# Communication-Efficient Federated Low-Rank Update Algorithm and its Connection to Implicit Regularization

arXiv: https://arxiv.org/abs/2409.12371 · HTML: https://mlsanity.com/paper/2409.12371/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 66 references that are in the map.
- First posted on arXiv 19 Sep 2024.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Gradient descent aligns the layers of deep linear networks](https://mlsanity.com/paper/1810.02032/) (2018)
- [Expanding the Reach of Federated Learning by Reducing Client Resource Requirements](https://mlsanity.com/paper/1812.07210/) (2018)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [KronA: Parameter Efficient Tuning with Kronecker Adapter](https://mlsanity.com/paper/2212.10650/) (2022)
- [OpenFedLLM: Training Large Language Models on Decentralized Private Data via Federated Learning](https://mlsanity.com/paper/2402.06954/) (2024)
- [Heterogeneous LoRA for Federated Fine-tuning of On-Device Foundation Models](https://mlsanity.com/paper/2401.06432/) (2024)
- [Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning](https://mlsanity.com/paper/2401.04151/) (2024)
- [Adaptive Quantization of Model Updates for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2102.04487/) (2021)

## Built on by (most cited first, 6 of 6)

- [DeMo: Decoupled Momentum Optimization](https://mlsanity.com/paper/2411.19870/) (2024)
- [On the Convergence Rate of LoRA Gradient Descent](https://mlsanity.com/paper/2512.18248/) (2025)
- [Federated Low-Rank Adaptation for Foundation Models: A Survey](https://mlsanity.com/paper/2505.13502/) (2025)
- [An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2509.05213/) (2025)
- [Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction](https://mlsanity.com/paper/2502.02761/) (2025)
- [Rethinking Factor Sharing in Federated LoRA: A Rank-Aware Adaptive Approach](https://mlsanity.com/paper/2608.09742/) (2026)

## Abstract (arXiv)

Federated Learning (FL) faces significant challenges related to communication efficiency and performance reduction when scaling to many clients. To address these issues, we explore the potential of using low-rank updates and provide the first theoretical study of rank properties in FL. Our theoretical analysis shows that a client's loss exhibits a higher-rank structure (i.e., gradients span higher-rank subspaces of the Hessian) compared to the server's loss, and that low-rank approximations of the clients' gradients have greater similarity. Based on this insight, we hypothesize that constraining client-side optimization to a low-rank subspace could provide an implicit regularization effect while reducing communication costs. Consequently, we propose FedLoRU, a general low-rank update framework for FL. Our framework enforces low-rank client-side updates and accumulates these updates to form a higher-rank model. We are able to establish convergence of the algorithm; the convergence rate matches FedAvg. Additionally, variants of FedLoRU can adapt to environments with statistical and model heterogeneity by employing multiple or hierarchical low-rank updates. Experimental results demonstrate that FedLoRU performs comparably to full-rank algorithms and exhibits robustness to heterogeneous and large numbers of clients.