# APFL: Analytic Personalized Federated Learning via Dual-Stream Least Squares

arXiv: https://arxiv.org/abs/2508.10732 · HTML: https://mlsanity.com/paper/2508.10732/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Builds on (most cited first, 19 of 19)

- [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)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Federated Learning from Pre-Trained Models: A Contrastive Learning Approach](https://mlsanity.com/paper/2209.10083/) (2022)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Dual-Personalizing Adapter for Federated Foundation Models](https://mlsanity.com/paper/2403.19211/) (2024)
- [Eliminating Domain Bias for Federated Learning in Representation Space](https://mlsanity.com/paper/2311.14975/) (2023)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [FedSelect: Personalized Federated Learning with Customized Selection of Parameters for Fine-Tuning](https://mlsanity.com/paper/2404.02478/) (2024)
- [GACL: Exemplar-Free Generalized Analytic Continual Learning](https://mlsanity.com/paper/2403.15706/) (2024)
- [Personalized Federated Continual Learning via Multi-granularity Prompt](https://mlsanity.com/paper/2407.00113/) (2024)
- [Multi-level Personalized Federated Learning on Heterogeneous and Long-Tailed Data](https://mlsanity.com/paper/2405.06413/) (2024)
- [PGFed: Personalize Each Client's Global Objective for Federated Learning](https://mlsanity.com/paper/2212.01448/) (2022)
- [Federated Learning While Providing Model as a Service: Joint Training and Inference Optimization](https://mlsanity.com/paper/2312.12863/) (2023)
- [Towards Efficient and Exact Forgetting Services in Pre-Trained-Model-based Continual Learning](https://mlsanity.com/paper/2505.12239/) (2025)
- [TS-ACL: Closed-Form Solution for Time Series-oriented Continual Learning](https://mlsanity.com/paper/2410.15954/) (2024)

## Built on by (most cited first, 2 of 2)

- [DeepAFL: Deep Analytic Federated Learning](https://mlsanity.com/paper/2603.00579/) (2026)
- [Accurate and Resource-Efficient Federated Continual Learning](https://mlsanity.com/paper/2606.11480/) (2026)

## Abstract (arXiv)

Personalized Federated Learning (PFL) has presented a significant challenge to deliver personalized models to individual clients through collaborative training. Existing PFL methods are often vulnerable to non-IID data, which severely hinders collective generalization and then compromises the subsequent personalization efforts. In this paper, to address this non-IID issue in PFL, we propose an Analytic Personalized Federated Learning (APFL) approach via dual-stream least squares. In our APFL, we use a foundation model as a frozen backbone for feature extraction. Subsequent to the feature extractor, we develop dual-stream analytic models to achieve both collective generalization and individual personalization. Specifically, our APFL incorporates a shared primary stream for global generalization across all clients, and a dedicated refinement stream for local personalization of each individual client. The analytical solutions of our APFL enable its ideal property of heterogeneity invariance, theoretically meaning that each personalized model remains identical regardless of how heterogeneous the data are distributed across all other clients. Empirical results across various datasets also validate the superiority of our APFL over state-of-the-art baselines, with advantages of at least 1.10%-15.45% in accuracy.