# Federated Deep Equilibrium Learning: Harnessing Compact Global Representations to Enhance Personalization

arXiv: https://arxiv.org/abs/2309.15659 · HTML: https://mlsanity.com/paper/2309.15659/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 55 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 30 of 34)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Distributed Mean Estimation with Limited Communication](https://mlsanity.com/paper/1611.00429/) (2016)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [FedMix: Approximation of Mixup under Mean Augmented Federated Learning](https://mlsanity.com/paper/2107.00233/) (2021)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Federated Reconstruction: Partially Local Federated Learning](https://mlsanity.com/paper/2102.03448/) (2021)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Personalized Federated Learning through Local Memorization](https://mlsanity.com/paper/2111.09360/) (2021)
- [FedAvg with Fine Tuning: Local Updates Lead to Representation Learning](https://mlsanity.com/paper/2205.13692/) (2022)
- [On the Theory of Implicit Deep Learning: Global Convergence with Implicit Layers](https://mlsanity.com/paper/2102.07346/) (2021)

## Abstract (arXiv)

Federated Learning (FL) has emerged as a groundbreaking distributed learning paradigm enabling clients to train a global model collaboratively without exchanging data. Despite enhancing privacy and efficiency in information retrieval and knowledge management contexts, training and deploying FL models confront significant challenges such as communication bottlenecks, data heterogeneity, and memory limitations. To comprehensively address these challenges, we introduce FeDEQ, a novel FL framework that incorporates deep equilibrium learning and consensus optimization to harness compact global data representations for efficient personalization. Specifically, we design a unique model structure featuring an equilibrium layer for global representation extraction, followed by explicit layers tailored for local personalization. We then propose a novel FL algorithm rooted in the alternating directions method of multipliers (ADMM), which enables the joint optimization of a shared equilibrium layer and individual personalized layers across distributed datasets. Our theoretical analysis confirms that FeDEQ converges to a stationary point, achieving both compact global representations and optimal personalized parameters for each client. Extensive experiments on various benchmarks demonstrate that FeDEQ matches the performance of state-of-the-art personalized FL methods, while significantly reducing communication size by up to 4 times and memory footprint by 1.5 times during training.