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

arXiv: https://arxiv.org/abs/2508.04470 · HTML: https://mlsanity.com/paper/2508.04470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Federated Learning from Pre-Trained Models: A Contrastive Learning Approach](https://mlsanity.com/paper/2209.10083/) (2022)
- [FedALA: Adaptive Local Aggregation for Personalized Federated Learning](https://mlsanity.com/paper/2212.01197/) (2022)
- [On the Importance and Applicability of Pre-Training for Federated Learning](https://mlsanity.com/paper/2206.11488/) (2022)
- [Where to Begin? On the Impact of Pre-Training and Initialization in Federated Learning](https://mlsanity.com/paper/2210.08090/) (2022)
- [FedDAT: An Approach for Foundation Model Finetuning in Multi-Modal Heterogeneous Federated Learning](https://mlsanity.com/paper/2308.12305/) (2023)
- [ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection](https://mlsanity.com/paper/2205.14922/) (2022)
- [Eliminating Domain Bias for Federated Learning in Representation Space](https://mlsanity.com/paper/2311.14975/) (2023)
- [FedSelect: Personalized Federated Learning with Customized Selection of Parameters for Fine-Tuning](https://mlsanity.com/paper/2404.02478/) (2024)
- [Multi-level Personalized Federated Learning on Heterogeneous and Long-Tailed Data](https://mlsanity.com/paper/2405.06413/) (2024)
- [Locality Sensitive Sparse Encoding for Learning World Models Online](https://mlsanity.com/paper/2401.13034/) (2024)
- [AFL: A Single-Round Analytic Approach for Federated Learning with Pre-trained Models](https://mlsanity.com/paper/2405.16240/) (2024)
- [Learning from the Kernel and the Range Space](https://mlsanity.com/paper/1810.09071/) (2018)
- [Federated Learning While Providing Model as a Service: Joint Training and Inference Optimization](https://mlsanity.com/paper/2312.12863/) (2023)
- [AugFL: Augmenting Federated Learning with Pretrained Models](https://mlsanity.com/paper/2503.02154/) (2025)

## Abstract (arXiv)

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.