposes a new research subfield focusing on data augmentation methods for signed graphs. Unlike the widely studied unsigned graph augmentation, this method targets the downstream task of link sign prediction rather than the mainstream node classification [1] or graph classification [2]. As far as I know, most current graph data augmentation methods mainly address node classification tasks, while there is relatively little enhancement work for edge tasks, or their effectiveness for link prediction is not significant [3]. Additionally, this article provides the first generalization error bound for signed graph neural networks, which is used to analyze why current commonly used data augmentation methods yield unstable results for signed graphs. In designing data augmentation methods, the article introduces a new perspective from curriculum learning.\n\n[1] Kazi, Anees, et al. \"Differentiable graph module (dgm) for graph convolutional networks.\" IEEE Transactions on Pattern Analysis and Machine Intelligence 45.2 (2022): 1606-1617.\n[2] Chen, Yu, Lingfei Wu, and Mohammed Zaki. \"Iterative deep graph learning for graph neural networks: Better and robust node embeddings.\" Advances in neural information processing systems 33 (2020): 19314-19326.\n[3] Gasteiger, Johannes, Stefan Weißenberger, and Stephan Günnemann. \"Diffusion improves graph learning.\" Advances in neural information processing systems 32 (2019).", "questions": "See weaknesses.", "limitations": "See weaknesses.", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- This paper proposes a new subfield of research with a wide range of applications. According to my investigation, this article is indeed the first paper on this topic.\n- This paper introduces a novel approach to data augmentation, which involves using curriculum learning to adjust the training weights of challenging edges. This perspective is quite insightful.\n- This paper presents the first generalization error bound for signed graph neural networks and, based on this, analyzes the reasons why current commonly used graph data augmentation methods (such as random edge deletion) yield unstable results for link sign prediction.", "weaknesses": "- Although the article introduces a new problem within a subfield, its application scope is relatively narrow compared to more generalized graph structures.\n- Why can't current graph augmentation methods be directly applied to signed graph representation learning? In the limitations, the authors mention that for datasets with poor balance, the effectiveness of this data augmentation method decreases. Are there any good solutions to this problem?\n- Can the authors provide a more detailed analysis of the factors affecting SGA's performance? Specifically, why do some unsigned and signed GNNs show significant performance enhancements on certain datasets, while others exhibit only marginal improvements or none at all?\n- Some typos: In line 231, there is a missing space after \"algorithm 2\". In line 236, there is also a missing space after \"the main result\".", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "(1) **For weakness 1 on application scope:**\n\nCompared to more generalized graphs, signed graph analysis has its exclusive downstream task (i.e., link sign prediction) which are important and very interesting, such as product reviews [10], bill votes [11], paper reviews, polarization study [14], echo chambers [12]. In addition to social networks, the field of bioinformatics also utilizes this approach, for example, to predict upregulation and downregulation relationships between diseases and genes [13].\n\n(2) **For weakness 2 on other graph augmentation methods and limitation issues:**\n\nRegarding the current graph data augmentation methods that cannot be directly applied to signed graphs, we primarily discuss this in the 3rd paragraph of the introduction. In summary, it mainly includes two aspects:\n\n1. Most methods are designed for node classification [5], graph classification [1-2], and link prediction tasks, with no existing approaches specifically targeting link sign prediction. Moreover, these methods rely on side information, such as node features and labels, which are often missing in most real-world signed graph datasets that contain only structural information [7-8].\n\n2. Random structural perturbation based augmentation methods [15] cannot improve SGNN performance. We have verified this from both experimental and theoretical perspectives. (see Fig.2 and Sec.4)\n\nRegarding the issues raised in the **limitations**:\n\nGiven that most current SGNN methods are designed based on the GCN architecture, and This paper [6] has demonstrated that current SGNN models based on such architectures are unable to learn suitable representations from unbalanced cycles. Our data augmentation method heavily relies on this kind of SGNN models to mine suitable potential candidates (i.e., edges), so designing a signed graph representation encoding framework based on alternative architectures could better address the current issue. For instance, using large language models to tackle this problem could be a promising approach. However, the integration of large language models with graphs is still relatively limited. According to our research, there is currently no studies specifically targeting signed graphs. Whether it is reliable to directly use some of the existing frameworks also needs further validation. Overall, this is a very worthwhile problem to explore.\n\n(3) **For weakness 3 on Experimental Results:**\n\nHere are **two observations** regarding the experimental results:\n\n1. The performance improvement of the methods based on balance theory architectures, namely SGCN [7] and SiGAT [8], is more significant compared to GS-GNN [9]. In other words, the improvements achieved by SGCN and SiGAT are more noticeable, whereas the improvements with GS-GNN are relatively smaller.\n\n2. The overall performance on the first four datasets (Bitcoin-alpha, Bitcoin-otc, Epinion, Slashdot) is better than on the last two datasets (Wiki-elec, Wiki-Rfa).\n\nRegarding Observation 1, from the perspective of method design, the information fusion mechanism of the model itself influences the performance of SGA. We believe the reasons might include two aspects. First, as indicated by the analysis in RSGNN [6], the current SGNN methods based on balanced theory [7] (i.e., SGCN, SiGAT) fail to learn appropriate representations from unbalanced cycles, whereas SGA effectively reduces the proportion of unbalanced cycles (see Table 3), leading to better enhancement for these two methods. Second, since GS-GNN [9] is not limited to the balanced theory assumption, it can handle unbalanced cycles well, thus the enhancement effect from SGA is less significant.\n\nRegarding Observation 2, from the perspective of dataset balance, we believe that the performance of SGA is related to the balance of the dataset. As shown in Table 3, the initial balance degree (BD %) of the first four datasets is better than that of the last two datasets. Considering that we use SGCN as the link sign prediction model to identify potential candidates, its prediction performance is poorer for datasets with low balance degree. As evidenced in Table 1, this conclusion holds true. Therefore, for datasets with low balance, it is more challenging to identify suitable potential candidates, leading to a decrease in the overall data augmentation effectiveness.\n\n(4) **For weakness 4 on typos:**\n\nThank you for the reviewer’s comments. We will carefully review the paper and correct typos in the final version.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "RpdwxLsNxR", "reviewer": "Reviewer_B6jA", "summary": "Link sign prediction is a significant downstream task in graph data analysis. Current graph data augmentation methods seldom explore this task. This paper analyzes, both theoretically and experimentally, why existing graph data augmentation methods perform poorly on this task and proposes a new data augmentation method tailored for signed graph analysis. Its main contributions include the following two aspects:\n\n- It provides a generalization error bound for signed graph neural networks and theoretically verifies that the widely used random edgedrop method is not suitable for the link sign prediction task.\n- It proposes a novel signed graph data augmentation framework to address two major issues in current signed graph neural networks (SGNNs), namely sparsity and imbalanced triads.", "questions": "Please refer to Weaknesses.", "limitations": "The paper argues that the data augmentation method can alleviate rather than completely solve the current obstacles of SGNN methods. This claim is supported by experimental and theoretical analyses. However, a limitation of this article is that it only addresses a subset of issues within GNN models and their impact on downstream tasks, thus its influence may be somewhat limited.", "rating": 7, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. Although significant progress has been made in the field of graph augmentation, data augmentation methods specifically for signed graphs and link sign prediction are relatively new research directions. Currently, there are relatively few data augmentation methods specifically designed for edge-level tasks in graph augmentation. \n2. In this data augmentation module, the authors propose an intriguing new approach, which is to treat the training difficulty of training samples as a feature for augmentation, thereby adjusting the training weights of these samples.\n3. The paper is well structured, logically coherent and very easy to understand.", "weaknesses": "1. According to the authors' theoretical analysis, reducing the number of training samples does not contribute to improving model performance. However, in Section 3.2, we observed that some training samples were removed because they belonged to imbalanced triplets. Does this observation contradict the theoretical analysis?\n2. The authors mention in the limitations section that \"for real-world datasets that do not strongly conform to balance theory, our data augmentation may be less effective.\" What is the basis for this statement? Are there possible solutions proposed by the authors for this issue?\n3. Some typographical errors: on line 164, the concatenation operation should use [,] instead of [.]. On line 225, there is a missing space between SGNN and \"our results\". Also, some formulas have punctuation while some do not.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "(1) **For Weakness 1 on some training samples removed :**\n\nOur theoretical analysis indeed demonstrates that reducing the number of edges during training can degrade model performance. However, the SGA method does not reduce the overall number of edges. Specifically, we take a cautious approach to edge removal by setting a high threshold (over 0.9, up to 1) before executing any edge removal operation, as detailed in our published code. As a result, the number of edges in the training set actually increases after the data augmentation process. This is corroborated by Table 2, where the graph density is shown to improve following data augmentation.\n\n(2) **For Weakness 2 on limitation part:**\n\nRegarding the issues raised in the *limitations*:\n\nMost existing SGNN methods are built on the GCN architecture, and it has been shown [6] that such models struggle to learn appropriate representations from unbalanced cycles. Our data augmentation method relies heavily on these SGNN models to identify suitable potential candidates (i.e., edges). Therefore, designing a signed graph representation framework based on alternative architectures could better address this issue. For example, leveraging large language models (LLMs) could be a promising approach. However, the integration of LLMs with graph structures is still in its early stages, and, to our knowledge, no studies have specifically targeted signed graphs. The reliability of directly applying existing frameworks to this context remains uncertain and requires further validation. Overall, this is a problem worth exploring in greater depth.\n\n(3) **For Weakness 3 on typos:**\n\nThank you for the reviewer’s comments. We will correct the typos in the final version of the paper.\n\n(4) **For Limitations on influence:**\n\nSigned graphs, which assign positive or negative signs to edges, are powerful tools for modeling complex relationships across various fields. They offer valuable insights into social network dynamics, biological and chemical interactions, recommendation systems, and international relations. By capturing both positive and negative interactions, signed graphs facilitate a deeper understanding of intricate systems, providing sophisticated analytical methods to address challenges in multiple disciplines.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "K3aKKxqHYx", "reviewer": "Reviewer_QdQs", "summary": "This work addresses the scarcity of effective data augmentation strategies tailored for signed graphs, especially considering the dearth of auxiliary information in real-world datasets. By presenting the generalization error bound for SGNNs and disproving the universal benefit of random DropEdge, this paper introduces Signed Graph Augmentation (SGA). SGA innovates with a structure augmentation module identifying potential edges from network patterns and employs a selective strategy to enrich training data. The proposed method significantly improves SGNN performance.", "questions": "1. In Section 4, according to ‘the generalization performance of the model is affected by the number of edges’, will randomly adding edges will be more effective than dropping edges in signed graphs? Is there any empirical evidence about this?\n2. Lack of complexity analysis and cost time comparison. Is SGA efficient in large-size datasets?\n\n### After rebuttal\nMost of my concerns have been addressed. I raise my score to 6.", "limitations": "The authors discussed the limitations of the proposed method.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is well structured and has clear writing. The task of signed graph augmentation is interesting and novel. The experimental results show the effectivity of the proposed method.", "weaknesses": "1. Regarding the experimental results shown in Table 1, the paper only shows the results of solely using the backbone model and with SGA augmentation method. The efficiency of the proposed method will be more convincing if it can be compared with another augmentation method. In addition to the DropEdge method, there are still other augmentation methods, e.g., mixup-based methods [1,2] and spectrum-based methods [3,4]. \n2. Though the performance when using SGA is better, compared to do not using any augmentation method, it introduces many modules to train, e.g., the encoder and the MLG classifier, thus introducing many more parameters. A comparison of a number of parameters and the training time will be better.\n3. Minor comments: Figure 3 can be improved to be more clear. The Encoder, MLG classifier, and the classifier loss are not explicitly shown in the figure.\n\nReference:\n[1] G-mixup: Graph data augmentation for graph classification. ICLR’22\n[2] Graph mixup with soft alignments. ICML’23\n[3] Spectral augmentation for self-supervised learning on graphs. ICLR’22\n[4] Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification. arXiv'24", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**For Weakness 1 on other augmentation methods:**\n\nThank you for the reviewers' suggestions. We carefully reviewed the recommended papers [1-4]. Although the data augmentation methods discussed in those articles are not specifically designed for the link sign prediction task, their underlying concepts have been highly inspiring for our work. We will include a discussion of the aforementioned methods in the Related Work section of the final version. We selected one method each from the mixup-based methods and spectrum-based methods as augmentation techniques, namely S-Mixup [2] and DP-noise [4], to be applied in link sign prediction on Bitcoin-otc dataset.\n\n|Model|AUC|F1|Micro|Macro|\n|:-:|:-:|:-:|:-:|:-:|\n|SGCN|78.3 ± 1.4|90.5 ± 2.6|84.0 ± 3.9|69.2  ± 4.1|\n|SGCN+S-Mixup|76.8 ± 2.3|88.8 ± 2.9|81.5 ± 4.1|67.4 ± 3.5|\n|improv.|-1.9% $\\downarrow$|-1.9% $\\downarrow$|-3.0% $\\downarrow$|-2.6% $\\downarrow$|\n|GSGNN|89.1 ± 1.2|96.5 ± 0.7|93.6 ± 1.2|80.8 ± 2.0|\n|GSGNN+S-Mixup|87.0 ± 2.1|96.2 ± 0.2|93.1 ± 0.3|79.4 ± 1.7|\n|improv.|-2.4% $\\downarrow$|-0.3% $\\downarrow$|-0.5% $\\downarrow$|-1.7% $\\downarrow$|\n|SiGAT|76.5 ± 2.5|94.9 ± 0.2|90.4 ± 0.3|59.2 ± 1.6|\n|SiGAT+S-Mixup|57.1 ± 4.4|65.9 ± 22.2|56.2 ± 21.2|43.5 ± 12.2|\n|improv.|-25.4% $\\downarrow$|-30.6% $\\downarrow$|-37.8% $\\downarrow$|-26.5% $\\downarrow$|\n\n\n|Model|         AUC         |         F1          |        Micro        |        Macro        |\n|:-: |:-------------------:|:-------------------:|:-------------------:|:-------------------:|\n|SGCN|    84.20 ± 0.12     |    93.69 ± 0.16     |    89.07 ± 0.26     |    76.55 ± 0.35     |\n| SGCN+DP-noise |    79.26 ± 0.41     |    92.74 ± 0.48     |    87.42 ± 0.76     |    72.84 ± 0.67     |\n|improv. | -5.85% $\\downarrow$ | -0.99% $\\downarrow$ | -1.92% $\\downarrow$ | -4.92% $\\downarrow$ |\n| GSGNN |    71.19 ± 7.73     |    96.28 ± 0.60     |    93.13 ± 1.19     |    75.29 ± 8.70     |\n| GSGNN+DP-noise |    70.36 ± 6.30     |    96.03 ± 0.39     |    92.69 ± 0.81     |    74.36 ± 6.60     |\n|improv. | -1.16% $\\downarrow$ | -0.26% $\\downarrow$ | -0.47% $\\downarrow$ | -1.23% $\\downarrow$ |\n|SiGAT |    76.52 ± 1.98     |    94.85 ± 0.17     |    91.08 ± 0.31     |    59.24 ± 1.61     |\n| SiGAT+DP-noise |    85.20 ± 0.65     |    95.11 ± 0.49     |    91.10 ± 0.50     |    70.87 ± 2.80     |\n|improv.|  11.34% $\\uparrow$  |  +0.00%   |  +0.00%  |  19.63% $\\uparrow$  |\n\nBased on the experimental results, S-Mixup did not effectively enhance the baseline, because the fusion operation of the S-Mixup at the feature level loses the structural information of the graph. However, DP-noise demonstrated effectiveness on certain metrics, and we believe that this kind of method of preserving the graph structure is worth further exploring. We will include these experimental results in the final version.\n\n**For Weakness 2 and Q2 on parameter number and training time**:\n\n1. Model parameter statistics\n\n|Model|#params|#change|\n|:-:|:-:|:-:|\n| SGCN |14851|-|\n|GSGNN |30580|-|\n|SiGAT |185600|-|\n|SGCN+SGA|29702|14851 $\\uparrow$|\n|GSGNN+SGA|45431|14851 $\\uparrow$|\n|SiGAT+SGA|200451| 14851$\\uparrow$|\n\n2. Model training cost time statistics\n\nBitcoin-alpha:\n|Model|time(s)|change(s)|\n|:-:|:-:|:-:|\n|SGCN|51.0 ± 5.3|-|\n|GSGNN|186.8 ± 42.5|-|\n|SiGAT|257.6 ± 25.8|-|\n|SGCN+SGA|197.4 ± 74.1|146.4 $\\uparrow$|\n|GSGNN+SGA|295.2 ± 65.9|108.4 $\\uparrow$|\n|SiGAT+SGA|395 ± 79.6|137.4 $\\uparrow$|\n\nBitcoinOTC:\n|Model|time(s)|change(s)|\n|:-:|:-:|:-:|\n|SGCN|75.4 ± 6.4|-|\n|GSGNN|142.8 ± 17.2|-|\n|SiGAT|277.0 ± 30.7|-|\n|SGCN+SGA|149.6 ± 42.7|74.2 $\\uparrow$|\n|GSGNN+SGA|5217 ± 48.0|5074.2 $\\uparrow$|\n|SiGAT+SGA|351.2 ± 41.2|74.2 $\\uparrow$|\n\n3. Complexity analysis please see Common Concern.\n\nOverall, the amount of additional parameters and training time for our method is relatively stable. When the model is large, our method does not bring greater computational complexity. Training can be carried out in a relatively short amount of time.\n\n**For Weakness 3 on Figure 3**:\n\nThank you for your suggestion. We have made revisions to Figure 3 and have submitted a revised version, which is included in the uploaded PDF. Due to time constraints, we will continue making further modifications later.\n\n**For Q1 on randomly adding edges**：\n\nDue to space limitations, we only present the performance of different baselines on the bitcoin-otc dataset with a randomly increased proportion of edges. The performance on other datasets is provided in the uploaded PDF file. Please refer to the uploaded PDF for detailed statistical results across more datasets.\n\n\nSGCN:\n|add_edge|AUC|F1|Micro|Macro|\n|:-:|:-:|:-:|:-:|:-:|\n|0%|78.3 ± 1.4|90.5 ± 2.6|84.0 ± 3.9|69.2  ± 4.1|\n|5%|77.4 ± 2.5|89.1 ± 1.9|81.8 ± 2.8|66.8 ± 3.0|\n|10%|75.5 ± 1.5|85.6 ± 2.9|76.8 ± 4.0|62.5 ± 3.0|\n|15%|74.7 ± 1.6|85.4 ± 2.9|76.4 ± 4.1|61.9 ± 3.1|\n|20%|67.5 ± 9.0|64.2 ± 32.3|57.7 ± 24.4|47.3 ± 19.4|\n\nGSGNN:\n|add_edge |AUC|F1|Micro|Macro|\n|:-:|:-:|:-:|:-:|:-:|\n|0%\t|89.1 ± 1.2|96.5 ± 0.7|93.6 ± 1.2|80.8 ± 2.0|\n|5%\t|87.1 ± 1.6|96.1 ± 0.1|92.9 ± 0.3|78.7 ± 1.0|\n|10%|86.4 ± 1.1|96.1 ± 0.1|92.8 ± 0.2\t|78.1 ± 1.1|\n|15%|84.5 ± 1.1|95.9 ± 0.2|92.5 ± 0.4|77.7 ± 0.6|\n|20%|85.2 ± 1.4|95.7 ± 0.3|92.2 ± 0.5|77.3 ± 1.4|\n\nSiGAT:\n|add_edge|AUC|F1|Micro|Macro|\n|:-:|:-:|:-:|:-:|:-:|\n| 0%| 76.5 ± 2.5| 94.9 ± 0.2|90.4 ± 0.3|59.2 ± 1.6|\n| 5% | 72.8 ± 3.7 | 94.7 ± 0.2  | 90.0 ± 0.4| 55.4 ± 4.3 |\n| 10%| 69.8 ± 5.3| 94.6 ± 0.1| 89.8 ± 0.2 | 54.7 ± 3.1  |\n| 15% | 70.1 ± 4.2 | 94.5 ± 0.1| 89.7 ± 0.2  | 54.4 ± 2.4 |\n| 20% | 70.3 ± 3.0| 94.6 ± 0.1 | 89.9 ± 0.2  | 55.2 ± 2.4 |\n\n\nOverall, randomly adding edges tends to degrade the model's performance, and the decline is more significant compared to randomly removing edges (refer to Fig.2 in the paper).", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "qQQBJhnBOW", "reviewer": "Reviewer_ShtJ", "summary": "The paper presents a novel Signed Graph Augmentation (SGA) framework designed to enhance the performance of Signed Graph Neural Networks (SGNNs). The primary focus is on addressing two persistent issues in SGNNs: graph sparsity and unbalanced triangles. The authors demonstrate that the commonly used DropEdge method is ineffective for signed graph augmentation. Instead, they propose SGA, which integrates structure augmentation, candidate edge selection, and a new data augmentation perspective to improve training. Experiments on six real-world datasets show significant performance improvements in link sign prediction tasks.", "questions": "- Can the proposed SGA framework be adapted for other signed graph tasks, such as node classification or community detection?\n\n- How does the performance of SGA scale with larger datasets or more complex network structures?\n\n- What are the computational overheads associated with the different components of the SGA framework, and are there ways to optimize them?", "limitations": "The authors acknowledge that their data augmentation method is based on balance theory, which may not be applicable to all real-world signed graph datasets. Additionally, the method has only been validated on link sign prediction tasks, and its effectiveness on other tasks remains untested. To improve, the authors could explore the generalization of SGA to other tasks and consider alternative theoretical frameworks for signed graph augmentation. Potential societal impacts, especially in contexts involving negative social interactions, should also be addressed.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "Originality: The paper introduces a new augmentation framework specifically designed for SGNNs, which addresses the unique challenges of signed graphs.\n\nQuality: The methodology is well-validated through extensive experiments on multiple real-world datasets, demonstrating substantial improvements in performance metrics.\n\nClarity: The paper is well-organized, with clear explanations of the proposed methods and thorough discussions of experimental results.\n\nSignificance: This work provides valuable insights and tools for improving SGNNs, which are crucial for tasks like link sign prediction in social networks.", "weaknesses": "Generalization: The effectiveness of SGA on other types of signed graph tasks, such as node classification or community detection, has not been explored.\n\nComplexity: The proposed framework involves multiple steps and parameters, which may complicate its implementation and tuning.\n\nResource Intensive: The computational requirements for the proposed method may be high, potentially limiting its practical application in resource-constrained environments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**For Weakness 1 and Q1 on more downstream tasks:**\n\nThanks for your constructive comments. Existing SGNN methods focus primarily on the link sign prediction task, and they ignore the performance on other tasks. We experiment with the performance (metric: Average Accuracy± standard deviation) of SGA on different baselines in node classification and community detection tasks. The datasets were sourced from [16] .\n\n1. Node Classification \n\n|model|        rainfall        |        samspon         |\n|:-:|:----------------------:|:----------------------:|\n|SGCN|    0.72 ± 0.05     |    0.76 ± 0.17     |\n|SGCN+SGA |    0.75 ± 0.03     |    0.72 ± 0.18     |\n|improv.|  **4.2% $\\uparrow$**   | **-5.3% $\\downarrow$** |\n|GSGNN|    0.72 ± 0.06     |    0.44 ± 0.30     |\n|GSGNN+SGA|    0.68 ± 0.02     |    0.44 ± 0.26     |\n|improv.| **-5.6% $\\downarrow$** |       **0% -**   |\n|SiGAT|    0.64 ± 0.23     |    0.60 ± 0.20     |\n|SiGAT+SGA|    0.65 ± 0.13     |    0.68 ± 0.18     |\n|improv.|  **1.2% $\\uparrow$**   |  **13.3% $\\uparrow$**  |\n\n2. Community Detection\n\n|model|rainfall|          ppi           |\n|:-:|:-:|:----------------------:|\n|SGCN|0.49 ± 0.15|    0.26 ± 0.09     |\n|SGCN+SGA |0.60 ± 0.04 |    0.26 ± 0.09     |\n|improv.|**22.4% $\\uparrow$**|        **0% -**        |\n|GSGNN|0.39 ± 0.02|    0.36 ± 0.01     |\n|GSGNN+SGA|0.40 ± 0.01 |    0.33 ± 0.06     |\n|improv.|**2.6% $\\uparrow$**| **-8.3% $\\downarrow$** |\n|SiGAT|0.53 ± 0.15|    0.14 ± 0.01     |\n|SiGAT+SGA|0.60 ± 0.08 |    0.16 ± 0.02     |\n|improv.|**13.2% $\\uparrow$**|  **14.3% $\\uparrow$**  |\n\nBased on the experimental results, the SGA shows minimal improvement for the node classification task, but it significantly enhanced the performance for the community detection task.\n\n**For Weakness 2:**\n\nPlease see Common Concern.\n\n**For Weakness 3 and Q3 on computational overheads:**\n\n1. Model parameter statistics\n|Model|#params|\n|:-:|:-:|\n| SGCN |14851|\n|GSGNN |30580|\n|SiGAT |185600|\n|SGCN+SGA|29702| \n|GSGNN+SGA|45431|\n|SiGAT+SGA|200451| \n\n2. model training time cost\nBitcoinOTC:\n|Model|time(s)|\n|:-:|:-:|\n|SGCN|75.4 ± 6.4|\n|GSGNN|142.8 ± 17.2|\n|SiGAT|277.0 ± 30.7|\n|SGCN+SGA|149.6 ± 42.7|\n|GSGNN+SGA|5217 ± 48.0|\n|SiGAT+SGA|351.2 ± 41.2|\n\nThe method proposed maintains a relatively stable number of additional parameters and training time, even for large models, avoiding increased computational complexity. Training is efficient and can be completed quickly. The additional operations required by the method can be optimized using parallelization, divide-and-conquer strategies, and feature reduction algorithms. More detailed statistical results are available in the referenced PDF.\n\n**For Q2 on the performance on large datasets:**\n\nWe tested the performance of SGA on the Amazon-CD dataset [17]. The dataset contains 895,266 edges and 97,731 nodes, making it one of the larger signed graph datasets we could find.\n\n|            | AUC              | F1-Binary  | F1-Micro   | F1-Macro   |\n|------------|------------------|------------|------------|------------|\n| SGCN       | 61.65 ± 0.14 | 69.11 ± 1.41 | 58.56 ± 1.14 | 53.04 ± 0.69 |\n| SGCN+SGA   | 58.26 ± 0.37       | 83.08 ± 1.47 | 72.47 ± 1.65 | 57.44 ± 0.39 |\n| SIGAT      | 55.08 ± 1.45       | 89.96 ± 0.29 | 81.76 ± 0.48 | 45.02 ± 0.48 |\n| SIGAT+SGA  | 64.58 ± 0.29     | 89.51 ± 0.32 |  81.83 ± 0.20  |53.28 ± 0.17   |\n\nBased on the experimental results, our method improves the performance of the baselines on the Amazon-cd dataset.\n\n**For Limitation on alternative theoretical framework:**\n\nRegarding the analysis of SGA's generalization, we have conducted the following brief discussion.\n\nSGA prevents the formation of unbalanced triangles in the input graph while selecting beneficial training samples. This stabilization of the graph structure preserves the eigenvalue distribution, thereby enhancing the quality of the graph embedding. Let $L$ be the Laplacian matrix with unbalanced triangles and $\\lambda_i$ its eigenvalues. After eliminating unbalanced triangles, the Laplacian matrix and eigenvalues become $L'$ and $\\lambda'_i$, with $\\Delta L$ representing the matrix perturbation. The corresponding change in eigenvalues can be expressed as\n\n$$\\Delta\\lambda_i=\\lambda_i^{'}-\\lambda_i=\\mathbf{v}_i^T\\Delta L\\mathbf{v}_i,$$\n\nWhere $v_i$ the eigenvector of $L$, $Z$ the original embedding vector, and $Z'$ the embedding vector after eliminating unbalanced triangles. Removing unbalanced triangles reduces the absolute values of the Laplacian matrix's non-diagonal elements, decreasing the perturbation matrix $\\Delta L$. Consequently, the change in eigenvalues $\\lambda_i$ decreases, leading to $\\mathrm{Var}(\\lambda) > \\mathrm{Var}(\\lambda')$. By Spectral Graph Theory, this implies $\\mathrm{Var}(Z) > \\mathrm{Var}(Z')$.\n\nLet $H$ be the original embedding space and $H^{'}$ be the embedding space after variance reduction. Since the variance of the embedding vectors becomes smaller, the distribution range of the embedding vectors becomes smaller. We have:$$\\|\\|\\mathbf{Z}_i-\\bar{\\mathbf{Z}}\\|\\|^2>\\|\\|\\mathbf{Z}_i^{'}-\\bar{\\mathbf{Z}}^{'}\\|\\|^2.$$\n\n\nThus, coverage number $N(\\epsilon,\\mathrm{H}^{\\prime},\\|\\cdot\\|)$ will be less than coverage number $N(\\epsilon,\\mathcal{H},\\|\\cdot\\|)$ for the same $\\epsilon$.\n\nIn particular, the covering number can be used to define an upper bound on Rademacher complexity [15]. $H$ is the hypothesis space, $N(\\epsilon,\\mathcal{H},\\|\\|\\cdot\\|\\|)$ is the number of covers, and Rademacher complexity \n$R_n(H)$ can be defined by the following inequality:\n\n$$\\mathrm{R}_n(\\mathrm{H})\\leq2\\epsilon+3\\sqrt{\\frac{\\log N(\\epsilon,\\mathrm{H},\\|\\|\\cdot\\|\\|)}n}.$$\n\nWe've got $$\\log N(\\epsilon,\\mathrm{H}^{'},\\|\\|\\cdot\\|\\|)<\\log N(\\epsilon,\\mathrm{H},\\\\||\\cdot\\|\\|).$$\n\nThus we finally show that SGA can be useful in improving the generalization performance by decreasing the number of coverages in the embedding space while increasing the number of samples, which ultimately shrinks the upper bound of $R_n(H)$.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:
Thank all reviewers for their valuable and constructive comments. We address the common concern here and believe the quality of the paper has been improved following the reviewers' suggestions.

**Common Concern: Time and Space Complexity of SGA**

Suppose we are given a signed graph $\mathcal{G}=(\mathcal{V},\mathcal{E}^+,\mathcal{E}^- )$, where $\mathcal{V} = ({v_1, \ldots, v_{|\mathcal{V}|}})$  represent the set of nodes, $\mathcal{E}^+$  and $\mathcal{E}^-$ respectively denote the positive and negative edges, and the structure of $\mathcal{G}$ is represented by the adjacency matrix $A∈\mathbb{R}^{|\mathcal{V}|×|\mathcal{V}|}$. 

**Background**

The computation of the l-th layer of a SGNN network is:
$$
X^{L+1}=σ(AX^l W^l)
                             =σ(A^+ X^l W^l+A^- X^l W^l)
$$

Where $σ()$ is a non-linear activation function, $W^l$ is a feature transformation matrix $∈\mathbb{R}^{F_l×F_{l+1}}$, and $A^+$ and $A^-$ are the adjacency matrix of positive edges and negative edges, respectively. For simplicity, we assume the node features at every layer are size-F. As such, $W^l$ is an $F×F$ matrix. 

**Time Complexity Analysis:**

1) SGNN

     We analyze the complexity of the SGNN by three high-level operations: 

	i. feature transformation ($Z^L=X^l W^l$),

	ii. neighborhood aggregation ($A^+ Z^L,A^- Z^L$),

	iii. activation function ($σ()$).

Part i. is a dense matrix multiplication between matrices of size $N×F_l$ and $F_l×F_{l+1}$. As our assumption $F_l=F_{l+1}=F$, the complexity is $O(NF^2)$.

Part ii. is a multiplication between matrices of size $N×N$ and $N×F$, yielding $O(N^2 F)$. We use a sparse operator, neighborhood aggregation for each node therefore requires $O(d^+ F+d^- F)$, where $d^+$ and $d^-$ respectively represent the positive and negative neighbors of each node on average. Finally, we have a total complexity of $O(NdF)$, where $d=d^++d^-$.

Part iii. is simply an element-wise function, so its cost is $O(N)$.

Over $L$ layers, the complexity is $O(L×(NF^2+NdF+N)$ for one forward propagation.
The time complexity of backpropagation is usually the same as that of forward propagation because it requires the gradient to be computed and the parameters to be updated is the same as forward propagation.

2) SGA

	We decompose the complexity of the SGA by two operations:

	i. Updating training data by similarity calculation,

	ii. Training model by curriculum learning.

Part i. involves a dense matrix multiplication between two matrices of size $N×F$, yielding $O(N^2 F)$. Note that, this part runs only once and does not participate in forward and backward propagation.  In our experiments, this process can be optimized in parallel, and its time complexity is lower than that of SGN.

Part ii. is an upgraded version of the original SGNN. Similar to the analysis in section 1, we can have a complexity of $O(L×(NF^2+NdF+N))$ in this part.

Finally, we conclude that the complexity of SGA is the same as that of SGNN, which is $O(L×(NF^2+NdF+N))$.

**Space Complexity Analysis:**

1) SGNN

	i. The space complexity of the input feature matrix X is $O(NF)$.

	ii. The adjacency matrix A: $O(N^2)$ which can be optimized by sparse operator $O(Nd)$.

	iii. The space complexity of the output feature matrix $H^{l+1}$ is $O(NF)$, where $l$ represents the current layer and $l+1$ represents the next layer.

	iV. The space complexity of the weight matrix W is $O(F^2 )$.

The space complexity of SGNN is $O(Nd+NF+F^2 )$ for one layer network.

2) SGA


	i. The space complexity of the input feature matrix X is $O(NF)$.

	ii. The adjacency matrix A: $O(Nd+M)$ where M is the augmented edges and $M<Nd$.

	iii. The space complexity of the output feature matrix $H^{l+1}$ is $O(NF)$, where $l$ represents the current layer and $l+1$ represents the next layer.

	iV. The space complexity of the weight matrix W is $O(F^2 )$.

In the case of using the same activation function, the space complexity of SGA is also $O(Nd+NF+F^2 )$.

**Experimental Setup**:  Our experimental results are reported as the mean and standard deviation calculated over 5 runs. The uploaded PDF includes supplementary experimental results and an updated framework figure.

**References throughout the entire rebuttal:**

[1] Han, Xiaotian, et al. G-mixup: Graph data augmentation for graph classification. ICML'22.

[2] Ling, Hongyi, et al. Graph mixup with soft alignments. ICML'23.

[3] Lin, Lu, et al. Spectral augmentation for self-supervised learning on graphs. ICLR'22

[4] Xia, Yutong, et al. Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification. arXiv'2024.

[5] Zhao, Tong, et al. Data augmentation for graph neural networks. AAAI'21.

[6] Zhang, Zeyu, et al. Rsgnn: A model-agnostic approach for enhancing the robustness of signed graph neural networks. WWW'23.

[7] Derr, Tyler, Signed graph convolutional networks. ICDM'18.

[8] Huang, Junjie, et al. Signed graph attention networks.ICANN'19

[9] Liu, Haoxin, et al. Signed graph neural network with latent groups. KDD'21. 

[10] Seo, Changwon, et al. SiReN: Sign-aware recommendation using graph neural networks. TNNLS'23.

[11] Huang, Junjie, et al. Signed bipartite graph neural networks. CIKM'21.

[12] Tzeng, Ruo-Chun, et al. Discovering conflicting groups in signed networks. Neurips'20.

[13] Zhang, Guangzhan, et al. SGNNMD: signed graph neural network for predicting deregulation 
types of miRNA-disease associations. BIBM'22.

[14] Xiao, Han, et al. Searching for polarization in signed graphs: a local spectral approach. WWW'20.

[15] Tang, Huayi, et al. Towards understanding generalization of graph neural networks. ICML'23.

[16] He, Yixuan, et al. SSSNET: semi-supervised signed network clustering. SDM'22.

[17] Chen, Sirui, et al. SIGformer: Sign-aware Graph Transformer for Recommendation. SIGIR'24.

Meta-review: The paper studies the problem of data augmentation in signed GNNs (SGNNs). Specifically, it first derives generalization bounds for SGNNs, while it also introduces a new augmentation strategy to improve upon DropEdge's performance on link sign prediction. The proposed approach has merits that the reviewers have highlighted. These mostly include the novelty of the methodology as well as the theoretical and empirical support.  The authors have adequately addressed most of the reviewers' concerns. Therefore, I recommend accepting the paper.
Decision: Accept (poster)