# DeepAFL: Deep Analytic Federated Learning

arXiv: https://arxiv.org/abs/2603.00579 · HTML: https://mlsanity.com/paper/2603.00579/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 66 references that are in the map.
- First posted on arXiv 28 Feb 2026.

## Builds on (most cited first, 30 of 45)

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [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 Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Data-Free Knowledge Distillation for Heterogeneous Federated Learning](https://mlsanity.com/paper/2105.10056/) (2021)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Practical Secure Aggregation for Federated Learning on User-Held Data](https://mlsanity.com/paper/1611.04482/) (2016)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Preservation of the Global Knowledge by Not-True Distillation in Federated Learning](https://mlsanity.com/paper/2106.03097/) (2021)
- [Where to Begin? On the Impact of Pre-Training and Initialization in Federated Learning](https://mlsanity.com/paper/2210.08090/) (2022)
- [FedDisco: Federated Learning with Discrepancy-Aware Collaboration](https://mlsanity.com/paper/2305.19229/) (2023)
- [ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection](https://mlsanity.com/paper/2205.14922/) (2022)
- [FedFed: Feature Distillation against Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2310.05077/) (2023)
- [Securing Secure Aggregation: Mitigating Multi-Round Privacy Leakage in Federated Learning](https://mlsanity.com/paper/2106.03328/) (2021)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [Federated Learning with Sparsified Model Perturbation: Improving Accuracy under Client-Level Differential Privacy](https://mlsanity.com/paper/2202.07178/) (2022)
- [Error Bounds for Learning with Vector-Valued Random Features](https://mlsanity.com/paper/2305.17170/) (2023)
- [Unleashing the Power of Continual Learning on Non-Centralized Devices: A Survey](https://mlsanity.com/paper/2412.13840/) (2024)
- [FedLPA: One-shot Federated Learning with Layer-Wise Posterior Aggregation](https://mlsanity.com/paper/2310.00339/) (2023)
- [Sampling weights of deep neural networks](https://mlsanity.com/paper/2306.16830/) (2023)
- [Personalized Federated Continual Learning via Multi-granularity Prompt](https://mlsanity.com/paper/2407.00113/) (2024)
- [FedAWA: Adaptive Optimization of Aggregation Weights in Federated Learning Using Client Vectors](https://mlsanity.com/paper/2503.15842/) (2025)
- [FedVLA: Federated Vision-Language-Action Learning with Dual Gating Mixture-of-Experts for Robotic Manipulation](https://mlsanity.com/paper/2508.02190/) (2025)
- [A Survey for Federated Learning Evaluations: Goals and Measures](https://mlsanity.com/paper/2308.11841/) (2023)

## Built on by (most cited first, 1 of 1)

- [FedOPAL: One-Shot Federated Learning via Analytic Visual Prompt Tuning](https://mlsanity.com/paper/2607.08368/) (2026)

## Abstract (arXiv)

Federated Learning (FL) is a popular distributed learning paradigm to break down data silo. Traditional FL approaches largely rely on gradient-based updates, facing significant issues about heterogeneity, scalability, convergence, and overhead, etc. Recently, some analytic-learning-based work has attempted to handle these issues by eliminating gradient-based updates via analytical (i.e., closed-form) solutions. Despite achieving superior invariance to data heterogeneity, these approaches are fundamentally limited by their single-layer linear model with a frozen pre-trained backbone. As a result, they can only achieve suboptimal performance due to their lack of representation learning capabilities. In this paper, to enable representable analytic models while preserving the ideal invariance to data heterogeneity for FL, we propose our Deep Analytic Federated Learning approach, named DeepAFL. Drawing inspiration from the great success of ResNet in gradient-based learning, we design gradient-free residual blocks in our DeepAFL with analytical solutions. We introduce an efficient layer-wise protocol for training our deep analytic models layer by layer in FL through least squares. Both theoretical analyses and empirical evaluations validate our DeepAFL's superior performance with its dual advantages in heterogeneity invariance and representation learning, outperforming state-of-the-art baselines by up to 5.68%-8.42% across three benchmark datasets.