FedHiP: Heterogeneity-Invariant Personalized Federated Learning Through Closed-Form Solutions

• URL: http://arxiv.org/abs/2508.04470v1
• Date: Wed, 06 Aug 2025 14:15:57 GMT
• Title: FedHiP: Heterogeneity-Invariant Personalized Federated Learning Through Closed-Form Solutions
• Authors: Jianheng Tang, Zhirui Yang, Jingchao Wang, Kejia Fan, Jinfeng Xu, Huiping Zhuang, Anfeng Liu, Houbing Herbert Song, Leye Wang, Yunhuai Liu,
• Abstract summary: We propose a Heterogeneity-invariant Personalized Federated learning scheme, named FedHiP, through analytical (i.e., closed-form) solutions to avoid gradient-based updates.<n>Our scheme incorporates three phases: analytic local training, analytic global aggregation, and analytic local personalization.<n>Experiments on benchmark datasets validate the superiority of our FedHiP scheme, outperforming the state-of-the-art baselines by at least 5.79%-20.97% in accuracy.
• Score: 22.424881385529783
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Lately, Personalized Federated Learning (PFL) has emerged as a prevalent paradigm to deliver personalized models by collaboratively training while simultaneously adapting to each client's local applications. Existing PFL methods typically face a significant challenge due to the ubiquitous data heterogeneity (i.e., non-IID data) across clients, which severely hinders convergence and degrades performance. We identify that the root issue lies in the long-standing reliance on gradient-based updates, which are inherently sensitive to non-IID data. To fundamentally address this issue and bridge the research gap, in this paper, we propose a Heterogeneity-invariant Personalized Federated learning scheme, named FedHiP, through analytical (i.e., closed-form) solutions to avoid gradient-based updates. Specifically, we exploit the trend of self-supervised pre-training, leveraging a foundation model as a frozen backbone for gradient-free feature extraction. Following the feature extractor, we further develop an analytic classifier for gradient-free training. To support both collective generalization and individual personalization, our FedHiP scheme incorporates three phases: analytic local training, analytic global aggregation, and analytic local personalization. The closed-form solutions of our FedHiP scheme enable its ideal property of heterogeneity invariance, meaning that each personalized model remains identical regardless of how non-IID the data are distributed across all other clients. Extensive experiments on benchmark datasets validate the superiority of our FedHiP scheme, outperforming the state-of-the-art baselines by at least 5.79%-20.97% in accuracy.

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