Title: Personalized Subgraph Federated Learning with Differentiable Auxiliary Projections
Venue: NeurIPS 2025
Accepted: yes
Keywords: Graph Neural Networks

Federated Learning

Node Classification

Graph Representation Learning
Abstract: Federated Learning (FL) on graph-structured data typically faces non-IID challenges, particularly in scenarios where each client holds a distinct subgraph sampled from a global graph. In this paper, we introduce **Fed**erated learning with **Aux**iliary projections (FedAux), a personalized subgraph FL framework that learns to align, compare, and aggregate heterogeneously distributed local models without sharing raw data or node embeddings. In FedAux, each client jointly trains (i) a local GNN and (ii) a learnable auxiliary projection vector (APV) that differentiably projects node embeddings onto a 1D space. A soft-sorting operation followed by a lightweight 1D convolution refines these embeddings in the ordered space, enabling the APV to effectively capture client-specific information. After local training, these APVs serve as compact signatures that the server uses to compute inter‑client similarities and perform similarity‑weighted parameter mixing, yielding personalized models while preserving cross‑client knowledge transfer. Moreover, we provide rigorous theoretical analysis to establish the convergence and rationality of our design. Empirical evaluations across diverse graph benchmarks demonstrate that FedAux substantially outperforms existing baselines in both accuracy and personalization performance. The code is available at [https://github.com/JhuoW/FedAux](https://github.com/JhuoW/FedAux).


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes FedAux, a novel framework for personalized federated learning (FL) on graphs where each client holds a local subgraph from a global graph. The key idea is to introduce a learnable auxiliary projection vector (APV) per client, which projects node embeddings to a 1D latent space. Through a soft-sorting mechanism and 1D convolution (or kernel smoothing), each client generates a compact summary of its local graph structure. These APVs are sent to the server for computing inter-client similarity to enable personalized aggregation without sharing raw data or embeddings.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n1. Strong Novelty and Motivation:\n\nThe paper tackles a real and under-explored problem: non-IID subgraph federated learning with privacy constraints.\n\nThe proposed use of differentiable 1D auxiliary projections (APVs) is new, elegant, and well-motivated.\n\n2. Compact and Privacy-Preserving Representation:\n\nAPVs serve as low-dimensional summaries of each client's subgraph, without leaking node features or embeddings.\n\nThis makes the method scalable and communication-efficient, and compliant with strong privacy assumptions.\n\n3. Solid Theoretical Foundations:\n\nThe APV is proven to converge to the first principal component of node embeddings (Theorem 3.1).\n\nThe equivalence between soft aggregation and hard sorting is also well-analyzed (Theorem 3.2).\n\nA global linear convergence guarantee is provided (Theorem 3.3), which is rare in graph FL work.\n\n4. Comprehensive Experiments:\n\nExperiments span 6 real-world datasets with varying heterogeneity (Cora, CiteSeer, Pubmed, ogbn-arxiv, Amazon).\n\nFedAux consistently outperforms strong baselines such as FedAvg, FedPer, GCFL, FED-PUB, etc.\n\nDetailed analysis on non-IIDness, convergence, similarity visualization, and ablation studies are included.\n\n5. Efficient Server-side Aggregation:\n\nUnlike previous clustering-based personalization methods, FedAux only computes pairwise cosine similarities between APVs, leading to much lower memory and time overhead.\n\nWeaknesses\n\n1. No Explicit Evaluation on Real Privacy Attacks:\n\nAlthough APV is designed to be privacy-preserving, no empirical privacy evaluation (e.g., membership inference, reconstruction) is included.\n\nThis weakens the privacy claim, even if the design is principled.\n\n2. Scalability on Large Graphs:\n\nThe kernel-based aggregation step has O(N²) cost per client (w.r.t. node count), which may not scale well for clients with large subgraphs.\n\nNo empirical analysis or ablation on scalability vs. subgraph size is presented.\n\n3. Limited Diversity in FL Protocols:\n\nThe method is only evaluated under full-participation FL. It is unclear whether FedAux can work under partial participation or asynchronous FL, which are more practical settings.\n\nQUESTIONS:\nSee above.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes FedAux, an aggregation strategy designed to advance the field of personalized Federated Graph Learning (FGL). The core innovation of FedAux lies in the introduction of Auxiliary Projection Vectors (APV), which differentiably project node embeddings onto a one-dimensional space. These projections serve as auxiliary representations of clients’ data distributions and are utilized during server-side training to compute inter-client similarities. The resulting similarity scores are then used to derive personalized aggregation weights, enabling the construction of tailored global models for each client. Furthermore, this work provides theoretical proofs to validate the effectiveness of APV in capturing client-specific data distributions, along with convergence guarantees for the proposed method.\n\nSTRENGTHS AND WEAKNESSES:\nStrength: \n1.The theoratical prof of the APV and the discussion of methodology is comprehensive and necessary. \n2.The explanation of method design is accessible to readers with limited domain knowledge, and often highlight the key takeaways to offer intuitive insights. \nExtensive appendix well supports the main contents, especially to the extra profs of theorem, which is commendable. \n\nWeakness\nContribution is lacking \n1.While the motivation of this work is clear as it stated in Introduction, couple flaws are noticable: \n1.The motivation for this work is drawn from the limitations of representative approaches such as GCFL and FedPUB; however, it lacks a comprehensive discussion of more recent advances in personalized Federated Graph Learning. \n2.While the rationale behind the design of the proposed method is clearly articulated, the scope of the research appears limited. Notably, the method relies heavily on the effectiveness of the Auxiliary Projection Vector (APV), which essentially performs a sorting operation on nodes within each client’s subgraph. Given that the APV is subsequently used as an auxiliary mechanism to compute inter-client similarity—based on data distribution—and to determine aggregation weights, the experimental evaluation should encompass both homogeneous and heterogeneous global graph scenarios. However, the current experiments are restricted to homogeneous graphs, which may fundamentally contribute to the method’s favorable performance. Although the use of METIS and corresponding non-IID evaluation metrics is acknowledged, extending the evaluation to heterogeneous graph settings would enhance the generalizability and practical impact of the proposed method.\n2.A natural question that arises when reading this paper is whether FedAux or its core component, APV, can be integrated with alternative backbone models or other Federated Graph Learning (FGL) methods to enhance their performance. Such an investigation would help to demonstrate the broader applicability and utility of FedAux beyond the current experimental setting. \nPresentation-wise \nThis section concerns with the coherence of the paper organization \n1.The contribution section should provide a concise summary of the impact and significance of the proposed method, rather than offering a detailed explanation of the model’s training pipeline.\n2.The organization of the locations of tables and figures can be optimized to make it more reader friendly. For instance, Figure 1 should be located closer to the Section 3, and Table 1 should be located on the same page with detailed experimental evaluation. \n3.Figure 3 is not referenced or discussed in the main text, which may confuse readers who are unclear about its purpose or relevance to the overall narrative.\nExperiments \n1.Figure 4: The comparison appears limited due to the inclusion of only a few baseline methods, which may be insufficient to convincingly demonstrate the effectiveness of the proposed approach.\n2.Figure 5: Similar to Figure 4, this figure suffers from the same limitation—namely, the lack of comprehensive baseline comparisons—which undermines the strength of the evaluation.\n\nQUESTIONS:\nsee weakness\n\nLIMITATIONS:\nsee weakness", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposed a new personalized subgraph federated learning framework with Auxiliary projections without sharing raw data or node embeddings in clients. Each client jointly trains a local GNN and a learnable auxiliary projection vector (APV), which can differentially projects node embeddings onto a 1D space and capture client-specific information. APVs serve as compact signatures that the server uses to compute inter-client similarities and perform similarity-weighted parameter mixing, yielding personalized models while preserving cross-client knowledge transfer. The experimental results across diverse graph benchmarks demonstrate that the proposed method substantially outperformed existing baselines in both accuracy and personalization performance.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1.\tThis paper proposed a new personalized subgraph federated learning framework with Auxiliary projections without sharing raw data or node embeddings in clients. Each client jointly trains a local GNN and a learnable auxiliary projection vector (APV), which serve as compact signatures that the server uses to compute inter-client similarities and perform similarity-weighted parameter mixing, yielding personalized models while preserving cross-client knowledge transfer. This idea seems to be interesting.\n2.\tThis paper evaluated the proposed method on 6 widely used datasets, and the experimental results across diverse graph benchmarks demonstrate that the proposed method substantially outperformed existing 8 baselines in both accuracy and personalization performance. \n3.\tThis paper also provided theoretical analysis on fidelity of APV introduced in the method.\n\nWeaknesses:\n1. There are no experiments about the privacy preservation of APV-based federated learning, which can be evaluated by verifying the efficiency of some membership inference attacks in the server.\n\nQUESTIONS:\nThere are no experiments about the privacy preservation of APV-based federated learning, which can be evaluated by verifying the efficiency of some membership inference attacks in the server.\n\nLIMITATIONS:\nThere are no experiments about the privacy preservation of APV-based federated learning, which can be evaluated by verifying the efficiency of some membership inference attacks in the server.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the non-IID challenge in federated learning on graph-structured data by proposing FedAux, a personalized subgraph FL framework. The core idea is to use learnable auxiliary projection vectors (APVs) to project node embeddings into a 1D latent space, enabling each client to generate a compact, privacy-preserving signature. These APVs guide similarity-based aggregation on the server without sharing raw data or embeddings.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper introduces a novel and theoretically grounded mechanism — the auxiliary projection vector (APV) — which enables clients to share compact, privacy-preserving subgraph representations while avoiding raw data or embedding leakage.\n\n2. The proposed FedAux framework is validated both theoretically (with convergence guarantees and principal component analysis) and empirically, demonstrating clear performance improvements over strong baselines on diverse graph datasets with varying non-IID conditions.\n\nWeaknesses:\n\n1. While the APV is theoretically shown to converge to the principal direction of local embeddings, the paper does not clarify how robust this alignment remains when local data is extremely sparse or weakly informative — in such cases, the APV may fail to capture meaningful non-IID structural differences across clients, limiting its intended role as a reliable similarity proxy for personalized aggregation.\n\n2. The paper lacks a detailed empirical analysis of how the APV specifically contributes to the final performance, and does not discuss alternative design choices for APVs or how different projection strategies might affect generalization under realistic non-IID settings. This leaves open questions about the stability and robustness of the APV mechanism when deployed in practical, more complex graph scenarios.\n\n3. The paper does not provide a clear and rigorous discussion of whether and how the learned APVs might leak sensitive structural or semantic information about local subgraphs, leaving it unclear whether the APV truly guarantees privacy preservation beyond the absence of raw data or embeddings. A more formal privacy analysis would strengthen the claim that FedAux meets strict privacy requirements in practical federated settings.\n\nQUESTIONS:\nSee the above\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}