# Communication-efficient Vertical Federated Learning via Compressed Error Feedback

arXiv: https://arxiv.org/abs/2406.14420 · HTML: https://mlsanity.com/paper/2406.14420/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 20 Jun 2024.

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

- [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)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [Asynchronous Federated Optimization](https://mlsanity.com/paper/1903.03934/) (2019)
- [The Convergence of Sparsified Gradient Methods](https://mlsanity.com/paper/1809.10505/) (2018)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [Federated Learning with Compression: Unified Analysis and Sharp Guarantees](https://mlsanity.com/paper/2007.01154/) (2020)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [On Biased Compression for Distributed Learning](https://mlsanity.com/paper/2002.12410/) (2020)
- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [Distributed Learning with Compressed Gradient Differences](https://mlsanity.com/paper/1901.09269/) (2019)
- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Scaling Distributed Machine Learning with In-Network Aggregation](https://mlsanity.com/paper/1903.06701/) (2019)
- [SplitNN-driven Vertical Partitioning](https://mlsanity.com/paper/2008.04137/) (2020)
- [BEER: Fast O(1/T) Rate for Decentralized Nonconvex Optimization with Communication Compression](https://mlsanity.com/paper/2201.13320/) (2022)
- [Compressed-VFL: Communication-Efficient Learning with Vertically Partitioned Data](https://mlsanity.com/paper/2206.08330/) (2022)
- [SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression](https://mlsanity.com/paper/2206.09888/) (2022)
- [High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning](https://mlsanity.com/paper/1910.03865/) (2019)
- [A Survey on Vertical Federated Learning: From a Layered Perspective](https://mlsanity.com/paper/2304.01829/) (2023)
- [Flexible Vertical Federated Learning with Heterogeneous Parties](https://mlsanity.com/paper/2208.12672/) (2022)
- [Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression](https://mlsanity.com/paper/2305.09896/) (2023)
- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [Supervised Learning Under Distributed Features](https://mlsanity.com/paper/1805.11384/) (2018)
- [A Multi-Token Coordinate Descent Method for Semi-Decentralized Vertical Federated Learning](https://mlsanity.com/paper/2309.09977/) (2023)

## Built on by (most cited first, 3 of 3)

- [Vertical Federated Learning with Missing Features During Training and Inference](https://mlsanity.com/paper/2410.22564/) (2024)
- [Vertical Federated Learning in Practice: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2502.08160/) (2025)
- [FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Data](https://mlsanity.com/paper/2504.11903/) (2025)

## Abstract (arXiv)

Communication overhead is a known bottleneck in federated learning (FL). To address this, lossy compression is commonly used on the information communicated between the server and clients during training. In horizontal FL, where each client holds a subset of the samples, such communication-compressed training methods have recently seen significant progress. However, in their vertical FL counterparts, where each client holds a subset of the features, our understanding remains limited. To address this, we propose an error feedback compressed vertical federated learning (EF-VFL) method to train split neural networks. In contrast to previous communication-compressed methods for vertical FL, EF-VFL does not require a vanishing compression error for the gradient norm to converge to zero for smooth nonconvex problems. By leveraging error feedback, our method can achieve a O(1/T) convergence rate for a sufficiently large batch size, improving over the state-of-the-art O(1/√T) rate under O(1/√T) compression error, and matching the rate of uncompressed methods. Further, when the objective function satisfies the Polyak-Lojasiewicz inequality, our method converges linearly. In addition to improving convergence, our method also supports the use of private labels. Numerical experiments show that EF-VFL significantly improves over the prior art, confirming our theoretical results. The code for this work can be found at https://github.com/Valdeira/EF-VFL.