# Analytic Personalized Federated Meta-Learning

arXiv: https://arxiv.org/abs/2502.06915 · HTML: https://mlsanity.com/paper/2502.06915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 49 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [The Secret Revealer: Generative Model-Inversion Attacks Against Deep Neural Networks](https://mlsanity.com/paper/1911.07135/) (2019)
- [Federated Bayesian Optimization via Thompson Sampling](https://mlsanity.com/paper/2010.10154/) (2020)
- [Advances and Challenges in Meta-Learning: A Technical Review](https://mlsanity.com/paper/2307.04722/) (2023)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [FedGT: Identification of Malicious Clients in Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2305.05506/) (2023)
- [Zeroth-Order Algorithms for Stochastic Distributed Nonconvex Optimization](https://mlsanity.com/paper/2106.02958/) (2021)
- [BAFFLE: A Baseline of Backpropagation-Free Federated Learning](https://mlsanity.com/paper/2301.12195/) (2023)
- [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)
- [NaturalInversion: Data-Free Image Synthesis Improving Real-World Consistency](https://mlsanity.com/paper/2306.16661/) (2023)
- [ZORB: A Derivative-Free Backpropagation Algorithm for Neural Networks](https://mlsanity.com/paper/2011.08895/) (2020)
- [Random orthogonal additive filters: a solution to the vanishing/exploding gradient of deep neural networks](https://mlsanity.com/paper/2210.01245/) (2022)
- [Fed-Sophia: A Communication-Efficient Second-Order Federated Learning Algorithm](https://mlsanity.com/paper/2406.06655/) (2024)

## Abstract (arXiv)

Analytic Federated Learning (AFL) is an enhanced gradient-free federated learning (FL) paradigm designed to accelerate training by updating the global model in a single step with closed-form least-square (LS) solutions. However, the obtained global model suffers performance degradation across clients with heterogeneous data distribution. Meta-learning is a common approach to tackle this problem by delivering personalized local models for individual clients. Yet, integrating meta-learning with AFL presents significant challenges: First, conventional AFL frameworks cannot support deep neural network (DNN) training which can influence the fast adaption capability of meta-learning for complex FL tasks. Second, the existing meta-learning method requires gradient information, which is not involved in AFL. To overcome the first challenge, we propose an AFL framework, namely FedACnnL, in which a layer-wise DNN collaborative training method is designed by modeling the training of each layer as a distributed LS problem. For the second challenge, we further propose an analytic personalized federated meta-learning framework, namely pFedACnnL. It generates a personalized model for each client by analytically solving a local objective which bridges the gap between the global model and the individual data distribution. FedACnnL is theoretically proven to require significantly shorter training time than the conventional FL frameworks on DNN training while the reduction ratio is 83%~99% in the experiment. Meanwhile, pFedACnnL excels at test accuracy with the vanilla FedACnnL by 4%~8% and it achieves state-of-the-art (SOTA) model performance in most cases of convex and non-convex settings compared with previous SOTA frameworks.