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Low-pass Personalized Subgraph Federated Recommendation

Wooseok Sim, Hogun Park

Abstract

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.

Low-pass Personalized Subgraph Federated Recommendation

Abstract

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.
Paper Structure (72 sections, 5 theorems, 65 equations, 4 figures, 12 tables, 1 algorithm)

This paper contains 72 sections, 5 theorems, 65 equations, 4 figures, 12 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Federated Recommender System
  4. Graph Fourier Transform (GFT)
  5. Low-pass Graph Filter & Convolution
  6. Methodology
  7. Training of Client Models
  8. Client Models.
  9. Subgraph Structural Signals Extraction.
  10. Localized Popularity Bias-aware Optimization.
  11. Localized Popularity Bias Information Computation.
  12. Computing Structural Similarity
  13. Aggregating and Distributing Parameters on the Server
  14. Initialization.
  15. Aggregation.
  16. ...and 57 more sections

Key Result

Theorem 3.1

Let $G_1=(\mathcal{V}_1,\mathcal{E}_1)$ and $G_2=(\mathcal{V}_2,\mathcal{E}_2)$ be graphs with $n_1=|\mathcal{V}_1|$ and $n_2=|\mathcal{V}_2|$ nodes and $k$ communities each. $\mathcal{E}_1$ and $\mathcal{E}_2$ are sets of edges of $G_1$ and $G_2$, respectively. Moreover, $\mathit{\Phi}~(<n)$ denote Under Assumption assumption:idealized, let $D_{\text{struct}} = D_{KL}(\mathbf{K}^1_{\text{struct}}

Figures (4)

  • Figure 1: Empirical observations from the federated recommender systems on the Amazon-BookLightGCN dataset. (a) Subgraph size-degree variation: each point is one of 15 client subgraphs, partitioned using spectral clustering, grouped into Large-Dense (LD), Medium-Balanced (MB), Small-Sparse (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 FedAvg, PFedRec PFedRec, FedPUB FedPUB, and Ours across groups, showing that performance varies significantly depending on subgraph structure. Detailed experimental results in Table \ref{['tab:rq2_heterogeneity']}.
  • 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: Hyperparameter sensitivity on the Amazon-Book dataset: (a) Bias-aware margin strength $\gamma$; (b) Impact of $\gamma$ on Bias Amplification in Imbalanced set; (c) Low-pass cut-off frequency $\mathit{\Phi}$; (d) Loss Temperature $\tau$.
  • Figure : LPSFed: Low-pass Personalized Subgraph Federated Recommendation

Theorems & Definitions (10)

  • Theorem 3.1: Structural Comparison via Spectral Distributions
  • Theorem 3.2: Spectral Regularization
  • Lemma 1: Low-pass Filter Preservation
  • proof
  • Lemma 2: Spectral Measure Convergence
  • proof
  • Lemma 3: Filter Stability
  • proof
  • proof
  • proof