Revolutionizing Graph Aggregation: From Suppression to Amplification via BoostGCN
Authors: Jiaxin Wu
Chenglong Pang
Guangxiong Chen
Jie Zhao
Venue: NeurIPS 2025 poster ()
Keywords: Graph Convolutional Networks
Collaborative Filtering
Recommendation System
Graph Aggregation
Information Amplification
Primary area: general_machine_learning
TL;DR: BoostGCN makes a breakthrough in transforming graph aggregation from information suppression to information amplification, resulting in significant improvements in performance and efficiency.

Abstract: Graph Convolutional Networks (GCNs) based on linear aggregation  have been widely applied across various domains due to their exceptional performance. To enhance performance, these networks often utilize the graph Laplacian norm to suppress the propagation of information from first-order neighbors. However, this approach may dilute valuable interaction information and make the model slowly learn sparse interaction relationships from neighbors, which increases training time and negatively affects performance. To address these issues, we introduce BoostGCN, a novel linear GCN model that focuses on amplifying significant interactions with first-order neighbors, which enables the model to accurately and quickly capture significant relationships. BoostGCN has relatively fixed parameters, making it user-friendly. Experiments on four real-world datasets demonstrate that BoostGCN outperforms existing state-of-the-art GCN models in both performance and efficiency.

Revolutionizing Graph Aggregation: From Suppression to Amplification via BoostGCN
Jiaxin Wu School of Management
Chenglong Pang
School of Computer Science and Technology Donghua University, China
Guangdong University of Technology. China 704276515@qp) com
clongdwyyx@163.com
Guangxiong Chen School of Management
Jie Zhao'
School of Management Guangdong University of Technology, China edu. cn
Guangdong University of Technology, China 31220033500mai12 gdut. edu.
Abstract
Graph Convolutional Networks (GCNs) based on linear aggregation have been widely applied across various domains due to their exceptional performance. To enhance performance, these networks often utilize the graph Laplacian norm to suppress the propagation of information from first-order neighbors. However, this approach may dilute valuable interaction information and make the model slowly learn sparse interaction relationships from neighbors, which increases training time and negatively affects performance. To address these issues, we introduce BoostGCN, novel linear GCN model that focuses amplifying significant interactions with first-order neighbors, which enables the model to accurately and quickly capture significant relationships. BoostGCN has relatively fixed parameters, making it user- vre-friendly. Experiments on four real-world datasets demonstrate that BoostGCN outperforms existing state-of-the-arr GCN models in both performance and efficiency.
Introduction
In recent years, Graph Convolutional Network (GCN) 1 has emerged powerful tool for learning from graph-structured data, with applications various fields, such as fair recommendation [2]
bundle recommendation 54.6, (),, sequential recommendation [7 g g [0] and others. The success of GCNs depends on their ability to accurately capture the user and item representation, which is achieved through aggregation process that effectively combines collaborative signals from the nuanced interactions within the user-item graph. For example, Neural Graph Collaborative Filtering (NGCF) [T] captures user-item relationships by effectively leveraging high-order interactions through its aggregation approach. It is worth noting that some subsequent studies [12 [3 have shown that the use of feature transformations and nonlinear activation functions aggregation can lead significant performance degradation. Consequently. the linear aggregation-based GCN [12] has emerged as the dominant framework in this field. Then, based on the linear GCN framework, the improved methods
that incorporate multimodal information [14] 15 16 17
18 19], attention mechanism [14] 20 21].
constraint loss 222 23 [3,, edge-wise dropout 24 and layer dropout [25] have blossomed.
To preserve the distinctiveness of individual nodes, existing GCN models 12 13 25
use the graph
Laplacian norm ①1 suppress information propagation, especially from first-order neighbors. As
Cooresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Information Suppression
Information Amplification
(a)
(b)
Figure 1: Problem presentation. The red node represents the target node, while the green nodes denote its first-order second-order neighbors. (a) shows that information propagation the red node via the graph Laplacian norm can lead to information suppression due to considering first-order and second-order neighbors. (b) shows
paradigm that amplifies the significant interaction information from the first-order neighbors in the information propagation.
shown in Figure I the red node represents the target node for information aggregation, while the green nodes represent first-order high-order neighbors. Figure aa) shows the of first-order and second-order neighbor information GCN models, highlighting how the graph Laplacian norm stabilizes the representation scales without growth due to convolutions. While aaplacian-based models have established dominance and performance, we argue that their designs may excessively suppress the propagation of valuable information. Such models employ some stereotypical strategies that suppress items with higher interactions. However, relying solely on the number of interactions to assess the value of item may inevitably overlook its comprehensiveness, leading to the neglect of some significant items. Specifically, the first-order neighbors, as the immediate interaction objects of the red target node in Figure [[),, are replete with significant interaction relationships, such as conformity [26], trust (27 28 and so on, which are particularly significant in the context of recommendation systems. The use of the graph Laplacian norm in this way can inadvertently dilute information about these significant interactions as information propagates to red nodes, which leads protracted and sub-optimal learning trajectory for the model.
To confirm our hypotheses, we perform an in-depth investigation of LightGCN, quintessential representative of Laplacian-basee models. As shown in Table experimental results on Amazon- Book from LightGCN [12] show that the mean-based aggregation method outperforms the graph Laplacian norm-ban based method, which suggests that information suppression via the graph Laplacian norm may miss significant interaction information, especially for large datasets.
Table 1: Overall performance comparison between mean-based aggregation and Laplacian- based aggregation on Amazon-Book Mean-based aggregation represents averaging the surrounding infor- mation according to the number of first-order neighbors. Laplacian- aggregation represents further consideration of second-order neighhors to weaken the entry of surrounding information.
Datasets
Amazon-Book
Metrics
Recall@
NDCG@20
Laplacian-based
0.0411
0.0315
Mean-based
0.0419
0.0320
Improv.(%)
+1.95%
+1.59%
Motivated by these empirical findings, we explore the significant interactions within the first-order neighbors, and propose a novel linear GCN model, namely BoostGCN. As shown in Figure bb), mining and amplifying the significant interactions the information propagation from the first-order neighbors can be a new paradigm to improve model performance and efficiency in GCN. Accordingly, BoostGCN skilfully uses the amplification function to amplify the significant interactions in the information aggregation process, equipped with the sensitivity quickly and accurately capture

---

the sigmificant interaction cues. Moreover, this refined focus on first-order neighbor interactions is expected result a model that not only leams faster, but also achieves higher levels of performance.
The major contributions of this paper are listed as follows:
We innovate graph aggregation with BoostGCN, moving from suppression to strategic amplification of significant interactions in GCNs.
We deliberately design the amplification function interaction significance used in Boost- GCN to be sensitive to significant interactions, thereby increasing performance and effi- ciency.
Extensive experiments across four real-world datasets clearly show that our proposed BoostGCN has the best performance in terms of both recommendation performance and efficiency.
Preliminaries
For recommendations, the general GCN [12] based on linear aggregation achieves impressive perfor- mance through straightforward process. To understand its general framework in depth, we define the interactions between and items in graph as: g {(u, i) lu U, I), where U and I are the user and item sets, respectively. Also, in the graph, cu and e, are the ID embeddings user u and item é. Thus,
obtain all the original inputs:
E (eu, U, EI
where e, E R l and e; embedding size.
R
x
and [Z] are the number of users and items; d is the [
Interestingly, existing linear GCNs 12 1 25 all leverage the graph Laplacian norm for information
aggregation, as illustrated by the following formula:
(++1) = EE
Σ
R3)
E.N. VWN.VVA
WENS VWTVWW
where No and Mt are the neighbor node sets of user u and item i; [Wall and [W]] are the number
of neighbors of user u and item i; VivalvIN the graph Laplacian norm; (*)) and e are embeddings of user and item at layer k.
3 BoostGCN
3.1 Significant Interactions
In recommender systems, it critical to accurately measure and learn user preferences from historical interactions. While it's clear that first-order neighbors with the most direct interactions have the influence, it's sigmificant to recognize that not all interactions are created equal. The assumption that all interactions carry the same weight contradicts intuitive understanding.
As a result, we introduce a measure interaction significance St+m. which represents the significance of each item i M, in the historical interaction relationships of user u::
S = f(x)
where X; = { 1, F2 .... Fi,n) represents factor set of item i that contains different factors Zi.m related to interaction significance; f(-) is the function that transforms these factors into interaction significance.
have discovered that user behavior patterns, such as conformity, trust and etc., are reflected in the interaction relationships, which are critical for mining user preferences. Consequently, they are key factors measuring interaction significance.
Drawing from previous research 26 28
Given that the factors of conformity, trust and etc., are {I 24,2 m.. Fi,m J. then we can get factor subset & { 1, Z4,2, ... Ti.m) for each item i, where X, S X. Based Eq.
get the
3

---

relationship between &g and Si as follows:
Sp-m 5 (8)
where f1(-) and f2(-) represent different transformation functions that are used to achieve the consistent effect of the segmented subsets and full sets of factors.
Interestingly, the effects of conformity, trust and etc., approximately match the trend of the interaction volume of items [27] [26 28), that is, the interaction edges [NG] of items in GCN. Therefore, we can always find way that establishes the following approximate relationship:
f1(2)) LA1 + Å
(5)
where PIA is the estimate of f(X;) quantified by [Wi]; Å is used compensate for the estimation bias of P/
Based on Eq. and Eq. we can easily obtain:
S
PW A
(6)
where A represents the influence of the factors in X \ Rr and the estimation bias compensation À of p/
3.2 Significant Interaction Amplification
we recognize that the higher the level of trust or conformity associated with an item, the greater the trend for user selection. Based on this insight, it is reasonable assume that the more pronounced the positive effects of such factors in L, the higher the interaction significance with item i. Consequently, we can deduce the following relationship:
According to previous findings 27 26 28
Si x IMI
On the basis (). considering the balance between model sensitivity to interaction significance and model ability handle large [N1], we choose the logarithmic function rather than the softmax method to quantify S. by [.a]. thereby amplifying significant interactions from neighboring items. Accordingly, ( can be rewritten as:
S Amp
Φb log + Alog
(
where /oo ([V logs(-) is the amplification function and Alog denotes the offset under [AG
the logarithmic function. Based on Eq. we can set , > 1 and llg > 0 to keep SAme x [Wi..
Amp is the difference in the interaction significance of items ăp. in E Ny, then we can Given that (Kp.ky)
get:
Amp (5p.5g)
S.App
-.oogg log [N/
$ log
IAG
On the basis of (q. we can know that the impact of the significance estimation bias between ip and in mainly stems from Amp ((pp,g))' The advantage of the logarithmic function is that the significance estimation bias can adjusted directly by changing 3 in the amplification function.
Therefore, for each user E l and his historical interactions with a set of items {ir, i2, in) where in E Ni. we can obtain the following amplified interaction significance for each historical interaction relationship between u and i,:
Amp Nu = (5 -u: Sry
Amp
S -uu
(10)
3.3 GCN with Information Amplification
According to the above analysis, we propose Boost Graph Convolution (BGC) method that focuses on amplifying significant interactions with first-order neighbors on the basis of Eq,10), which allows

---

the model to accurately and quickly capture significant relationships. In BoostGCN, as shown in the graph convolution operation is:
Figure 2
S Amm
S Amp b-
(k+1)
(k),
(++1)
Σ
(11)
Nul
[N
N
uEN,
Also, El can be rewritten as:
11
$ blog NG
+ A log
blog Ng
+ A Alog
(k++1)
W e, ;0;
(l) (k+1)
(12)
Wil
where Log calculated by the amplification function logg([>Vi):; 3 and Aoog > 0 (we set Nil
Alog = 1 in the following experiments to keep the purpose of amplification by making S, > 1). (k)
eu and e, (8) are the emheddings of user and item at layer kt (0) eu and e; (0) [W] are the number of neighbors of user u and item i.
exc Wild and
In BoosIGCN, each k-th layer captures distinct information. To integrate this information ef- fectively, we have applied weighted sum in the combination of layers, thereby making the representation more comprehensive. After K layers, we obtain the ultimate representation for user (or item) through weighted combina- tion of embeddings from each layer, which can be articulated as follows:
Prediction
Cu
Weighted Combination
Weighted Loyer Combination
S TAVT
Layer
Interaction La Amelification,
Interaction Amplification
K
K
S With J.:
C/ = Σ
(k).
è; = -=Emee 2
(13)
K=0
k=0
Us
Uy
where 2 O denotes the significant of the k-tth layer embedding, and uniformly Yok to K+I in the following experiments.
Boost Graph Convolution (B6C)
107
Input
Then, the model prediction can be defined as:
F(u.i) = e e
(14)
Figure 2: The overview of BoostGCN.
which is used determine the ranking score for the recommendation.
Following the previous research described as follows:
12
we Bayesian Personalized Ranking (BPR) loss, which is
CBPR =
Σ W.Y, ER
-In(o(F(u.0) - ((w,)))) 11
(15)
where R {(u,i, ( E (u, R- is the training dataset including the observed inter-
actions R and the unobserved interactions R R= (.)) and À denote the sigmod function and regulariza- tion weight, respectively; the trainable parameters of BoostGCN are only the initial embeddings of the
O-th layer of users and items, i.e., θ = [E))),, where |E Eneu lle (0) 1|2 + Ever |le ||a
4 Theoretical Analysis of BoostGCN
The selection criteria for the amplification function. To balance the signal gain, robustness and learnability of significant interactions, we propose the following three criteria for selecting node amplification function: (i) should increase monotonically with the number of interactions so that nodes with high number of interactions contribute more information; (ii) it should exhibit non-linear growth to prevent over-amplifying extremely interactive nodes and introducing noise; and (ii) it should be a closed-form form, differentiable expression for efficient gradient-baut optimization.
5

---

Consequently, the logarithmic amplification function is the optimal closed- form solution under these criteria. Comparative analysis with other amplification functions provided in Appendix AA.2
Advantages of the logarithmic amplification function. The logarithmic amplifier in Eq. 8 exposes single scalar 3 that instantiates tunable trade-off between magnitude amplification and model sensitivity. A larger / compresses inter-item differences Amp
((g,+ty)* yielding more uniform signal landscape, whereas a smaller 3 stretches these gaps, heightening sensitivity to subtle interaction sparsity. Detailed derivations and analysis provided in Appendix A.2
While Appendix AA.3 details the advantages of BoostGCN's aggregation over the aggregation using graph attention, we here focus on its general-purpont properties as universal aggregation paradigm.
(Smaller aggregation error) With Boos/GCN's aggregation in Eq. (2, the error bound decays at the rate of O(loga() ([;1)++) as the neighbor cardinality [Ng] increases, guaranteeing diminishing aggregation error even for highly interactive nodes.
Proposition 4.1
Proposition 4.2
(Near-optinal provable linear convergence rate) By using the logarithmic amplifier in Eq. BoostGCN can achieve a spectral-radius bound arbitrarily close to the infimum of the sub-lineat family and yield near-optimal provable linear convergence rate.
Next, give the stochastic convergence bounds of BoostGCN under stochastic training conditions.
Theorem 4.3 Under independent and identically distributed (i.i.d.) mini-batch sampling, bounded gradients and L-smoothness, BoostGCN's 's expected error bound is
(lIIH(() ( "" < (1- 2n/A)* Ao + 7/22/(2))
(16)
And BoostGCN's high-probability bound is
Log K
[H(K) |1(K) =0[(ogg(marr +1
with probability at least 1-5. (17)
where H(K) is the current embedding matrix of all users and items after K rounds update of random training and Htr is the ideal embedding when the loss function converges to the minimum value, where (K)), H E {
is the learning rate and X is the regularization term; G is the boundary of gradients, where G >> O and ||V I G for any mini-batch; Do = E|] - H [1%)] and 8 (0, 1) is confidence parameter. The proofs of the above-mentioned properties be referred to Appendix A.4
5 Experiments
In our experiments, the following questions will be answered:
RQI: How does the performance of BoostGCN compare with state-of-the-art GCN models?
RQ2: How efficient is BoostGCN?
RQ3: How do different hyper-pane parameter settings affect BoostGCN?
RQ4: What benefits does the amplification of significant interactions offer to the representa- tion?
RQS:
How does BoostGCN perform in terms of popularity debiasing and noise resistance?
5.1
Experimental Settings
Datasets:
To comprehensively demonstrate the effectiveness of BoostGCN, evaluate model on
four distinct datasets, including MovieLens- 100k (denoted by 100k) [29] MovieLens-IM (denoted
by IM) 229] Gowalla (denoted by Gowa.) (30] and Yelp2018 (denoted by Yelp) [I]] as detailed in
Table 2 The datasets utilized in this paper are all publicly available and can be directly downloaded
from their respective sources. Detailed dataset descriptions are given in Appendix A.6 A.6

---

Table 3: The comparison of overall performance on four real-world datasets. Bold means the optimal performance, and underline means the sub-optimal performance.
Dataset Metric
MF-BPR MMGCK
NGCF
UlraOCN
IMP-GCN NSE-GCN LayerOCN
LightGCN
LTGNN
TransCNNN
GAT
[BoosCCCN
R@5
0.263
0.246
0,2318
0.2647
0.2864
0.296
0.2851
0.2861
0.2833
0,2733
0.2879
0.2982
100k
N@s
0.6599
0.6181
0.6067
0.6575
0.7029
0.7209
0.6840
0.6971
0.6872
0.6630
0.6983
0.7234
R@15
0,5289
0.4953
0.4929
0.5393
0.5611
0.5886
0.5563
0.5669
0.5612
0.5415
0.5703
0.5908
N1
0.6616
0.6190
0.6126
0.6662
0.7028
0.7%1
0.6894
0.7044
0.6952
0.6708
0.7065
0.7319
R@5
0,2165
0.2178
0.2081
0.2389
0,2424
0.2546
0.2599
0.2476
0.2570
0.2581
0.2537
0.2641
IM
N@s
0,7220
0,7183
0.7128
0.7554
0.7624
0.7863
0. 0.7949
0.7770
0.7235
0.788]
0.7844
0.8063
0.46119
0,4668
0.4545
0.5057
0,4965
0.5128
0.5251
0.5058
0.4770
0.519
0.5316
18
0,7041
0,7011
0.6934
0,7464
0.7441
0.7651
0.7782
0.7571
0.7075
0.7707
0.7574
0.7885
R65
0.199
0.0706
0.1485
0.2288
0,2808
0,2946
0.2932
0.2521
0.2178
0.2913
0.288.
0.2965
Nee
0.1122
0,1892
0.3131
0.3733
0.3901
0,3890
0.3408
0,2893
0.3863
0.3937
R@ 15
0,3447
0.1100
0.3310
0.3851
0.4868
0.5123
0.5092
0:4476
0.3780
0.5055
0.5003
0.5145
15
0,3125
0.1251
0,2506
0.3460
0.4235
0.4468
0.4444
0.3883
0.3298
0.4410
0.4365
0.4489
R495
0.1225
0,0826
0,0984
0.1435
0.1753
0.1677
0.1 0848
0.1545
0.1375
0,1640
0.1635
0.2001
Yelp
N@s
0.2225
0.1582
0.1747
0.2581
0.3
0.2945
0.3238
0.2747
0.2416
0.2883
0.2874
0.3517
R5
0,2592
0,1900
0,2460
0.5021
0.3567
0.3478
0.3722
0.3213
0.2726
0.1253
0.3243
0.3968
15
0.1819
0.2186
0.2901
0.3455
0.3324
0.3611
0.3086
0.2658
0,3172
0.3869
Data Pre-processing: Each dataset is divided into training (60%), validation (20%), and test sets (20%). The training set maintains a 1:1 ratio of positive to negative samples. For MovieLens- 100k and Moviel Lens- IM datasets, we add 150 unused negative samples for each user the val- idation and test sets, respectively. Correspond- ingly, for Gowalla and Yelp2018 datasets, we increase the number to 1500 negative samples. The negative samples of the training set, validation set and test set are all randomly selected without popular bias.
Table 2: The description of datasets.
Datasets
#Interactions #Users fltems Sparsity
MovieLens-100k
91,076
943
1,286
92.49%
MovieLens-IM
898.224
6,036
2.864
94.80%
Gowalla
1,027,370
29,858
40,981
99.92%
Yelp2018
1,561,406
31,668
38,048
99.87%
Evaluation Metrics:
We employ Recall (R) and Normalized Discounted Cumulative Gain (N) [1] as the main performance metrics for Top-N recommendations (32), where N = (5, 15). For the sake of convergence, the early stop and total epochs are set to 10 and 1000, respectively. We run each experiment ten times and report the average results.
Baselines: We compare some representative models, ranging from traditional matrix factorization models to state-of-the-e GCN-based models: MF-BPR (33), MMGCN [29], NGCF MI Light-
GCN 12). UltraGCN [3), IMP-GCN 34,, NSE-GCN (35), LCyerGCN 25). LTGNN (36), TransGNN (37] and GAT-LightGCN (combining LightGCN with Graph Attention Network). In order to make a fair comparison, we carefully tune the parameters of each model based on their respective published papers and hyper- parameter studies. All baselines compared in this paper can be obtained directly from the corresponding literature. Detailed baseline descriptions are given in Appendix A.5
Implementation Details: To ensure a fair comparison, we set the embedding size to 64, a learning rate of 10 with Adam (38) and initialize the embedding parameters with the Xavier method [3]] which is the same as other baselines. To show the high generalization of BoostGCN on different datasets without parameter tuning, we set the fixed parameters: batch size of 512, 8 = {e) and
Alog in Eq. 12). Also, we provide guidance on X for different types of datasets to optimize model performance. We employ À < (1e-0) for datasets of #Interactions 2 1 x 10 == (1e-1} for datasets of # #Interactions < 5 x 10 and X = (1e-5) for others. Our code can be available on https::// tig..b....... com/ / ClongPang/ wwwoogggg/ooostCCC// /BoostCCN
5.2 Experimental Results
Performance Comparison (RQ1): Due to the excellent performance of most baselines at layer 2, we set K = 2 to evaluate overall performance for a fair comparison, as shown in Table From Table 3 we can easily see that: BoostGCN maintains the best performance against all baselines across four datasets of different sparsity and data size, which shows that it has stable performance in handling different types of datasets.
7

---

Table 4: The comparison of performance between BoostGCN and LightGCN different layers. Bold indicates the optimal performance at each layer on four datasets. represents the best performance of different layers on the target dataset. Improv. denotes the improvement of BoostGCN against LightGCN at each layer.
Dataset
100k
IM
Yelp
Gowa.
#Layer
Model
R@5
N@5
R@5
N@5
R@5
N@s
R@5
N@5
LightGCN
0.2840
0.6937
0.2413
0.7647
0.1630
0.2895
0.2614
0.3517
BoostGCN
0.2946
0.7157
0.2607
0.7997
0.1824
0.3258
0.2746
0.3631
Improv.
+3.73%
+3.17%
+8.04%
+4.58%
+11.90%
+12.54% %
+5.05%
+3.24%
LightGCN
0.2861
0.6971
0.2476
0.7770
0.1545
0.2747
0.2521
0.3408
2
BoostGCN
0.2982*
0.7234
0.2641
0.8063
0.2000
0,3517
0.2965
0,3937
Improv. +4.23%
+3.77% %
+6.66%
+3.77% %
+29.51
+28.03 %
+17.61 %
+15.52%
LightGCN
0.2727
0.6719
0.2467
0.7763
0.1461
0,2598
0.2468
0.3329
BoostGCN
0.2894
0.7075
0.2601
0.7959
0.1991
0.3493
0,3030
0.4031
Improv.
+6.12%
+5.30%
+5.43%
+2.51
+36.28% %
+34.45% %
+22.77% %
+21.09%
LightGCN 0.2021
0.5339
0.2405
0.7643
0.1396
0,2494
0.2294
0.3138
BoostGCN
0,2973
0.7134
0,2373
0.7556
0.2026
0.3547
0.3165
0.4151
Improv.
+47.11 %
+33.62%
-1.33%
-1.14%
+45.13%
+42.22%
+37.97%
+32.28%
Table 5: The comparison of efficiency on various datasets. Experiments are tested on the same Intel(R) Xeon(R) Platinum 8255C CPU @2.50GHz machine with a GeForce RTX 2080Ti GPU, Improv. in training time refers (8).
Datuset
Model
Best R@5
Training Time
LightGCN
0.2861
45s
100k (K=2)
BoostGCN
0,2982
23s
Improv.
+4.23%
+49%
LightGCN
0.2476
1174s
IM (K=2)
BoostGCN
0.2641
440s
Improv.
+6.66 %
+63%
LightGCN
0.2294
2762s
Gowa. (K=4)
BoosIGCN
0.3165
859s
Improv.
+37.97%
LightGCN
0.1396
4525s
Yelp (K=4)
BoostGCN
0.2026
438s
Improv.
+45.13%
+90%
Next, we compare our proposed BoostGCN with the basic framework LightGCN at different layers on four datasets, the results of which are shown in Table We have the following observations: 1) BoostGCN outperforms LightGCN on almost all layers of four datasets, with the exception of only one case. 2) For relatively small datasets (# Interrcctions < 10%) such as 100k and 1M, BoostGCN achieves optimal performance at the second layer. This could be due to the fact that these datasets, despite their smaller size, have sufficiently dense user interaction profile, allowing the model to effectively capture the necessary interaction information within a limited number of layers. 3) For large datasets (# Interactions 2 x 10%) such as Gowalla and Yclp2018, BoostGCN consistently outperforms LightGCN across all four layers, with the most notable performance achieved at the fourth layer. This performance demonstrates BoostGCN's ability to effectively penetrate deeper into the network layers.
Efficiency Comparison (RQ2): To thoroughly show the advantages BoostGCN, we perform an efficiency comparison between BoostGCN and LightGCN on different datasets. Our performance analysis, as detailed in Table allows us to identify the optimal layer configuration for BoostGCN on each dataset. For the relative improvement of time efficiency in Table 5 we employ the following formula:
Long Short
Improv.
x 100%
(18)
Long
where "Long" and "Short" represent the long and short training time of the two compared models, respectively.
We present the results in Table 5 and easy to find that: 1) BoostGCN not only demonstrates superior efficiency across all datasets, but also maintains significant improvement in performance.
8

---

2) Across the four datasets, BoostGCN records a minimum efficiency improvement of nearly 50%. More importantly, on larger dataset such as Yelp2018, BoostGCN achieves significant leap with an efficiency improvement of 90% and a performance improvement of 45. 13...%
5.3
Parameter Analysis (RQ3)
1J00-05 1.815-45 LIKE-W 1.01--33
1/803-06
1,08--55 LIM8-04
0.10
0.7
RecalligS
0.27
NDCG@5
Reallight
NBCIEeS
0.24
Bod performnce
0.6
performnee
0.5
6.5
0.31
644
6.3
1000--77 1.80244 LIME-05
1.912-94
1/00-47
LIME-8
100E-64
100k 1M
Gowalla
Yele2018
Figure The performance of BoostGCN at K 2 with different regularization weights on four datasets. For 100k and 1M datasets, explore the performance variation with À {le ..., 1e --.. For Yelp2018 and Gowalla datasets, we explore the performance variation {le 1e- 4).
Figure 4: The performance of BoostGCN at via different 3 in Eq.(8) on four datasets. The pa- rameter 33 ranges from [0.5e, 0.75e, e, 2e, 3e, 4e). On these four datasets, the optimal performance of BoostGCN is when the parameter {e).
Effect of Parameter A: Figure B vividly illustrates the impact of the regularization weight on the performance of BoostGCN across various datasets, and there are three key observations: 1) On all datasets, Boost- GCN shows stable performance within À = {le-7 7,1e- le $e_ which indicates that BoostGCN is robust to parameter variations. 2) For relatively large datasets such as 1M, Gowalla and Yelp2018, a smaller À is more beneficial for performance improvement. 3) Our analysis yields the following guideline for parameter for BoostGCN:
#Usse 3455
MUser33156
(1e-b)
#Interactions 2 X 10
Effect of Parameter 3: To demonstrate the simplicity of our model and the robustness conduct experiments the parameter 33 of amplification function in 88. detailed in Figure 4 and have the following results: 1) BoostGCN achieves optimal performance with B {e} on all datasets when the parameter 3 ranges from (0.5e, 0.75e, e, 2e, 3e, 4e). 2) According to (8. we can easily know that with the de- crease of B, the interaction significant Amp of each item i is amplified more and the model tends to be improved more. 3) This result validates the correctness of focusing on significant interactions and shows the effec- tiveness and superiority of information am- plification in BoostGCN.
to parameters,
UUser 1453
LighiGCN
BesHGGNN
Figure 5: The visualization comparison between BoostGCN and LightGCN K on Yelp2018 dataset. Red, purple, and green represent positive samples of three different users in the test set.

---

5,4 Visualization Analysis (RQ4)
To further demonstrate the benefits of amplifying significant interactions on model performance. we conduct visualization analysis on Yelp2018 dataset. We randomly select three users and compare the distribution of their positive sample representations in the test set, which are displayed under the BoostGCN and LightGCN models at K = 4 respectively. As shown in Figure [ two observations are found: 1) For LightGCN, the dispersed and sparse distribution of positive samples aggregation method may struggle to
among these users suggests that the model's suppression- capture their full preferences, potentially biasing node representations. 2) Conversely, BoostGiN effectively concentrates the positive samples of the same users into compact space, demonstrating its ability to capture comprehensive user preferences. This capability underscores BoostGCN's superior performance in providing both comprehensive and personalized recommendations.
5.5
Analysis of Popularity Debiasing and Noise Resistance (RQ5)
Papuber Hems
Unpepstar an
Luiin
20.21
A
BoostGCN
LightGCN
3588%
$0.33%
0.59
Recallin
NDCG@11
BausOON
47.77%
60.70%
74%%
0.58
0.71
0.72
0.57
12.3%
X3.2%%
31.20%
MoricLeems-8tt
MovieLam--LM
5%
10%
15%
20%
5%
10%
15%
20%
Figure 6: Proportion of popular and unpopular items Top@ 15. BoostGCN able to recom- mend around 26% more unpopular items.
Figure 7: Performance comparison between BoostGCN (3 = e) and LightGCN differ- ent noise levels on ML-100k
Popularity debiasing: To show the popularity debiasing performance of BoostGCN, we show the results of Top@ 15 by the proportion of popular and unpopular items (the statistical tests across four datasets all yield p-value 0.01), shown in Figure 6 Specifically, we categorize the positive samples of each user in the test set based on interaction numbers, with the top 50% as popular items and the bottom 50% as unpopular items. Experiments show that BoostGCN is able to recommend about 2 -66 more unpopular items, achieving a better performance of popularity debiasing. Noise resistance: To evaluate the noise resistance of BoostGCN, we randomly added 5%-20% spurious interactions to the dataset and compared it with LightGCN, as shown in Figure 7 We can see that BoostGCN outperforms LightGCN at different noise levels, demonstrating its superior noise resistance.
5.6 Limitations
BoostGCN is designed based static graphs, which means it has significant room for improvement when dealing with real-time data. In Appendix A.7] we additionally examine BoostGCN's 's transfer potential and generalization scenarios across diverse domains. The amplification function we proposed performs best in the current exploration phase but is not necessarily optimal. Future research can further explore different amplification functions recommendation fairesss. Notably, BoostGCN is designed to replace the base model LightGCN. Therefore, can be combined with other advanced techniques further improve performance.
achieve better performance, efficiency, and
6 Conclusion
In this paper, we propose novel linear GCN model, namely BoostGCN. This model abandons the conventional approach of suppressing information propagation via the graph Laplacian norm, and instead explores and amplifies significant interactions within the interaction graph, thereby achieving a dual optimization of performance and efficiency. Also, we provide new method for quantifying significant interactions. BoostGCN has relatively fixed parameters and stable performance, which is convenient for future improvements and applications. Notably, our visualization experiments ensure that BoostGCN is free from bias in recommendations.
10

---

Acknowledgements
This work was supported by the National Natural Science Foundation of China (72271063, 71871069), and Guangdong Province Philosophy and Social Science Planning 2024 Annual General Project (GD24CGL45).
References
[T] K. and M. Welling, "Semi-supervised classification with graph convolutional networks," in International Conference on Learning Representations, 2017.
[2] C. Wei, Y. Wu, Z. Zhang, F. Zhuang, Z. He, R. Xie, and F. Xia, "Fairgap: Fairness-aware recommendation via generating counterfactual graph," ACM Transactions on Information Systems, vol. 42, no. 2, pp. 1-25, 2024.
[3] Z. Chen, L. Wu, P. Shao, K. Zhang, R. Hong, and M. Wang, "Fair representation learning for recommendation: A mutual information perspective," in Proceedings of the AAAI Conference on Artificial Intelligence, 2023, pp. 4911-4919.
[4] W. Nan, J. Sun, and J. Li, "Cross-level relational graph contrastive learning for bundle recom- mendation," " in IEEE International Conference on Web Services, 2023, pp. 112-117.
[5] C. Jianxin, C. Gao, X. He, D. Jin, and Y. Li, "Bundle recommendation and generation with graph neural networks," IEEE Transactions Knowledge and Data Engineering, vol. 35, no. 3, pp. 2326-2340, 2021.
[6] Y. Zhouxin, J. Li. L. Chen, and Z. Zheng, "Unifying bundle recommendation." Knowledge-Band Based Systems, vol. 255, p. 109755, 2022.
through hypergraph for
[7] Q. Lianyong. Y. Liu, W. Liu, S. Pei, X. Xu, X. Zhang, Y. Wang, and W. Dou, 'Counterfactual user sequence synthesis augmented with continuous time dynamic preference modeling for sequential poi recommendation," in Proceedings of the 33rd International Joint Conference Artificial Intelligence, 2024, pp. 2306-2314.
[8] Z. Lingzi, X. Zhou, Z. Zeng, and Z. Shen, "Dual-view whitening on pre-trained text embed- dings for sequential recommendation," in Proceedings of the AAAI Conference Artificial Intelligence, 2024, pp. 9332-9340.
[9] Z. Mengqi, S. Wu, X. Yu, Q. Liu, and L. Wang, "Dynamic graph neural networks for sequential recommendation." IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 5, pp. 4741-4753, 2022.
[10] C. Jianxin, C. Gao, Y. Zheng, Y. Hui, Y. Niu, Y. Song, D. Jin, and Y. Li, "Sequential recom- mendation with graph neural networks." in Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval, 2021, pp. 378-387.
[11] W. Xiang, X. He, M. Wang, F. Feng, and T.-S. Chua, "Neural graph collaborative filtering," in Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval, 2019, pp. 165-174.
[12] H. Xiangnan, K. Deng, X. Wang, Y. Li. Y. Zhang, and M. Wang, "Lightgen: Simplifying and powering graph convolution network for recommendation." in Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval, 2020, pp. 639-648.
[13] M. Kelong, Zhu, X. Xiao, Lu, Z. Wang, and X. He, "Ultragen: Ultra simplification of graph convolutional networks for recommendation." in Proceedings of the 30th ACM International Conference on Information & Knowledge Management, 2021, pp. 1 1262..
[14] K. Yungi, T. Kim, W.-Y. Shin, S.-W. Kim, "Monet: Modality embracing graph convolutional network and target-aware attention for multimedia recommendation," in Proceedings of the 17th ACM International Conference on Web Search and Data Mining, 2024, pp. 332-340.
[15] M. Chang, H. Zhang, W. Guo, Guo, Liu, Y. Zhang, H. Zheng, R. Tang, X. Li, and R. Zhang. "Hierarchical projection enhanced multi-behavior recommendation." in Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2023, pp. 4649-4660.
11

---

[16] L. Kang, F. Xue, D. Guo, L. Wu, S. Li, and R. Hong, "Megef: Multimodal entity graph collaborative filtering for personalized recommendation" ACM Transactions on Information Systems, vol. 41, no. 2, pp. 1-27, 2023.
[17] 7. Xin and Z. Shen, "A tale of two graphs: Freezing and denoising graph structures for multimodal recommendation," in Proceedings of the 31st ACM International Conference on Multimedia, 2023, pp. 935-943.
[18) W. Qifan, Y. Wei, J. J. Wu, X. Song, and L. Nie, "Dualgnn: Dual graph neural network for multimedia recommendation; IEEE Transactions on Multimedia, vol. 25, pp. 1074-1084, 2021.
[19] Z. Jinghao, Y. Zhu, Q. Liu, S. Wu, S. Wang, and L. Wang, "Mining latent structures for multimedia recommendation," Proceedings of the 29th ACM International Conference on Multimedia, 2021, pp. 3872-3880.
[20] X. Fei, H. Sun, G. Luo, S. Pan, M. Qiu, and L. Wang, "Graph attention network with high-order neighbor information propagation for social recommendation," in Proceedings of the 33rd International Joint Conference Artificial Intelligence, 2024, pp. 2478 2486.
[21] B. Shaked, U. Alon, and E. Yahav, "How attentive are graph attention networks?" in Interna- tional Conference on Learning Representations, 2022.
[22] P. Qiyao, W. Wang. H. Liu, C. Huo, and M. Shao, "Graph collaborative expert finding with contrastive learning,"" in Proceedings of the 33rd International Joint Conference on Artificial Intelligence, 2024, pp. 2288-2296.
[23] W. Chenhao, Y. Liu, Y. Yang, and W. Li, "Hetergel: Graph contrastive learning framework on heterophilic graph," in Proceedings of the 33rd International Joint Conference on Artificial Intelligence, 2024, pp. 2397-2405.
[24] C. Feiyu, J. Wang, Y. Wei, H.-T. Zheng, and J. Shao, "Breaking isolation: Multimodal graph fusion for multimedia recommendation by edge-wise modulation," in Proceedings of the 30th ACM International Conference on Multimedia, 2022, pp. 385-394.
[25] Z. Xin, D. Lin, Y. Liu, and C. Miao, "Layer-refined graph convolutional networks for recom- mendation," " in IEEE 39th International Conference on Data Engineering, 2023, pp. 1247-1259.
[26] Z. Yu, C. Gao, X. Li, X. He, Y. Li, and D. Jin, "Disentangling user interest and conformity for recommendation with causal embedding,"" " in Proceedings of the Web Conference, 2021, pp. 2980-2991.
[27] H. Tian- J.WW Bi, Z.-H. Wei, and Y. Yao, "Visual cues and consumer's booking intention in p2p accommodation:
Exploring the role of social and emotional signals from hosts' profile photos." " Tourism Management, vol. 102. p. 104884, 2024.
[28] Y. Bo, Y. Lei, Liu, and W. Li, "Social collaborative filtering by trust." IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, no. 8, pp. 1633-1647, 2016.
[29] W. Yinwei, X. Wang, L. Nic, X. He, R. Hong, and T.-S. Chua, "Mmgen: Multi-modal graph convolution network for personalized recommendation of micro-video."" in Proceedings of the 27th ACM International Conference on Multimedia, 2019, pp. 1437-1445.
[30] L. Dawen, L. Charlin, J. McInerney, and D. M. Blei, "Modeling user exposure in recommen- dation," " in Proceedings of the 25th International Conference on World Wide Web, 2016, pp. 951-961.
[31] H. Xiangnan, T. Chen, M.-Y. Kan, and X. Chen, "Trirank: Review-awant aware explainable recom- mendation by modeling aspects," in Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, 2015, pp. 1661-1670.
[32] G. Zhiqiang, J. Li, G. Li, C. Wang, S. Shi, and B. Ruan, "Lgmrec: Local and global graph learning for multimodal recommendation," in Proceedings of the AAAI Conference on Artificial Intelligence, 2024, pp. 8454-8462.
[33] K. Yehuda, R. Bell, and C. Volinsky, "Matrix factorization techniques for recommender systems," Computer, vol. 42, no. 8, pp. 30-37, 2009.
[34] I. Fan, Z. Cheng. I. Zhu, Z. Gao, and I.. Nie, "Interest-aware bussage-passingg gen for recommendation," in Proceedings of the Web Conference, 2021, pp. 1296-1305.
12

---

[35] J. Xinzhou, Li. Y. Xie, L. Chen, B. Kong, L. Cheng, B. Hu, Z. Li, and Z. Zheng, "Enhancing graph collaborative filtering via neighborhood structure embedding." in IEEE International Conference Data Mining, 2023, pp. 190-199.
[36] J. ZhZnn X. Rui, F. Wenqi, X. Xin, L. Qing, P. Jian, and L. Xiaorui, "Linear-time graph neural networks for scalable recommendations," in Proceedings of the ACM Web Conference, 2024,
pp. 3533-3544.
[37] Zhang. Y. Yuchen, Z. Xi, L. Chaozhuo, W. Senzhang. H. Feiran, and K. Sunghun, "Transgun: Harnessing the collaborative power of transformers and graph neural networks for recommender systems," " in Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, 2024, pp. 1285-1295.
[38] D. P. Kingma, "Adam: A method for stochastic optimization," https:/aarii.orr/aas//111.... 2014.
[39] G. Xavier and Y. Bengio, "Understanding the difficulty of training deep feedforward neural networks," in Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, 2020, pp. 249-256. 256.
[40] A. Blumer, E. Andrzej. H. David, and W. M. K., "Learnability and the vapnik-chervonenkiss dimension," " Journal of the ACM, vol. 36, no. 4, pp. 929-965, 1989.
[41] D. Sihao, Fuli, H. Xiangnan, L. Yong, S. Jun, and Z. Yongdong, "Causal incremental graph convolution for recommender system retraining." IEEE Transactions Neural Networks and Learning Systems, vol. 35, no. 4, pp. 4718-4728, 2022.
[42] A.-A Stoica, Nelly, and C. Augustin, "Fairness rising from the ranks: Hits and pagerank on homophilic networks," in Proceedings of the ACM Web Conference, 2024, pp.
[43] K. Sharma, L. -honn, N. Sivagami, S. Aditya, S. Shlok, K. Sang- Wook, and K. Srijan, "A survey of graph neural networks for social recommender systems," ACM Computing Surveys, vol. 56, no. 10, pp. 1-34, 2024.
[44] Z. Haohui, W. Juntong, L. Shichao, and H. Shen, "A pre-trained multi-repressntation fusion network for molecular property prediction," Information Fusion, vol. 103, p. 102092, 2024.
[45] T. Félix, S. E. H., and V. Oleksandr, "Using gnn property predictors as molecule generators," Nature Communications, vol. 16, no. 1, p. 4301, 2025.
[46] G. Zili, X. Jie, W. Rongsen, Z. Changming, W. Jin, L. Yunji, and Z. Chenlin, "Stgaformer: Spa- tial-temporal gated attention transformer based graph neural network for traffic flow forecasting," Information Fasion, vol. 105, p. 102228, 2024.
[47] K. Weiyang, G. Ziyu, and L. Yubao, "SSatio- pivotal graph neural networks for traffic flow forecasting," " Proceedings of the AAAI Conference on Artificial Intelligence, 2024, pp.
13

---

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: In the abstract and introduction of our paper, we clearly stated our contributions and that the scope was for the GCN-base recommendation system.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
We specifically discuss and point out the limitations of our work in subsection 4.6 (Limitations).
Justification:
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a 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 (c.g.. independence assumptions, noiseless settings, model sell-speciiiatiinn asymptotic approximations only holding locally). ). The authors should reflect on 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, e.g. if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-tex system might not be used reliably to provide closed captions for online lectures because it fails 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 address problems of privacy and faimesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
14

---

Answer: [Yes]
Justification: To the best of our knowledge, previous methods have mainly focused on suppression, while are the first to propose improving performance through amplification. Our amplification method is heuristic and based on the summary of previous textual theories. Therefore, our paper is more about verifying our heuristic theories through experiments.
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 theorems.
The proof's can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proof's provided in 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 ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless whether the code and data are provided or not)?
Answer: [Yes]
Justification: Our paper fully disclose all the information needed reproduce the main experimental results of the paper to the extent that it affects the main claims and conclusions of the paper.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or 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 be necessary to either make it possible for others to replicate the model with the same dataset, provide access 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 replicate the results, access a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
specific model and empirical evaluation, may
While NeurlPS does not require releasing code, the conference does require submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (c.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce 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 case authors are welcome describe the partieular way they provide for reproducibiliity In the case of closed-source models, it may be that access to the model is limited in
15

---

some way (e.g., to registered users), but it should be possible for other researchers have some path reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [No]
Justification: All of our datasets are public datasets and the citations are provided in the supplementary materials. Our baselines are all publicly accessible, and corresponding citations are also provided in the supplementary materials. The reproducible settings involved in the experiment are all given in our paper, and we promise that code will be sent out after the paper is accepted.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips cc/
for more details.
While we encourage the release of 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 (e.g., for 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
/ wttpps.cc/ppbllc////
for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. 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 to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: 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 to understand the results?
Answer: [Yes]
Our paper specify all the training and test details (e.g., data splits, hyperparam- eters, how they were chosen, type of optimizer, etc.) necessary to understand the results in subsection 4.1 (Experimental Settings).
Justification:
Guidelines:
The answer NA means that the paper does include experiments.
The experimental setting should be presented in the core the paper to a level detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: We run each experiment ten times and report the average results. Therefore, paper report error bars suitably and correctly defined.
16

---

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, or 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 run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: We have provided detailed information introductions where computer resources can affect the experimental results. For example, when conducting efficiency comparisons, we have provided detailed information on computer resources.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU GPU, internal cluster, or 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 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 make 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
Answer: [Yes]
Justification:
Our research is fully compliant with the NeurIPS Code of Ethics.
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 circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative socictal impacts of the work performed?
17

---

Answer: [Yes]
Justification: Our research belongs to foundational research, so it will not involve negative social impacts. Meanwhile, have discussed the potential advantages and disadvantages of our work in the introduction and limitations sections.
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact 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 specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and tied to particular applications, let alone deployments. However, if there is a 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, 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 is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of MI.).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The datasets we use our paper are all commonly used public datasets the field and do not involve such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring 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 releasing unsafe images.
We recognize that providing effective safeguards challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
The creators or original owners of assets (e.g., code, data, models), used in the paper, are properly credited and are the license and terms of use explicitly mentioned and properly respected.
Justification:
18

---

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, possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms use in the package should be provided. For popular datasets, paperswi thcode. com camdsatasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. If this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: The main experimental methods and related settings are fully recorded in our paper. Also, we promise that the code will be made public after the paper is accepted for others to use.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/cooe/mmodel as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: Our 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 the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurlPS Code of Ethics, workers involved in data collection, curation, other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals 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 on the requirements of your country or institution) were obtained?
19

---

Answer: [NA]
Justification:
Our paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does involve crowdsourcing nor research with
human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
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 the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, originality of the research, declaration is not required.
Answer: [NA]
Justification: The core method development in this research does not involve LLMs as any important, original, or non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not non non- stanstandard components.
involve LLMs as any important, original,
Please refer to our LLM policy for what should or should not be described.
20

---

A Appendices for BoostGCN
A.1 Detailed Explanation for Related Concepts
C.1: "Interaction significance' is defined as the degree to which a user is likely to choose an item, which influenced by various factors such as the item's ' quality, trust, price, etc [27 26 28 For example, in movie recommendation, among horror movies, those with higher quality are more likely to be chosen by users. The quality of movie can be partly obtained from modal information and partly inferred from interaction data. In this paper, we focus on mining such hidden information from interaction data.
C.2: Factors' are defined as broad term encompassing all factors that may influence a user's choice of an item, such as trust, quality, conformity, price and etc 27 26 28
C.3: "Key factors' are defined as those factors that can be quantified given the available data content. For example, in this paper focus only user-item interaction data; hence, the factors that can be quantified through interactions constitute the key factors of this study.
C.4: 'The more interactions an item has, the higher a user is associated with the item.' This finding derived from a synthesis relevant literature and real-world observations. For example, Yu et al. [26] have shown that items with more user interactions tend to induce conformity in users, thereby increasing the likelihood that these items will be chosen. addition, when purchasing goods, items with a higher number of interactions can give users impression of high quality and trustworthiness, which in turn encourages them to choose these items. Therefore, the ranking of the degree to which each item is chosen by users (referred to as "interaction significance") is consistent with the ranking of the number of interactions, i.c. S x [VG]. However, the increase in item quality, trustworthiness and other related factors is not linearly related to the increase in the degree of user choice. For this reason, we use a logarithmic function to quantify this hidden information in order to reduce errors.
C.5: 'The benefits of Amplification. From C.4, our amplification method compensates for the loss of information caused by the information suppression in the GCN basic framework. Notably, our method outperforms the most commonly used GCN frameworks terms of recommendation fairness and noise resistance, as shown in Figures and and 7
A.2 The Selection and Advantages of Logarithmic Amplification Functions
a) Reasons for amplifying first-order neighbors. From the perspective of spectral graph convo- lution, the standard Laplacian- normalized aggregation is e (k+1)
Σ
VIN.IvNV where
the significance of each item
W This aggregation will suppress those items with more loga (1
significant interactions. However, we instead use
VINi VINT which can emphasize neighbors with
more significant interactions, thereby accelerating the convergence of sparse interaction patterns and improving the quality of the representation.
b) The selection criteria for the amplification function. To balance the signal gain, robustness and learnability of significant interactions, we propose the following three criteria for selecting node amplification function:
(i) it should increase monotonically with the number of interactions so that nodes with a high number of interactions contribute more information;
(ii it should exhibit non-linear growth to prevent over-amplifying extremely interactive nodes and introducing noise;
(iii) it should be closed-form, differentiable expression for efficient gradient-based optimization.
However, the linear amplification function violates (ii); the exponential amplification function violates (ii) and (iii). Consequently, the logarithmic amplification function is the optimal closed-form solution under these criteria.
c) Advantages of the logarithmic amplification function. The logarithmic amplifier in Eq. ( exposes single scalar 3 that instantiates tunable trade-off between magnitude amplification and
21

---

model sensitivity. A larger 3 compresses inter-item differences ((y.d))) yielding more uniform signal landscape, whereas smaller stretches these gaps, heightening sensitivity subtle interaction sparsity.
Amp
Proof.
Let interaction amplification be S logs ([VG) + Aoo with B and A Alog > 0. For any Amp = logs([V;,.1) - logs (WV, Taking the two neighbor items ip and ig. define the difference (8prf.)
derivative w.r.t. 3 gives
deAme dø
(In( 100001n((WW)) In(( This derivative monotonically decreases
with 9. indicating that the greater 3, the gentler the difference cAmp, The smaller is, the stronger the difference is magnified.
d) Performance comparison with other amplification functions. To further verify that the logarith- mic amplification function is superior to other amplification functions, we compare the logarithmic amplification function with other amplification function variants: linear ([Ni)), square-root (N, and exponential (erp([W()) variants, shown in Figure 8
100k
1M
Yelp2018
0.6
0.4
0.5
1ecall@:
0.4
Recall
01.
Recall@:11
0.3
0.3
0.2
0.2
0.1
0.1
N/A
N/A
N/A
0.0
0.0
0.0
Linear
Squ.
Expo.
Log
Lincar
Squ.
Expo.
Log
Linear
Squ.
Expo.
Log
Figure 8: Performance comparison with other amplification functions.
From Figure 8 we can know that the linear and exponential amplification may cause gradient explosion and unstable training. Square-root amplification is relatively mild, but its performance is poor. The logarithmic amplification function provides the best balance among performance and stability.
A.3 Advantages of BoostGCN's Aggregation over the Aggregation using GAT
In this section, we provide a systematic, theoretical comparison of BoostGCN and GAT from three perspectives: expressive power, sample complexity, and stability.
a) Expressive Power
Here we use the Vapnik-Cherven Chervonenkis (VC) dimension to measure the expressive power of function class. The higher the VC dimension, the more complex the model becomes and the more likely it to overfit on a limited number of samples. When VC dimension is zero, the model contains no learnalle parameters and has the lowest complexity.
GAT learns attention oui = so ommar softmaaz(Teaayyyeee (L (We.|] [.Wel/WWW.... (ee,)) e,))), relying on the learnable parameter 0 and the feature mapping W.
The weight of BoostGCN is determined only by logs((N.)) ((N,) represents the node degree) and does not rely on additional learnable parameters. Therefore, the VC dimension is lower and it is less likely overfit in scenarios with sparse and node-free features.
(Expressive Power under Feature Scarcity): When d < log(n) (d represents the feature dimension of each node and represents the total number of nodes), GAT collapses to uniform weighting, whereas BoostGCN retains degree-based discrimination.
Statement
Proof.
22

---

From 44), the VC-dimension of soft-attention network with learnable parameters is lower- bounded by (pplogn). GAT's parameters PGAT 2 feet VCGAT (oa When foot < logn, VCGΛT VCuni i.e., GAT collapses to uniform weighting. BoostGCN uses fixed weights w logs( (WW.l): no additional parameters = VCBoOSGGCN 0. Therefore, BoostGCN retains degree-based discrimination.
b) Sample Complexity
The attention parameter of GAT requires ((nlogn) interaction samples to converge to stable weight with high probability. BoostGCN only requires O(n) samples to achieve the same generalization error because the weights are directly given by the degrees.
Statement 2 (Sample Complexity): To achieve error < e with probability 2 ō:
(1) GAT requires MGAT Sl(nlggn) interactions.
(2) BoostGCN requires m Boost = (n) interactions.
Proof.
GAT:
When the number of GAT's parameters is PGAT dfeat. standard VC bound 40
gives
MGAT (PG + logg) (nnlggn).
The weights of BoostGCN are directly given by degrees and are equivalent zero parameters. The error is only derived from the empirical estimation of the degree. By Hoeffding's inequality, Boost 24 log (n).
BoostGCN:
c) Stability under Noise
The sensitivity of GAT's attention weights to noise edges increases linearly. The logarithmic amplifi- cation of BoostGCN suppresses high-order noise sublinear manner, thus being more robust in sparse and noisy scenarios.
Statement 3 (Stability under Noise): Let each edge be perturbed independently with probability q.
(1) GAT's attention changes satisfy: EAT - @GAT 1|1 I CGArQn.
(2) BoostGCN's changes satisfy: Boost u Boost|] S Cooaaqlnn
Proof.
GAT: Attention weight change grows linearly with expected number noisy edges qn.
BoostGCN; The estimation error of the weight only depends on the degree. By Hoeffding's 's inequality, Eloogs (lW, logs (WW,D) < Iun (where m refers to the total number of observed edges), yielding /m sub-logarithmic total error ginn.
d) Overall Positioning
Sparse graphs, scarce features, or high noise: GAT's "learning" becomes a burden; BoostGCN offers parameter-free, sample-efficient noise-robust weighting.
Dense graphs with rich features: GAT remains complementary; BoostGCN can be freely combined with GAT.
A.4 The Proofs of BoostGCN's Properties
Proposition A.1 (Smaller aggregation error) With BoostGCN's aggregation in Eq. 12. the error bound decays at the rate of diminishing aggregation error even for highly interactive nodes.
as the neighbor cardinality [N:] increases, guaranteeing
Proof.
Let N₂, be the -hhop neighbors of user u, w; loggl N&D++ be the amplified weight, e be [N..]
the ground-truth embedding of item i, and c (k) be the embedding after is layers. Therefore, the
aggregation error can be defined Eu [/ee)t)) etrull, with e =ieN, w.e,ru.
(k+1) (k+1)
23

---

First, we can get error propagation as follows: e (k+1)
Eien, w,e! (K)
(k+1)
Eu
EiEN, (e ell S Σien, whe,
Next, we can assume that layer-wise error satisfies ef I C. 5(k) (consistent with LightGCN-style linear-GCN convergence analysís, 6 < 1 and C' is general constant).
Then, because Wi (+ and (oga([N[)) I logs(maz, we have ΣXEN, wi -
[.al
logn (maa IN,, )+1 [Nul = logs (mary (NGI) +
Wul
Finally, we combine the bounds Eu (k++) (log)(()V + +) 8(8)
S EiEN, mye (k) < (logs(marz)) (N + 1) C. 8(8))=
Hence, the aggregation error bound decays at the rate of (llgg (I+))) as the neighbor cardinality [ increases.
Proposition A.2 (Near-optimal provable linear convergence rate) By using the logarishmic amplifier in Eq. 8. BoostGCN can achieve spectral-radius bound arbitrarily close to the infimum of the sub-linear family and yield a near-optimal provable linear convergence rate.
Let node degree be d and the information weight be w(d), among the sub-linear family F (w]w(d)) d", 0 < < 1], the logarithmic function w(d) logs(d) exhibits the same asymptotic growth order as the limiting behavior of F(a + 0). thereby achieving a spectral-rading bound arbitrarily close to the infimum of the family and yielding near-optimal provable linear convergence rate.
Proof.
Consider the family of functions F = {w ((d) d 0 10<<<<>
For (d) = d the corresponding aggregation matrix Wa = D-1 diag(d?) (det) A.
Its infinite norm ||Walle bloe = max; E, d /d: S d
For wa (d) = d², the spectral radius satisfies p(Wa) S ||Walloo I dea (Gershgorin's direct inference), which is monotonically increasing a.
When a 0, difoz + is at its minimum. When & + 1, damax - dmax is at its maximum.
The logarithmic weight w(d) = logs(d) (d) at the limit of a - 0 satisfies w(d) limm (d" 1)/a- . 1/In3 x (d" 1) /)/a (first-order Taylor expansion, + e). hence it inherits the minimal growth rate of the family F in the limit.
Among the sub-linear family F, the bound p(W.) is minimized as 0. The logarithmic function exhibits the same growth order as this limit, thus achieving the tightest bound.
Theorem A.3 Under independent and identically distributed (i.id.) mini-batch sampling, bounded gradients and L-smoothness, BoostGCN's expected error bound
E (K) " S (1- Do + 7T2/((2))
(19)
And BoostGCN's high-probability bound is
[H(K) | = (0((a=00000(m + +1 log 3 ), with probability at least 1- (20)
where H(K) is the current embedding matrix of all users and items after K rounds update of random training and Hiro is the ideal embedding when the loss function converges to the minimum value, where H(K), H E R [[+ is the learning rate and X is the regularization term; G is the boundary of gradients, where G 0 and [| G for any mini-batch; Do E[I[H H and 8 E (0,1) 1) is confidence parameter.
Explicit assumptions:
24

---

A1. Independent and identically distributed (i.id.) mini-batch sampling: The positive and negative samples in each mini-batch are independently and identically distributed from the true distribution;
A2. Bounded gradients: there exists G > such that V |C G for any mini-batch;
A3. L-smoothness: the loss function is L-Lipschitz continuous in the embedding space.
Notation:
The embedding matrix is H E R (MI++
The regularization loss is ((H) Crea (H) + |/ where À makes loss A-strongly convex.
Suppose A1-A3: i.i.d. sampling, gradient norm v G, L-LLipschitz continuous gradient.
The learning rate is S 1/C.
The amplification matrix W satisfies p(W) z (logs(mazz) (NgI) 1) (previously proved).
Zx represents the martingale difference gradient noise generated by the k-th mini-batch.
MM represents the cumulative random enror matrix at the end of the K' iteration, which is the sum noises weighted by the amplification matrix W.
of all the
J stands for identity matrix.
Proof.
First, we prove the BoostGCN's expected error bound:
Single-step update (k++1) = (k) Ln, (H(*), where BN is the mini-batch corresponding to the k-th iteration.
Under assumptions A A1-A3 and X-strongly convexity, one step yields
[|]|[((++1 - 1 112
= -| - H - 2n < (k) - H VL(H(() > +o ) (H(
(21)
s (1 -2nA)| H ||2- + G2
Let A = [[]| (k) bru | then 641 -1-2211) 2n) + 122
For k = 0, 1, K 1
K-1
AK S (1-27)) Do + G² Σ 21/
1=0
= (1 - 21/A)* Do + 1200(1 - 2n12)* "5 ((27))
(22)
< (1 21/A) K Ao + 1/ (22/(22))))))))))))))))))()))(
21/A) K Ao + n/ (22)
Therefore, the expected error bound of BoostGCN is (K] - [|2]] S (1 2n n/ (2A). Next, prove the BoostGCN's high-probability bound:
Martingale Difference Sequence:
Z = VLB, (H(()) - VL(H(M), E[Zz] =0, 1Z S G
(23)
Cumulative Error:
K-1
MR Σ
n, k-
(24)
k=0
25

---

Norm Bound:
[I [[J-nW) [[J-クW) Zxlle S (p(W)) (o(W)))-k-1 K-k-IG
(maxs(maz))W3)) + 1) 1)--k-1G
(25)
Vector Azuma-Hoeffding Inequality:
t²
P(IMM|le 2 21) 2expl
(26)
2KG
Total Error Decomposition:
[[H(K) Htr & (logs(mar,) (NG) + +1)* H + ||
(27)
Final High-Probability Bound: Let = G. 2Klog then
P( -[[ Htr (logs(moz,lMVi) H H"""| GV 2Klog 2
1 - (28)
log |H(K) H O((oog( 1)x +
Therefore,
w.p. 1 6.
A.5 Baselines
We compare some representative models, ranging from traditional matrix factorization models to state-of-the-art GCN-based models.
MF-BPR
is a matrix factorization model optimized by a pairwise ranking loss Bayesian way.
33
MMGCN 29 is a classic multimodal recommendation model. the experiment, we only employ II) embedding as its input, denoted by MMGCN
NGCF leverages collaborative signals from high-order connectivity of the user-item graph via feature transformation and nonlinear activation functions.
LightGCN [22 is a linear GCN framework that uses only linear aggregation without feature transformation and nonlinear activation functions between neighbors. As it is the most basic GCN model, it serves as the main bascline for our comparison.
UltraGCN 13] with additional constraint loss further simplifies LightGCN by removing the stacking many graph convolution layers GCN.
IMP-GCN 34 categorizes users into unique subgroups aligned with their particular inter- ests, conducting advanced graph convolution operations exclusively within these subgroups.
NSE-GCN [35]
employs neighborhood structure embedding technique that relies first-order adjacency information to generate structural embeddings.
LayerGCN 225 is state-of-the-art GCN model with the DegreeDrop mechanism, which
refines layer representations during information propagation and node updating.
LTGNN (36] performs linear-time graph convolution, scaling GNN-based recommendation to the efficiency of classic MF while preserving high-order connectivity modeling.
TransGNN 377
alternates Transformer and GNN layers to globally enlarge the receptive field while disentangling edge-based aggregation.
GAT-LightG combines LightGCN with Graph Attention Network.
In order to make fair comparison, we carefully tune the hyper-parameters of each model based on their respective published papers and param--r studies. All baselines compared in this paper can be obtained directly from the corresponding literature.
26

---

A.6 Datasets
To comprehensively demonstrate the effectiveness of BoostGCN, we evaluate our model on four distinct datasets, including MovieL 100k (denoted by 100k) [29], MovieLLnss IM (denoted by
1M) 12]_. Gowalla (denoted by Gowa.) [30] and Yelp2018 (denoted by Yelp) [TT, as detailed in
Table 2 The datasets utilized in this paper are all publicly available and can be directly downloaded
from their respective sources.
The descriptions of these datasets are given below:
MovieLenss Dataset 29 This dataset has been widely used for the recommendation
evaluation, and it contains series of subsets such as MovieLens- and MovieLens- 1M.
Gowalla Dataset 30 : This dataset is check-in dataset obtained from Gowalla, in which users share their locations through checking-in.
Yelp2018 Dataset [
This dataset is adopted from the 2018 edition of the Yelp challenge.
The local businesses like restaurants and bars are considered as items.
Merikaa-MM
200
3750
2250-
3000
177
37
30
18"
16'
107
19
14
34
34
34
38'
34'
16
18
D5mm Interactionn
User Interaction
Figure 9: Long-tail items on Yelp and ML-IM datasets.
Figure 10: Long-tail users on Yelp and ML-1M datasets.
The reason why we chose these four datasets is that they vary greatly in size and sparsity, which is more conducive to demonstrating that our method is effective in different scenarios. For example, can be seen from Figure 9 and Figure I0 that the long-tail problem of Yelp is much more severe than that of ML-IM. However, shown in Table and Table of our paper, our performance on Yelp has improved the most, indicating that our performance can still be excellent when faced with the long-tail problem.
A.7 Discussion on the Potential Applications of BoostGCN
A.7.1 The Effect of Logarithmic Amplification Function on Non-linear GCN
Since BoostGCN's log-amplification is lin- ear re-weighting scheme, it can be grafted onto any non-linear GCN without structural changes- simply replace the original Laplacian weights with the BoostGCN weights, while keeping all non-linear activations, feature transformations and residual connections intact. To validate this, we conduct new experiments, as shown in Figure II We take NGCF (with Leaky-ReLU and fea- ture transformation) and substitute its Laplacian weights with BoostGCN weights. The value of the amplification function ,9 is searched from to 4e, and other settings remain consistent with NGCF We can find that adding our amplification function to the four datasets will all improve the model performance. Thus, BoostGCN is read- ily compatible with non-linear GCNs and yields consistent gains.
NGCRLogaampliictiion
NGCH(Non-Ilnaa)
0.56
0.48
Recallg15
0.40
0.32
0.24
100k
1M
Gowalla Yelp2018
Figure 11: The performance comparison between NGCF and NGCF with our log-amplification on four datasets.
27

---

A.7.2 Discussion on Dynamic Graph Scenarios
Remaining purely static in highly dynamic scenarios (real-time recommender systems, traffic forecast- ing) risks: Concept drift: user interests or item popularity can shift abruptly, causing performance drops. 2) Stale recommendations: outdated interactions are over-amplified, degrading user experi-
ence. Therefore, we can extend BoostGCN to dynamic graphs via two complementary mechanisms:
Time-aware amplification function: we plan to incorporate the interaction timestamp into
saliency:
SAmp
(og)((V(((t))) exp(->(t ((ast) log (i-nu,t)
(29)
where [t) counts interactions up to time f, À controls temporal decay, and llo retains the offset. This lets recent interactions dominate while older ones gradually fade.
Dynamic adjacency caching & incremental updates: upon each interaction (u, t), perform a rank-1 update on the local adjacency matrix and reuse the incremental-propeen proppaattiooo framework of LightGCN [4]] avoid full-graph re-computation, maintaining efficiency on par with the static version.
A.7.3 BoostGCN: From Recommendation to General Graph Representation
Generalizing the assumption: show that the amplification weight w; log([Wi)) mathemat- ically smooth re-scaling of node degree. Degree is a universal structural cue independent of the "item-selection" semantics. Hence. in other domains one can simply replace [WG] with any relevant structural count (e.g., number of friends in social networks, entity frequency in knowledge graphs) without changing the framework.
Robustness when the assumption is relaxed: Figure 7 reports a ablation where we randomly increase noise interactions by 5% to 20% in the 100k dataset, breaking the original correspondence between high interaction and high saliency. The performance of BoostGCN is still superior to that of LightGCN, which indicates that our proposed method resilient violations of the behavioral prior.
Future extension: we now state in the conclusion that if domain priors are unavailable, one can substitute (og((]]) with parameter-free alternatives such PageRank [42] scores or superviid odge-importance estimates without altering the BoostGCN pipeline or complexity.
A.7.4 Future Work
Although our work focuses recommendation. the core idea of ampllfyynnn salient first-order interactions via logarithmic weighting function is a general graph-aggregatiin principle. Consequently, the method is directly applicable any task that requires node representation learning with edge-importance weighting, such as:
influence maximization in social networks (up-weighting trust edges) 443
molecular property prediction (emphasizing bonds directly connected to functional groups)
44
traffic flow forecasting (amplifying interactions with frequently used neighboring road segments)
46 47
28


Reviews:
[{"review_id": "cSMVokvypg", "reviewer": "Reviewer_LuSH", "summary": "This paper presents the BoostGCN model, aiming to address the issue in traditional Graph Convolutional Networks (GCNs) where graph Laplacian normalization suppresses the information propagation of first - order neighbors. The authors argue that Laplacian normalization dilutes important interaction information, leading to inefficient model learning. BoostGCN enhances the significant interaction information of first - order neighbors through a designed logarithmic amplification function, enabling the model to capture key relationships more quickly and accurately. Experiments on four real - world datasets verify that BoostGCN outperforms existing state - of - the - art models in terms of both performance and efficiency. It also has fixed parameters and strong robustness. The main contributions include shifting the graph aggregation paradigm from “suppression” to “amplification”, designing an interaction saliency amplification function, and validating the model's advantages through experiments.", "questions": "1. Can the authors supplement the mathematical derivation of the interaction saliency amplification function? For example, prove the advantages of the logarithmic function in balancing “interaction quantity amplification” and “model sensitivity”, or explain through theoretical analysis why the amplification of first - order neighbor information can effectively improve the quality of representation learning. If there are other possible amplification functions (such as the exponential function), it is necessary to compare their performance differences and the reasons for choosing the logarithmic function.​\n2. Regarding the limitations of static graphs mentioned in the paper, do the authors have plans to expand to dynamic graph scenarios? For example, introduce temporal information to adjust the amplification function, or design a mechanism to adapt to the dynamic changes of interactions. If so, please explain the specific ideas; if not, it is necessary to discuss the potential risks of static models in dynamic scenarios.​\n3. The sampling strategy of negative samples in the experiment (such as whether it is based on popularity) is not clear, which may affect the model's ability to recommend unpopular items. In addition, Figure 6 shows that BoostGCN can recommend more non - popular items, but no statistical test (such as the t - test) is used to prove whether the difference from LightGCN is significant. It is recommended to supplement relevant analyses.​\n4. In the paper, β = e is fixed, but the interaction distributions of different datasets may vary greatly (for example, the sparsity of Yelp is much higher than that of MovieLens). Have the authors verified the sensitivity of β on different datasets? For example, whether there are scenarios where β = 2e or 3e performs better. If so, how to automatically adjust β to adapt to different data?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths：​\n1. It breaks through the traditional information suppression idea in GCNs and proposes to enhance the performance of the model by amplifying the significant interactions of first - order neighbors, providing a new research direction for graph aggregation.​\n2. Experiments show that BoostGCN can improve the training time by up to 90% compared with LightGCN. Moreover, with fixed parameters (such as β = e, △^log = 1), it reduces the cost of parameter tuning and is applicable to datasets of different scales and sparsities.​\n3. By comparing with 8 baseline models, conducting experiments on different layers, hyperparameter analysis, and visualization experiments, the effectiveness of the model is proven from multiple perspectives, especially showing advantages in handling long - tailed data and noise.\n\nWeaknesses：​\n1. The quantification of interaction saliency depends on the logarithmic function. However, in the paper, only a heuristic derivation is carried out through the “correlation between interaction quantity and trust/conformity behavior”, lacking strict theoretical proof or mathematical derivation. For example, there is no explanation on why the logarithmic function is superior to other non - linear functions, or whether there is a better - performing amplification function form.​\nRegarding the conclusion that “first - order neighbor interactions are more important”, there is no analysis of its rationality from the theoretical aspects of graph signal processing or representation learning. It only uses the experimental comparison of LightGCN as evidence, resulting in weak theoretical support.​\n2. Currently, only static graph scenarios have been verified, without considering dynamic graph data (such as temporal interactions). It may have limitations when dealing with real - time recommendations or the dynamic evolution of social networks (although it is mentioned in section 4.6, no improvement directions are provided).​\nThe amplification function is based on the assumption that “interaction quantity ≈ saliency”, which may ignore the diversity of user interests (such as unpopular but highly relevant items), and its performance in extremely long - tailed scenarios requires more verification.​\n3. Although it is mentioned that the code will be made public after acceptance, specific implementation details are not provided (such as the specific code logic of the amplification function, the weight calculation method of the weighted layer combination), which may affect the reproducibility of the research by other scholars.​\nIn the dataset pre - processing, it is mentioned that “negative samples are added”, but the sampling strategy for negative samples (such as random sampling, sampling based on popularity) is not clearly defined, which may have an impact on the model performance.", "was_revised": true, "final_justification": "The authors patiently responded to and resolved my concerns, providing persuasive experiments that demonstrate the soundness of their method, which has a certain degree of originality and practical significance. Therefore, my final rating is **Borderline Accept**.", "rebuttal": "Thank you for your constructive review! We appreciate your insights and suggestions. Please find our responses below:\n\n**Q1 & W1: Additional Mathematical Derivation of the Interaction Amplification Function**\n\nThank you for this insightful comment. We have added comprehensive mathematical derivations and theoretical analyses in the revised manuscript. The key points are summarized below:\n\n1. **Advantages of the logarithmic amplification function**\n\nWe formally derive:\nLet interaction amplification $S_{(i→u)}^{amp}=log_β(|N_i|)+Δ_{log}$ with $β>1$ and $Δ_{log}>0$. For any two neighbor items $p$ and $q$, define the difference $ε_{(p,q)}^{amp}=log_β(|N_p|)−log_β(|N_q|)$. Taking the derivative w.r.t. $β$ gives $dε^{amp}/dβ = (1/β)[ln(|N_p|)−ln(|N_q|)]$. This derivative monotonically decreases with $β$, indicating that the greater $β$, the gentler the difference $ε^{amp}$. The smaller $β$ is, the stronger the difference is magnified. Hence, $β$ acts as a smooth knob that trades off “quantity amplification” versus “model sensitivity.” In contrast, the exponential function exp(·) has a derivative that grows linearly with its input, causing extreme values and instability.\n\n2. **Reasons for amplifying first-order neighbors**\n\nFrom the perspective of spectral graph convolution, the standard Laplacian-normalized aggregation is\n$e_u^{(k+1)}=∑_{{i∈N_u}} 1/√(|N_u||N_i|) e_i^{(k)}$,\nwhere the weight of each item is  $1/√(|N_u||N_i|)$. This aggregation will suppress popular items.\n\nWe instead use\n$w_i = (log_β(|N_i|)+1)/√(|N_u||N_u|)$.\nIt is easy to show that for any $|N_i|>1$, $w_i > 1/√(|N_u||N_i|)$.\nTherefore, salient neighbors are up-weighted, accelerating the convergence of sparse interaction patterns and improving representation quality. **The aggregation error bound decreases at the rate $O(log(|N_i|)+1)$ as the neighbor degree increases.**\n\n**Proof.**\n\n• Let $N_u$ be the 1-hop neighbors of user $u$.\n\n• Define the amplified weight: $w_i = (log_β(|N_i|)+1)/|N_u|$.\n\n• Denote $e_i^{tru}$ as the ground-truth (expected) embedding of item $i$, and $e_i^{(k)}$ as the embedding after $k$ layers.\n\n• Aggregation error: $ε_u^{(k+1)} := ||e_u^{(k+1)} − e_u^{tru}||$, with $e_u^{tru} = Σ_{i∈N_u} w_i e_i^{tru}$.\n\n**Step 1**: Error propagation\n$e_u^{(k+1)} = Σ_{i∈N_u} w_i e_i^{(k)}$\n⇒ $ε_u^{(k+1)} = || Σ_{i∈N_u} w_i^2 (e_i^{(k)} − e_i^{tru})|| ≤ Σ_{i∈N_u} w_i ε_i^{(k)}$. \n\n**Step 2**: Assume layer-wise error satisfies $ε_i^{(k)} ≤ C·δ^{(k)}$\n(consistent with LightGCN-style linear-GCN convergence analyses, $δ<1$ and $C$ is general constant).\n\n**Step 3**: Bound the sum of squared weights:\n\n• Because $w_i = (log_β(|N_i|)+1)/|N_u|$ and $log_β(|N_i|) ≤ log_β(max_j |N_j|)$, \n\n• we have $Σ_{i∈N_u} w_i ≤ (log_β(max_j |N_j|)+1) / |N_u| · |N_u| = log_β(max_j |N_j|)+1$.\n\n**Step 4**: Combine the bounds:\n\n$ε_u^{(k+1)} ≤ Σ w_i ε_i^{(k)} ≤ (log_β(max_j |N_j|)+1)·C·δ^{(k)}\n= O(log(|N_i|)+1)·δ^{(k)}$.\n\nHence, the aggregation error bound decreases at the rate $O(log(|N_i|)+1)$ as the neighbor degree increases.\n\n3. **Comparison with other amplification functions**\n\nFollowing your suggestion, we further evaluate linear ($|N_i|$), square-root ($√|N_i|$) and exponential ($exp(|N_i|)$) variants:\n\n| Recall@15 | 100k | 1M |Yelp|\n|---------------|---------------|----------|----------|\n| BoostGCN (Linear)       | 0.5062 | 0.4647 | N/A |\n| BoostGCN  (Square-root) | 0.5583 | 0.5201 | 0.3477  |\n| BoostGCN (Exponential)   | N/A | N/A  | N/A  |\n| **BoostGCN (Log)** | **0.5908** | **0.5316** | **0.3968** |\n\n• Linear and exponential amplification may cause gradient explosion and unstable training.\n\n• Square-root amplification is relatively mild, but its performance is poor.\n\n• The logarithmic amplification function provides the best balance among performance and stability.\n\n**Q2 & W2: More Discussion on Dynamic Graph Scenarios**\n\nThank you for probing the static-graph limitation in detail. In the revised manuscript we have enriched the Limitations section and sketched concrete ideas for dynamic extensions. Following your suggestion, we will extend BoostGCN to dynamic graphs via two complementary mechanisms:\n\n• **Time-aware amplification function**: we plan to incorporate the interaction timestamp t into saliency:\n\n$S_{(i→u, t)}^{amp} = log_β(|N_i(t)|) · exp(−λ(t−t_{last})) + Δ^{log}$\n\nwhere $N_i(t)$ counts interactions up to time $t$, $λ$ controls temporal decay, and $Δ^{log}$ retains the offset. This lets recent interactions dominate while older ones gradually fade.\n\n• **Dynamic adjacency caching & incremental updates**: upon each new interaction $(u,i,t)$, we perform a rank-1 update on the local adjacency matrix and reuse the incremental-propagation framework of LightGCN [a1] to avoid full-graph re-computation, maintaining efficiency on par with the static version.\n\n[a1] Ding, S., et al., 2022. Causal incremental graph convolution for recommender system retraining. IEEE Transactions on Neural Networks and Learning Systems.\n\nRemaining purely static in highly dynamic scenarios (real-time recommender systems, traffic forecasting) risks:\n\n• **Concept drift**: user interests or item popularity can shift abruptly, causing performance drops.\n\n• **Stale recommendations**: outdated interactions are over-amplified, degrading user experience.\n\n**Q3 & W3: More Explanations for Negative Sampling and Significance Tests**\n\nThank you for pointing out the ambiguity in negative sampling and the lack of significance tests. We have addressed both issues in the revised manuscript as follows:\n\n1. **Clarification of negative sampling**\n\nWe adopt the standard LightGCN protocol:\n\n• Training: for each observed interaction $(u,i)$, one negative item is sampled uniformly at random from the unobserved set—**no popularity-based sampling** is used.\n\n• Validation/Test: for each user we randomly draw 150 (small datasets) or 1500 (large datasets) unseen items as candidates, again **without popularity bias**.\n\nThis description has been added to Section 4.1 “Data Pre-processing.”\n\n2. **Significance test on non-popular items**\n\nWe performed paired t-tests on the proportion of non-popular items in $Top@15$ recommendations (Figure 6):\n\n• Null hypothesis: no difference between BoostGCN and LightGCN.\n\n• Results: p < 0.01 on all four datasets (**100k: p=0.007, 1M: p=0.004, Gowalla: p=0.002, Yelp2018: p<0.001**), indicating that BoostGCN significantly increases the share of non-popular items.\n\n**Q4:  Discussion on the Sensitivity of $β$ on Different Datasets**\n\nThank you for raising this point. The sensitivity of $β$ has already been reported in Figure 4 of Section 4.3 (RQ3), where we evaluate $β ∈$ {e, 2e, 3e, 4e} across all four datasets. In the revised version, we extend the ablation study to $β$ ∈ {0.5e, 0.75e, e, 2e, 3e, 4e}. The results are shown as follows:\n\n| Recall@5 | 100k | 1M |Gowalla|Yelp|\n|---------------|---------------|----------|---------|---------|\n| $β = 0.5e$    | 0.2972 | 0.2633 | 0.2955  |0.1978|\n| $β = 0.75e$   | 0.2977 | 0.2636 | 0.2958  |0.1983 |\n| $β = e$ (**Optimal**)  | **0.2982**| **0.2641** | **0.2965** |**0.2001** |\n| $β = 2e$  | 0.2962 | 0.2615 | 0.2847 |0.1947 |\n| $β = 3e$  | 0.2928 | 0.2574 | 0.2816 |0.1917 |\n| $β = 4e$  | 0.2921 | 0.2547| 0.2802 |0.1884 |\n\n• $β$ = e yields the best performance on all datasets.\n\n• Datasets of different sparsity levels and sizes all show the same trend, confirming that $β$ = e is robust across sparsity levels and size scales.\n\n• **Consequently, we did not observe any scenario in which $β$ = 2e or 3e outperforms $β$ = e. We have now emphasized this finding in Figure 4 by highlighting the $β$ = e curve and adding explicit textual guidance to help readers locate the results**.\n\n**Thank you again for your helpful review and suggestions. We hope our rebuttal has answered your concerns. If there's anything else you'd like us to explain, please let us know -- we really appreciate your feedback!**"}, {"review_id": "J5uFeVViev", "reviewer": "Reviewer_cESK", "summary": "This paper highlights the information suppression problem in GCNs caused by graph Laplacian normalisation, which can dilute important first-order interaction signals, negatively impacting applications such as recommender systems. To overcome this issue, the paper introduces BoostGCN, a linear GCN variant that amplifies significant neighbour interactions through a logarithmic weighting scheme, enabling more effective and efficient representation learning. Significant interactions are identified based on neighbour degree, with higher-degree items assumed to carry stronger signals, motivated by behavioural factors such as trust and conformity, and their influence is selectively amplified during aggregation. Empirical evaluation seems to show that this modification results in a noticeable improvement over baselines.", "questions": "I would request the authors to rebut the points raised in the weakness section. If they provide convincing justifications, I will raise my score.", "limitations": "While the paper includes a brief limitations section focused on the static nature of BoostGCN and its amplification function design, it does not address broader concerns around the societal impacts of recommender systems. In particular, amplification of significant interactions, if tied to popularity or user conformity, could risk reinforcing filter bubbles or popularity bias. A more holistic discussion of potential harms or fairness considerations would improve the completeness and ethical framing of the work.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "The paper is well written and easy to follow. It clearly identifies a practical limitation in existing GCNs and provides a simple yet effective solution. The method demonstrates consistent performance and efficiency gains across multiple benchmark datasets. Moreover, the notion of interaction significance used in BoostGCN  is intuitive and aligns with real-world behavioural patterns. \n\nThe paper has following major issues:\n\n - The amplification function is based on empirical intuition, such as using degree as a proxy for significance, without formal justification or theoretical guarantees. \n - The paper does not address dynamic or temporal graphs (as mentioned in Limitations), which are common in recommendation scenarios. But this casts some doubts on the effectiveness of the method in real world settings. \n - The paper lacks theoretical analysis regarding convergence, stability, or generalisation under perturbations.\n - The method is benchmarked only on user–item graphs; it is unclear how well it generalises to other graph domains or tasks. How can we define significance interaction in generic graphs? A discussion on this would be very helpful. \n - The paper overlooks attention-based models such as GAT, which directly address uniform neighbour weighting; the core issue BoostGCN aims to solve. Including a GAT-based baseline (or a discussion of its limitations in this setting) would strengthen the empirical justification for the proposed method.", "was_revised": true, "final_justification": "The authors did not initially discuss GAT, a relevant existing model that could potentially address the same issue tackled by BoostGCN. During the response period, they provided some ablations and a basic theoretical comparison to position BoostGCN against GAT, but the theoretical analysis remained relatively weak.", "rebuttal": "Thank you for the positive evaluation and constructive feedback. Below we address your concerns:\n\n**W1: Theoretical Guarantees for the Amplification Function**\n\nThank you for this insightful comment. We have added comprehensive mathematical derivations and theoretical analyses for the amplification function:\n\n1. **Rationale for the logarithmic choice**\n\nLet node degree be $d$. We require the weight $w(d)$ to satisfy:\n\n(a) monotonic increase: higher-degree nodes contribute more;\n\n(b) sub-linear growth: avoid over-amplifying tail noise;\n\n(c) closed-form differentiability: amenable to gradient optimization.\n\nUnder these constraints we prove:\n\nlinear $w(d)=d$ violates (b);\n\nexponential $w(d)=e^d$ violates (b)(c);\n\nlogarithmic $w(d)=log_β(d)$ satisfies all three.\n\nHence, the log is the closed-form optimal function under the stated axioms\n\n2. **Advantages of the logarithmic amplification function**\n\nWe formally derive:\nLet interaction amplification $S_{(i→u)}^{amp}=log_β(|N_i|)+Δ_{log}$ with $β>1$ and $Δ_{log}>0$. For any two neighbor items $p$ and $q$, define the difference $ε_{(p,q)}^{amp}=log_β(|N_p|)−log_β(|N_q|)$. Taking the derivative w.r.t. $β$ gives $dε^{amp}/dβ = (1/β)[ln(|N_p|)−ln(|N_q|)]$. This derivative monotonically decreases with $β$, indicating that the greater $β$, the gentler the difference $ε^{amp}$. The smaller $β$ is, the stronger the difference is magnified. Hence, $β$ acts as a smooth knob that trades off “quantity amplification” versus “model sensitivity.” In contrast, the exponential function exp(·) has a derivative that grows linearly with its input, causing extreme values and instability.\n\n\n**W2: More Discussion on Dynamic Graph Scenarios**\n\nThank you for probing the static-graph limitation in detail. In the revised manuscript we have enriched the Limitations section and sketched concrete ideas for dynamic extensions. Following your suggestion, we will extend BoostGCN to dynamic graphs via two complementary mechanisms:\n\n• **Time-aware amplification function**: we plan to incorporate the interaction timestamp t into saliency:\n\n$S_{(i→u, t)}^{amp} = log_β(|N_i(t)|) · exp(−λ(t−t_{last})) + Δ^{log}$\n\nwhere $N_i(t)$ counts interactions up to time $t$, $λ$ controls temporal decay, and $Δ^{log}$ retains the offset. This lets recent interactions dominate while older ones gradually fade.\n\n• **Dynamic adjacency caching & incremental updates**: upon each new interaction $(u,i,t)$, we perform a rank-1 update on the local adjacency matrix and reuse the incremental-propagation framework of LightGCN [a1] to avoid full-graph re-computation, maintaining efficiency on par with the static version.\n\n[a1] Ding, S., et al., 2022. Causal incremental graph convolution for recommender system retraining. IEEE Transactions on Neural Networks and Learning Systems.\n\nRemaining purely static in highly dynamic scenarios (real-time recommender systems, traffic forecasting) risks:\n\n• **Concept drift**: user interests or item popularity can shift abruptly, causing performance drops.\n\n• **Stale recommendations**: outdated interactions are over-amplified, degrading user experience.\n\n**W3: Theoretical Analysis Regarding Stability and Convergence**\n\n1. **Stability: Smaller aggregation error**\n\nUsing logarithmic amplification function, the aggregation error bound decreases at the rate $O(log(|N_i|)+1)$ as the neighbor degree increases.\n\n**Proof.**\n\n• Let $N_u$ be the 1-hop neighbors of user $u$.\n\n• Define the amplified weight: $w_i = (log_β(|N_i|)+1)/|N_u|$.\n\n• Denote $e_i^{tru}$ as the ground-truth (expected) embedding of item $i$, and $e_i^{(k)}$ as the embedding after $k$ layers.\n\n• Aggregation error: $ε_u^{(k+1)} := ||e_u^{(k+1)} − e_u^{tru}||$, with $e_u^{tru} = Σ_{i∈N_u} w_i e_i^{tru}$.\n\n**Step 1**: Error propagation\n$e_u^{(k+1)} = Σ_{i∈N_u} w_i e_i^{(k)}$\n⇒ $ε_u^{(k+1)} = || Σ_{i∈N_u} w_i^2 (e_i^{(k)} − e_i^{tru})|| ≤ Σ_{i∈N_u} w_i ε_i^{(k)}$. \n\n**Step 2**: Assume layer-wise error satisfies $ε_i^{(k)} ≤ C·δ^{(k)}$\n(consistent with LightGCN-style linear-GCN convergence analyses, $δ<1$ and $C$ is general constant).\n\n**Step 3**: Bound the sum of squared weights:\n\n• Because $w_i = (log_β(|N_i|)+1)/|N_u|$ and $log_β(|N_i|) ≤ log_β(max_j |N_j|)$, \n\n• we have $Σ_{i∈N_u} w_i ≤ (log_β(max_j |N_j|)+1) / |N_u| · |N_u| = log_β(max_j |N_j|)+1$.\n\n**Step 4**: Combine the bounds:\n\n$ε_u^{(k+1)} ≤ Σ w_i ε_i^{(k)} ≤ (log_β(max_j |N_j|)+1)·C·δ^{(k)}\n= O(log(|N_i|)+1)·δ^{(k)}$.\n\nHence, the aggregation error bound decreases at the rate $O(log(|N_i|)+1)$ as the neighbor degree increases.\n\n2. **Convergence: Near-optimal provable linear convergence rate**\n\nLet node degree be $d$ and the information weight be $w(d)$, among the sub-linear family $F$ = {$w$ | $w(d)=d^α$, $0<α<1$}, the logarithmic function  $w(d)=log_β(d)$ exhibits the same asymptotic growth order as the limiting behavior of $F$ ($α→0$), thereby achieving a spectral-radius bound arbitrarily close to the infimum of the family and yielding near-optimal provable linear convergence rate. \n\n**Proof.**\n\n• Consider the family of functions $F$ = {$w(d)$=$d^α$, $0<α<1$}. \n\n• For $w_α(d)=d^α$, the corresponding aggregation matrix $W_α = D^{-1} · diag(d_i^α) · A$. \n\n• Its infinite norm $||W_α||_ {∞} = max_i Σ_j d_j^α / d_i ≤ d^α_{max}$. \n\n• For $w_α(d)=d^α$, the spectral radius satisfies $ρ(W_α) ≤ ||W_α||_ {∞} ≤ d_{max}^α$ (Gershgorin's direct inference), which is monotonically increasing in $α$. \n\n• When $α→0$, $d_{max}^α → 1$ is at its minimum. When $α→1$, $d_{max}^α → d_{max}$ is at its maximum. \n\n• The logarithmic weight $w(d)=log_β(d)$ at the limit of $α→0$ satisfies $w(d) = lim_{α→0^+} (d^α−1)/α · 1/lnβ ≈ (d^α − 1)/α $ (first-order Taylor expansion, $β → e$), hence it inherits the minimal growth rate of the family $F$ in the limit.\n\nAmong the sub-linear family $F$, the bound $ρ(W_α)$ is minimized as $α→0$. The logarithmic function exhibits the same growth order as this limit, thus achieving the tightest bound.\n\n**W4: Generalization to Other Graph Domains or Tasks**\n\nThank you for raising the generalization concern. Although the paper focuses on recommendation, the core idea of BoostGCN—amplifying salient first-order interactions via a logarithmic weighting function—is a general graph-aggregation principle. Consequently, **the method is directly applicable to any task that requires node representation learning with edge-importance weighting**, such as:\n\n• influence maximization in social networks (up-weighting trust edges) [b1];\n\n• molecular property prediction (emphasizing bonds directly connected to functional groups) [b2,b3];\n\n• traffic flow forecasting (amplifying interactions with frequently used neighboring road segments) [b4,b5].\n\nWe have added a paragraph in the “Conclusion and Future Work” section to highlight this universality and list the cross-domain examples above.\n\n[b1] Sharma, K., et al., 2024. A survey of graph neural networks for social recommender systems. *ACM Computing Surveys*.\n\n[b2] Zhang, H., et al., 2024. A pre-trained multi-representation fusion network for molecular property prediction. *Information Fusion*.\n\n[b3] Therrien, F., et al., 2025. Using GNN property predictors as molecule generators. *Nature Communications*.\n\n[b4] Geng, Z., et al., 2024. STGAFormer: Spatial–temporal gated attention transformer based graph neural network for traffic flow forecasting. *Information Fusion*.\n\n[b5] Kong, W., et al., 2024, March. Spatio-temporal pivotal graph neural networks for traffic flow forecasting. *AAAI*.\n\nIn the revised manuscript, we have also added a discussion on “Beyond Recommendation” to clarify how BoostGCN extends to generic graphs:\n\n• **Generalizing the assumption**: we show that the amplification weight $w_i ∝ log(|N_i|)$ is mathematically a smooth re-scaling of node degree. Degree is a universal structural cue independent of the “item-selection” semantics. Hence, in other domains one can simply replace $|N_i|$ with any relevant structural count (e.g., number of friends in social networks, entity frequency in knowledge graphs) without changing the framework.\n\n• **Robustness when the assumption is relaxed**: Figure 7 reports a ablation where we randomly increase noise interactions by 5% to 20% in the 100k dataset, breaking the original correspondence between high interaction and high saliency. The performance of BoostGCN is still superior to that of LightGCN, which indicates that our proposed method is resilient to violations of the behavioral prior.\n\n• **Future extension**: We now state in the conclusion that if domain priors are unavailable, one can substitute $log(|N_i|)$ with parameter-free alternatives such as PageRank [b6, b7] scores or self-supervised edge-importance estimates without altering the BoostGCN pipeline or complexity.\n\n[b6] Page, L., et al., 1999. The PageRank citation ranking: Bringing order to the web. *Stanford infolab*.\n\n[b7] Stoica, A.A., et al., 2024. Fairness rising from the ranks: HITS and pagerank on homophilic networks. *ACM Web Conference*.\n\n**W5: More Experiments for New Baselines**\n\nFollowing your suggestions, we have added three latest baselines, **LTGNN (WWW 2024)** [c1], **TransGNN (SIGIR 2024)** [c2] and **GAT-LightGCN (replacing the Laplacian weights of LightGCN with GAT attention)**.\n\n| Recall@15 | 100k | 1M |Yelp|\n|---------------|---------------|----------|---------|\n| LTGNN       | 0.5612 | 0.4770 | 0.2726 |\n| TransGNN   | 0.5415 | 0.5196 | 0.3253  |\n| GAT-LightGCN  | 0.5703 | 0.5106 | 0.3243  |\n| **BoostGCN (Ours)** | **0.5908** | **0.5316** | **0.3968** |\n\n• These results demonstrate that our BoostGCN achieves consistently better recommendation performance than the\n latest baselines (including GAT-based model).\n\n[c1] WWW 2024: Linear-time graph neural networks for scalable recommendations.\n\n[c2] SIGIR 2024: TransGNN: Harnessing the collaborative power of transformers and graph neural networks for recommender system.\n\n**We hope our rebuttal can address your concerns. We are looking forward to your further feedback.**"}, {"review_id": "GiBReQ0Tzv", "reviewer": "Reviewer_nbkc", "summary": "This paper proposes a measure of significant interactions inspired by previous research, then uses this measure to construct a GCN method that amplifies the significant interactions. The paper demonstrates the effectiveness of the method by conducting various analyses.", "questions": "1. How do you calculate the norm of the set $E^{(0)}$?\n2. Using the integer index set $\\lbrace 1,2,3,\\ldots,n\\rbrace$ for $\\mathcal{X}_i$ for any i is not proper when the factors depend on $i$; a similar problem for $\\hat{\\mathcal{X}}_i$\n3. Does the method only work for recommendation system?\n4. Does it work for non-linear GCN?", "limitations": "See weaknesses and questions.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength: \n1. The empirical analysis is multi-dimensional, including performance analysis, parameter analysis, noise analysis and so on.\n2. The performance is superior to the compared methods on four datasets.\n\nWeaknesses:\n1. The paper uses the observation of behavior patterns in user-item interactions from other research as an assumption. The assumption is very restrictive when dealing with more general graphs, which may have a negative impact on the applicability of the proposed method.\n2. It is unclear if the proposed method is effective for scenarios other than recommendation.", "was_revised": true, "final_justification": "I have read the discussions and reviews; my concerns are addressed. I believe that the whole paper will be qualified as a main track paper after revision.", "rebuttal": "Thank you for the positive evaluation and constructive feedback. Below we address your questions and concerns:\n\n**Q1: The Norm of the Set $E^{(0)}$**\n\nIn the regularization term $λ||E^{(0)}||^2$ of Eq. (15), $||E^{(0)}||$ denotes the L2 norm over all trainable embeddings:\n\n$||E^{(0)}||^2 = Σ_{u∈U} ||e_u^{(0)}||^2 + Σ_{i∈I} ||e_i^{(0)}||^2$\n\nwhere\n\n• $e_u^{(0)}$ is the initial embedding of user $u$ (dimension $d$),\n\n• $e_i^{(0)}$ is the initial embedding of item $i$ (dimension $d$),\n\n• The summation runs over all $|U|$ users and $|I|$ items,\n\n• $E^{(0)}$ is the embedding tensor of shape $(|U|+|I|) × d$.\n\n**Q2: The Integer Index Set for $X_i$ and $\\hat{X_i}$**\n\nThank you for pointing this out. We agree that using the common integer set {1,2,3,…,n} to index the factors of every item i is ambiguous. In the revised manuscript we have replaced it with item-specific notation:\n\nFor each item $i$, we now write\n\n  $X_i$ = {$x_{i,1}$, $x_{i,2}$, …, $x_{i,n}$},\n\n  $\\hat{X_i}$ = {$x_{i,1}$, $x_{i,2}$, …, $x_{i,m}$} $⊆ X_i$.\n\nThis ensures that the factor indices are disjoint across items and eliminates any confusion. Eq. (3)–(6) and the related descriptions have been updated accordingly.\n\n**Q3 & W2: The Expansion of Application Scenarios for BoostGCN**\n\nThank you for this question. Although the paper focuses on recommendation, the core idea of BoostGCN—amplifying salient first-order interactions via a logarithmic weighting function—is a general graph-aggregation principle. Consequently, **the method is directly applicable to any task that requires node representation learning with edge-importance weighting**, such as:\n\n• influence maximization in social networks (up-weighting trust edges) [a1];\n\n• molecular property prediction (emphasizing bonds directly connected to functional groups) [a2,a3];\n\n• traffic flow forecasting (amplifying interactions with frequently used neighboring road segments) [a4,a5].\n\nWe have added a paragraph in the “Conclusion and Future Work” section to highlight this universality and list the cross-domain examples above.\n\n[a1] Sharma, K., et al., 2024. A survey of graph neural networks for social recommender systems. *ACM Computing Surveys*.\n\n[a2] Zhang, H., et al., 2024. A pre-trained multi-representation fusion network for molecular property prediction. *Information Fusion*.\n\n[a3] Therrien, F., et al., 2025. Using GNN property predictors as molecule generators. *Nature Communications*.\n\n[a4] Geng, Z., et al., 2024. STGAFormer: Spatial–temporal gated attention transformer based graph neural network for traffic flow forecasting. *Information Fusion*.\n\n[a5] Kong, W., et al., 2024, March. Spatio-temporal pivotal graph neural networks for traffic flow forecasting. *AAAI*.\n\n**Q4: Work for Non-linear GCN**\n\nThank you for this crucial question. BoostGCN’s log-amplification is a linear re-weighting scheme; hence it can be grafted onto any non-linear GCN without structural changes—simply replace the original Laplacian weights with the BoostGCN weights while keeping all non-linear activations, feature transformations, and residual connections intact.\n\nTo validate this, we added new experiments:\n\n| Recall@15 | 100k | 1M |Gowalla|Yelp|\n|---------------|---------------|----------|----------|----------|\n| NGCF (Non-linear)       | 0.4929 | 0.4545 | 0.3310|0.2460|\n| **NGCF (Log-amplification)** | **0.5175** | **0.4731** | **0.3389** |**0.2630** |\n\n• We take NGCF (with Leaky-ReLU and feature transformation) and substitute its Laplacian weights with BoostGCN weights. The value of the amplification function $β$ is searched from $e$ to $4e$, and other settings remain consistent with NGCF. We can find that adding our amplification function to the four datasets will all improve the model performance. Thus, **BoostGCN is readily compatible with non-linear GCNs and yields consistent gains.**\n\n**W1: Discussion on the Applicability of the Proposed Method**\n\nThank you for highlighting this concern. We acknowledge that our reliance on the prior “items with more interactions are more likely to be chosen” may appear restrictive for general graphs. In the revised manuscript we address this limitation as follows:\n\n• **Generalizing the assumption**: we show that the amplification weight $w_i ∝ log(|N_i|)$ is mathematically a smooth re-scaling of node degree. Degree is a universal structural cue independent of the “item-selection” semantics. Hence, in other domains one can simply replace $|N_i|$ with any relevant structural count (e.g., number of friends in social networks, entity frequency in knowledge graphs) without changing the framework.\n\n• **Robustness when the assumption is relaxed**: Figure 7 reports a ablation where we randomly increase noise interactions by 5% to 20% in the 100k dataset, breaking the original correspondence between high interaction and high saliency. The performance of BoostGCN is still superior to that of LightGCN, which indicates that our proposed method is resilient to violations of the behavioral prior.\n\n• **Future extension**: We now state in the conclusion that if domain priors are unavailable, one can substitute $log(|N_i|)$ with parameter-free alternatives such as PageRank [a6, a7] scores or self-supervised edge-importance estimates without altering the BoostGCN pipeline or complexity.\n\n[a6] Page, L., et al., 1999. The PageRank citation ranking: Bringing order to the web. *Stanford infolab*.\n\n[a7] Stoica, A.A., et al., 2024. Fairness rising from the ranks: HITS and pagerank on homophilic networks. *ACM Web Conference*.\n\n**We will add these details in the final version. We hope our rebuttal has answered your concerns. If there's anything else you'd like us to explain, please let us know -- we really appreciate your feedback!**"}, {"review_id": "6uU0Ue0bcQ", "reviewer": "Reviewer_mC5z", "summary": "The paper introduces BoostGCN, a novel Graph Convolutional Network (GCN) model designed to amplify significant interactions among first-order neighbors in recommendation systems, diverging from traditional Laplacian-based suppression methods. The authors argue that existing GCNs overly suppress valuable interaction signals, leading to suboptimal performance and slower learning. BoostGCN employs a logarithmic amplification function to prioritize high-significance interactions, enhancing both efficiency and accuracy. Experiments demonstrate superior performance over state-of-the-art baselines, with notable improvements in training speed (up to 90% faster) and recommendation metrics (e.g., Recall, NDCG). The paper also highlights BoostGCN’s robustness to hyperparameters, popularity debiasing, and noise resistance.", "questions": "See weaknesses", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "### Strengths \n* The shift from suppression to amplification of interactions is a novel and well-motivated contribution, addressing a clear gap in GCN-based recommendation systems.\n* Extensive experiments across diverse datasets validate the model’s superiority in performance and efficiency, with detailed ablation studies (e.g., hyperparameter sensitivity, layer depth).\n* BoostGCN’s fixed parameters and logarithmic scaling make it computationally efficient, achieving significant speedups without sacrificing accuracy.\n\n### Weaknesses\n* While heuristic for $S_{i\\to u}$, the paper lacks formal theoretical analysis of the amplification function’s optimality or convergence guarantees. For example, about why choosing log for amplification.\n* Baselines in Table 1 are all before 2024, while the authors have cited references in 2024 in the paper. More recent baselines are needed.\n* While the author state that the lower for the $\\beta$ will increase the amplification, the ablation on $\\beta$ should cover values lower than $e$. In fact the author should show a 'peak' at the value they finally choose.", "was_revised": true, "final_justification": "My concerns are addressed by the rebuttal", "rebuttal": "Thank you for the constructive feedback and thoughtful questions. We address each point below:\n\n**W1: Additional Mathematical Derivation of the Interaction Amplification Function**\n\nThank you for this insightful comment. We have added comprehensive mathematical derivations and theoretical analyses for the amplification function:\n\n1. **Rationale for the logarithmic choice**\n\nLet node degree be $d$. We require the weight $w(d)$ to satisfy:\n\n(a) monotonic increase: higher-degree nodes contribute more;\n\n(b) sub-linear growth: avoid over-amplifying tail noise;\n\n(c) closed-form differentiability: amenable to gradient optimization.\n\nUnder these constraints we prove:\n\nlinear $w(d)=d$ violates (b);\n\nexponential $w(d)=e^d$ violates (b)(c);\n\nlogarithmic $w(d)=log_β(d)$ satisfies all three.\n\nHence, the log is the closed-form optimal function under the stated axioms\n\n2. **Advantages of the logarithmic amplification function**\n\nWe formally derive:\nLet interaction amplification $S_{(i→u)}^{amp}=log_β(|N_i|)+Δ_{log}$ with $β>1$ and $Δ_{log}>0$. For any two neighbor items $p$ and $q$, define the difference $ε_{(p,q)}^{amp}=log_β(|N_p|)−log_β(|N_q|)$. Taking the derivative w.r.t. $β$ gives $dε^{amp}/dβ = (1/β)[ln(|N_p|)−ln(|N_q|)]$. This derivative monotonically decreases with $β$, indicating that the greater $β$, the gentler the difference $ε^{amp}$. The smaller $β$ is, the stronger the difference is magnified. Hence, $β$ acts as a smooth knob that trades off “quantity amplification” versus “model sensitivity.” In contrast, the exponential function exp(·) has a derivative that grows linearly with its input, causing extreme values and instability.\n\n3. **Smaller aggregation error**\n\nUsing logarithmic amplification function, the aggregation error bound decreases at the rate $O(log(|N_i|)+1)$ as the neighbor degree increases.\n\n**Proof.**\n\n• Let $N_u$ be the 1-hop neighbors of user $u$.\n\n• Define the amplified weight: $w_i = (log_β(|N_i|)+1)/|N_u|$.\n\n• Denote $e_i^{tru}$ as the ground-truth (expected) embedding of item $i$, and $e_i^{(k)}$ as the embedding after $k$ layers.\n\n• Aggregation error: $ε_u^{(k+1)} := ||e_u^{(k+1)} − e_u^{tru}||$, with $e_u^{tru} = Σ_{i∈N_u} w_i e_i^{tru}$.\n\n**Step 1**: Error propagation\n$e_u^{(k+1)} = Σ_{i∈N_u} w_i e_i^{(k)}$\n⇒ $ε_u^{(k+1)} = || Σ_{i∈N_u} w_i^2 (e_i^{(k)} − e_i^{tru})|| ≤ Σ_{i∈N_u} w_i ε_i^{(k)}$. \n\n**Step 2**: Assume layer-wise error satisfies $ε_i^{(k)} ≤ C·δ^{(k)}$\n(consistent with LightGCN-style linear-GCN convergence analyses, $δ<1$ and $C$ is general constant).\n\n**Step 3**: Bound the sum of squared weights:\n\n• Because $w_i = (log_β(|N_i|)+1)/|N_u|$ and $log_β(|N_i|) ≤ log_β(max_j |N_j|)$, \n\n• we have $Σ_{i∈N_u} w_i ≤ (log_β(max_j |N_j|)+1) / |N_u| · |N_u| = log_β(max_j |N_j|)+1$.\n\n**Step 4**: Combine the bounds:\n\n$ε_u^{(k+1)} ≤ Σ w_i ε_i^{(k)} ≤ (log_β(max_j |N_j|)+1)·C·δ^{(k)}\n= O(log(|N_i|)+1)·δ^{(k)}$.\n\nHence, the aggregation error bound decreases at the rate $O(log(|N_i|)+1)$ as the neighbor degree increases.\n\n4. **Near-optimal provable linear convergence rate**\n\nLet node degree be $d$ and the information weight be $w(d)$, among the sub-linear family $F$ = {$w$ | $w(d)=d^α$, $0<α<1$}, the logarithmic function  $w(d)=log_β(d)$ exhibits the same asymptotic growth order as the limiting behavior of $F$ ($α→0$), thereby achieving a spectral-radius bound arbitrarily close to the infimum of the family and yielding near-optimal provable linear convergence rate. \n\n**Proof.**\n\n• Consider the family of functions $F$ = {$w(d)$=$d^α$, $0<α<1$}. \n\n• For $w_α(d)=d^α$, the corresponding aggregation matrix $W_α = D^{-1} · diag(d_i^α) · A$. \n\n• Its infinite norm $||W_α||_ {∞} = max_i Σ_j d_j^α / d_i ≤ d^α_{max}$. \n\n• For $w_α(d)=d^α$, the spectral radius satisfies $ρ(W_α) ≤ ||W_α||_ {∞} ≤ d_{max}^α$ (Gershgorin's direct inference), which is monotonically increasing in $α$. \n\n• When $α→0$, $d_{max}^α → 1$ is at its minimum. When $α→1$, $d_{max}^α → d_{max}$ is at its maximum. \n\n• The logarithmic weight $w(d)=log_β(d)$ at the limit of $α→0$ satisfies $w(d) = lim_{α→0^+} (d^α−1)/α · 1/lnβ ≈ (d^α − 1)/α $ (first-order Taylor expansion, $β → e$), hence it inherits the minimal growth rate of the family $F$ in the limit.\n\nAmong the sub-linear family $F$, the bound $ρ(W_α)$ is minimized as $α→0$. The logarithmic function exhibits the same growth order as this limit, thus achieving the tightest bound.\n\n**W2: More Experiments for the Latest Baselines**\n\nFollowing your suggestions, we have added three latest baselines, **LTGNN (WWW 2024)** [1], **TransGNN (SIGIR 2024)** [2] and **GAT-LightGCN (replacing the Laplacian weights of LightGCN with GAT attention)**.\n\n| Recall@15 | 100k | 1M |Yelp|\n|---------------|---------------|----------|---------|\n| LTGNN       | 0.5612 | 0.4770 | 0.2726 |\n| TransGNN   | 0.5415 | 0.5196 | 0.3253  |\n| GAT-LightGCN  | 0.5703 | 0.5106 | 0.3243  |\n| **BoostGCN (Ours)** | **0.5908** | **0.5316** | **0.3968** |\n\n• These results demonstrate that our BoostGCN achieves consistently better recommendation performance than the\n latest baselines. We will also add the following literature in our paper:\n\n[1] WWW 2024: Linear-time graph neural networks for scalable recommendations.\n\n[2] SIGIR 2024: TransGNN: Harnessing the collaborative power of transformers and graph neural networks for recommender system.\n\n\n**W3: More Ablation Experiments on $β$**\n\nThank you for the suggestion. In the revised version, we extend the ablation study to $β$ ∈ {0.5e, 0.75e, e, 2e, 3e, 4e}. The results are shown as follows:\n\n| Recall@5 | 100k | 1M |Gowalla|Yelp|\n|---------------|---------------|----------|---------|---------|\n| $β = 0.5e$    | 0.2972 | 0.2633 | 0.2955  |0.1978|\n| $β = 0.75e$   | 0.2977 | 0.2636 | 0.2958  |0.1983 |\n| $β = e$ (**Optimal**)  | **0.2982**| **0.2641** | **0.2965** |**0.2001** |\n| $β = 2e$  | 0.2962 | 0.2615 | 0.2847 |0.1947 |\n| $β = 3e$  | 0.2928 | 0.2574 | 0.2816 |0.1917 |\n| $β = 4e$  | 0.2921 | 0.2547| 0.2802 |0.1884 |\n\n• $β$ = e yields the best performance on all datasets.\n\n• Datasets of different sparsity levels and sizes all show the same trend, confirming that $β$ = e is robust across sparsity levels and size scales.\n\n• **We will mark the position of the $β$ peak with a red asterisk in the new graph.**\n\n**We will add these improvements into the final version. We hope that our rebuttal can address your concerns. If there's anything else you'd like us to explain, please let us know -- we really appreciate your feedback!**"}]

Author rebuttal:

Meta-review: Traditional Graph Convolutional Networks (GCNs) that use graph Laplacian norm to suppress first-order neighbor information can dilute valuable interactions and slow down the learning of sparse relationships. The authors propose BoostGCN, a novel linear GCN model that amplifies significant interactions with first-order neighbors, enabling faster and more accurate capture of key relationships. After rebuttal, most of the concerns have been addressed, while the theoretical analysis remained relatively weak.
Decision: Accept (poster)