Federated Recommender Systems (FRS) preserve privacy by training decentralized models on client-specific user-item subgraphs without sharing raw data. However, FRS faces a unique challenge: subgraph structural imbalance, where drastic variations in subgraph scale (user/item counts) and connectivity (item degree) misalign client representations, making it challenging to train a robust model that respects each client's unique structural characteristics. To address this, we propose a Low-pass Personalized Subgraph Federated recommender system (LPSFed). LPSFed leverages graph Fourier transforms and low-pass spectral filtering to extract low-frequency structural signals that remain stable across subgraphs of varying size and degree, allowing robust personalized parameter updates guided by similarity to a neutral structural anchor. Additionally, we leverage a localized popularity bias-aware margin that captures item-degree imbalance within each subgraph and incorporates it into a personalized bias correction term to mitigate recommendation bias. Supported by theoretical analysis and validated on five real-world datasets, LPSFed achieves superior recommendation accuracy and enhances model robustness.
Figures & tables
Figure 1: Empirical observations from the federated recommender systems on the Amazon-Book ( He et al., 2020 ) dataset. (a) Subgraph size-degree variation: each point is one of 15 client subgraphs, partitioned using spectral clustering, grouped into L arge- D ense ( LD ), M edium- B alanced ( MB ), S mall- S parse ( SS ) by node count and average degree. (b) Structural divergence: Laplacian eigenvalue histograms averaged over each group, highlighting distinct spectral signals. (c) Group-wise Performance Gap: NDCG@20 for FedAvg ( McMahan et al., 2017 ) , PFedRec ( Zhang et al., 2023a ) , FedPUB ( Baek et al., 2023 ) , and Ours across groups, showing that performance varies significantly depending on subgraph structure. Detailed experimental results in Table 2 .
Figure 2: Overview of LPSFed - On the Client: Stage 1 applies low-pass GCN and a localized popularity bias-aware loss to train client subgraphs. Stage 2 computes similarities between each client subgraph and a server-provided random graph using structural signals. On the Server: Stage 3 aggregates client parameters and distributes them based on personalized similarity scores. Colored arrows indicate stage-wise interactions.
Figure 3
Dataset
Amazon-Book
Gowalla
Movielens-1M
Yelp2018
Tmall-Buy
Model
Recall
NDCG
Recall
NDCG
Recall
NDCG
Recall
NDCG
Recall
NDCG
FedAvg
0.0642
0.0312
0.1425
0.0660
0.2454
0.1240
0.0721
0.0292
0.0317
0.0164
FedPUB
0.0633
0.0322
0.1433
0.0667
0.2558
0.1209
0.0684
0.0296
0.0333
0.0180
FedMF
0.0153
0.0072
0.0765
0.0409
0.1679
0.0906
0.0318
0.0150
0.0122
0.0063
F2MF
0.0451
0.0225
0.0961
0.0565
0.1788
0.1120
0.0510
0.0247
0.0207
0.0132
PFedRec
0.0713
0.0242
0.1371
0.0478
0.1508
0.0997
0.0750
0.0225
0.0323
0.0170
Table 1: The overall performance comparison Recall@20 and NDCG@20 on five datasets, with the best scores highlighted in bold and the second-best in underlined . The improvement row highlights the gains achieved by our model ( LPSFed ) compared to the second-best-performing model.
Group
Large-Dense
Medium-Balanced
Small-Sparse
Overall
Model
Recall
NDCG
Recall
NDCG
Recall
NDCG
Recall
NDCG
FedAvg
0.0620
0.0280
0.0411
0.0208
0.0275
0.0117
0.0334
0.0152
FedPUB
0.0605
0.0355
0.0528
0.0267
0.0300
0.0123
0.0381
0.0177
FedMF
0.0176
0.0094
0.0127
0.0056
0.0058
0.0027
0.0084
0.0039
F2MF
0.0402
0.0231
0.0341
0.0174
0.0225
0.0085
0.0268
0.0118
PFedRec
0.0619
0.0250
0.0525
0.0185
0.0310
0.0131
0.0388
0.0153
Table 2: Performance for measuring the impact of subgraph structural imbalance on the Amazon-Book dataset, evaluated using Recall@20 and NDCG@20 across a 15-client partition. Clients are grouped into three categories: L arge- D ense, M edium- B alanced, S mall- S parse, and Overall (averaged across all clients). The best scores are highlighted in bold and the second-best in underlined . The improvement row shows the gains achieved by our model ( LPSFed ) compared to the second-best-performing model.
Data Setting
Balanced Dataset [NDCG@20]
Imbalanced Dataset [NDCG@20]
Model
Tail
Mid
Head
Overall
Tail
Mid
Head
Overall
FedAvg
0.0017
0.0077
0.0570
0.0264
0.0040
0.0108
0.0924
0.0312
FedPUB
0.0024 ↑ 41
0.008 ↑ 16
0.0620 ↑ 9
0.0279 ↑ 6
0.0064 ↑ 60
0.0130 ↑ 20
0.0998 ↑ 8
0.0322 ↑ 3
FedMF
0.0002 ↓ 88
0.0009 ↓ 88
0.0130 ↓ 77
0.0074 ↓ 72
0.0003 ↓ 92
0.0013 ↓ 88
0.0140 ↓ 85
0.0072 ↓ 77
F2MF
0.0037 ↑ 118
0.0112 ↑ 45
0.0438 ↓ 23
0.0225 ↓ 15
0.0050 ↑ 25
0.0119 ↑ 10
0.0436 ↓ 53
0.0225 ↓ 28
PFedRec
0.0055 ↑ 224
0.0125 ↑ 62
0.0277 ↓ 51
0.0244 ↓ 8
0.0068 ↑ 70
0.0145 ↑ 34
0.0262 ↓ 72
0.0242 ↓ 22
Table 3: Comparison of the localized popularity bias mitigation on the Amazon-Book using NDCG@20. Best scores are in bold . Balanced data includes all data, while the imbalanced dataset excludes less active participants. Arrows show (%) change relative to FedAvg: ↑ gain (%) , ↓ loss (%) .
Dataset
Amazon-Book
Gowalla
Movielens-1M
Yelp2018
Tmall-Buy
Model
Recall
NDCG
Recall
NDCG
Recall
NDCG
Recall
NDCG
Recall
NDCG
w/o LGCN
0.0388
0.0216
0.0965
0.0427
0.1622
0.0893
0.0471
0.0207
0.0256
0.0121
w/o bias-aware
0.0643
0.0322
0.1529
0.0711
0.2604
0.1281
0.0769
0.0301
0.0362
0.0186
w/o per
0.0652
0.0368
0.1576
0.0788
0.2625
0.1299
0.0775
0.0315
0.0370
0.0190
w/o per & bias-aware
0.0642
0.0312
0.1425
0.0660
0.2454
0.1240
0.0712
0.0292
0.0317
0.0164
w/o statistics for GR
0.0714
0.0403
0.1581
0.0856
0.2625
0.1330
0.0764
0.0372
0.0393
0.0199
Table 4: Ablation study of LPSFed on five datasets, reporting Recall@20 and NDCG@20 for different model variants. Bold indicates best performance per column, and the last row shows relative improvements over the second-best.
Figure 3: Hyperparameter sensitivity on the Amazon-Book dataset: (a) Bias-aware margin strength γ ; (b) Impact of γ on Bias Amplification in Imbalanced set; (c) Low-pass cut-off frequency Φ ; (d) Loss Temperature τ .
Symbol
Description
General Notations
C
The total number of clients
c
An index for a specific client, c∈{1,...,C}
u,i
A user and an item, respectively
U,I
The sets of all users and items in a given graph
M,N
The number of users and items in a given graph
Table 5: Table of Notations.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
Movielens-1M
Gowalla
Yelp2018
Amazon-Book
Tmall-Buy
Number of Users
6,040
29,858
31,668
52,643
885,759
Number of Items
3,900
40,981
38,048
91,599
1,144,124
Number of Interactions
1,000,290
1,027,370
1,561,406
2,984,108
7,592,214
Density
5.431%
0.084%
0.130%
0.062%
0.010%
Appendix
Table 6: The statistics of datasets.
Method (Avg.±std)
Ego-graph
Random-Const.
Interconnected-Const.
Spectral-Clust.
Avg. Subgraph Size
141.1±16.8
172.8±9.8
2105.6±135.7
196.2±36.2
Size variance
22276.8±6905.9
3198.5±1039.8
85083.4±45597.3
33370.3±17210.8
Avg. Degree
1.97±0.0
5.68±0.24
7.29±0.47
7.57±1.07
Degree Variance
1.0±0.0
6.34±0.08
2.19±1.08
30.22±11.45
Avg. Density
0.032±0.004
0.035±0.001
0.003±0.000
0.070±0.022
Spectral Entropy
1.0±0.0
6.34±0.08
6.42±0.15
5.69±0.68
Appendix
Table 7: Comparison of different client construction strategies on Movielens-1M .
Anchor Design
Amazon-Book
Gowalla
ML-1M
Yelp2018
Tmall-Buy
ER
0.0734
0.1599
0.2631
0.0767
0.0410
GNMK
0.0738
0.1621
0.2646
0.0783
0.0419
w/o statistics for GR (GNMK)
0.0714
0.1581
0.2625
0.0764
0.0393
Appendix
Table 8: Sensitivity analysis of the anchor graph design in LPSFed. Performance is reported using Recall@20 across five datasets. "w/o statistics for GR (GNMK)" constructs the GNMK reference solely from global assumptions, without any client-derived statistics. Bold indicates best performance per column.
Model
Time/Epoch
#Epoch
Training Time
Memory Usage
FedAvg
20s
90
30m
6.2GB
FedPUB
25s
90
37m
10.2GB
FedMF
23m 48s
150
59h 30m
6.2GB
F2MF
39m 12s
100
65h 20m
6.4GB
PFedRec
38m 47s
135
87h 16m
1.4GB
FedRAP
73m 29s
160
195h 56m
1.6GB
Appendix
Table 9: Comparison of training efficiency across different models. Metrics include time per epoch, number of epochs to converge, total training time, and memory usage, with the best scores highlighted in bold .
Iteration
20
40
60
80
100
γ = 0.0
0.0482
0.0497
0.0536
0.0568
0.0600
γ = 0.3
0.0478
0.0490
0.0529
0.0554
0.0592
γ = 0.5
0.0477
0.0489
0.0522
0.0544
0.0576
γ = 0.7
0.0476
0.0486
0.0512
0.0541
0.0570
γ = 1.0
0.0474
0.0478
0.0501
0.0522
0.0553
Appendix
Table 10: Average Jaccard index for paired users over iterations, with rows corresponding to margin strengths γ and columns to training iterations.
Cut-off Frequency Φ
2
4
6
8
Recall@20
0.2556
0.2614
0.2615
0.2622
Eigengap δ
1.17×10−15
4.36×10−3
1.61×10−2
1.46×10−1
Pearson Correlation (Recall ↔δ )
0.5004
Appendix
Table 11: Correlation analysis between eigengap and model performance in Movielens-1M . Recall@20 and corresponding eigengap values are reported for different cut-off frequencies Φ . Pearson correlation quantifies linear dependence between eigengap magnitude and model performance.
# of Clients
4
10
20
Model
Recall
NDCG
Recall
NDCG
Recall
NDCG
FedAvg
0.0642
0.0312
0.0395
0.0186
0.0220
0.0098
FedPUB
0.0633
0.0322
0.0417
0.0180
0.0232
0.0102
FedMF
0.0153
0.0072
0.0091
0.0058
0.0033
0.0035
F2MF
0.0451
0.0225
0.0325
0.0182
0.0158
0.0078
PFedRec
0 .0713
0.0242
0.0406
0.0169
0.0236
0.0100
Appendix
Table 12: Effect of client variability on performance using the Amazon-Book dataset. Metrics include Recall@20 and NDCG@20, bold indicates the best results and underlined the second-best results in each setting.
Graph neural network (GNN)-based federated recommendation systems effectively capture user-item relationships while preserving data privacy. However, existing methods often face slow convergence on graph data and privacy leakage risks during collaboration. To address these challenges, we propose FastPFRec (Fast Personalized Federated Recommendation with Secure Sharing), a novel framework that enhances both training efficiency and data security. FastPFRec accelerates model convergence through an efficient local update strategy and introduces a privacy-aware parameter sharing mechanism to mitigate leakage risks. Experiments on four real-world datasets (Yelp, Kindle, Gowalla-100k, and Gowalla-1m) show that FastPFRec achieves 32.0% fewer training rounds, 34.1% shorter training time, and 8.1% higher accuracy compared with existing baselines. These results demonstrate that FastPFRec provides an efficient and privacy-preserving solution for scalable federated recommendation.
Zhenxing Yan, Jidong Yuan, Yongqi Sun +2
Key Laboratory of Big Data & Artificial Intelligence in Transportation (Beijing Jiaotong University), Ministry of Education, Beijing, 100044, China · School of Computer Science and Technology, Beijing Jiaotong University, Beijing, 100044, China
Graph-based recommender systems are highly effective at extracting collaborative signals from user--item interactions, and federated learning (FL) allows these models to be trained while preserving user privacy. However, aggregating graph representations across distributed, non-IID clients remains a challenge; structural embeddings learned locally often misalign, and naive averaging fails to capture meaningful cross-client relationships. Most existing federated graph methods rely exclusively on structural aggregation, neglecting the rich, global semantic context available in large language models (LLMs). In this paper, we propose a novel framework that uses LLM-encoded knowledge to guide federated graph recommendation. Specifically, clients learn structural representations from local graphs while simultaneously summarizing their typical interaction patterns into compact semantic vectors via a frozen LLM. The central server then uses these LLM-encoded semantic signals to discover related preference patterns across clients, guiding the selective aggregation of their structural representations. This enables semantically informed cross-client collaboration without exposing raw data. Extensive experiments on standard benchmarks show that guiding structural alignment with LLM-encoded knowledge consistently improves recommendation accuracy over existing federated graph baselines.
Thi Minh Chau Nguyen, Hien Trang Nguyen, Duc Anh Nguyen +3
Federated recommendation (FedRec) enables personalized modeling without centralizing users' interaction histories, but most existing methods assume a fixed item pool and thus overlook the practical cold-item setting where new items continuously arrive. Under the dual-sided constraint, where the server cannot access clients' interactions while clients cannot access the server's proprietary item attribute features, prior federated cold-start recommendation approaches suffer from three structural limitations: a lack of personalization, compositionality failure caused by forcing heterogeneous semantics into a single embedding space, and training- and communication-inefficiency arising from explicit alignment between separate collaborative and attribute representations. To address these challenges, we propose Personalized and Multi-view Representation for Federated Cold-Start Recommendation (PMFRec). PMFRec learns a personalized representation generator to produce user-specific item representations from attribute features, and introduces a global multi-view encoder with item-adaptive gating and an orthogonality objective to capture complementary semantic views while reducing cross-view redundancy. In addition, PMFRec fuses collaborative and attribute knowledge into a single exchanged item representation, eliminating the need for an explicit client-side regularizer and reducing communication overhead. Extensive experiments on real-world datasets show that PMFRec consistently outperforms strong baselines in cold-item recommendation and further improves user-level fairness, warm-scenario adaptability, and robustness under Local Differential Privacy (LDP).
Jaehyung Lim, Wonbin Kweon, Woojoo Kim +3
Pohang University of Science and Technology Pohang, Republic of Korea · University of Illinois Urbana-Champaign Champaign, IL, USA