通过可学习投影向量实现个性化图联邦学习，不共享数据也能精准聚合

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 Federated learning with Auxiliary 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.