# Step-Ahead Error Feedback for Distributed Training with Compressed Gradient

arXiv: https://arxiv.org/abs/2008.05823 · HTML: https://mlsanity.com/paper/2008.05823/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 9 of 9)

- [Closing the Generalization Gap of Cross-silo Federated Medical Image Segmentation](https://mlsanity.com/paper/2203.10144/) (2022)
- [Lower Bounds and Nearly Optimal Algorithms in Distributed Learning with Communication Compression](https://mlsanity.com/paper/2206.03665/) (2022)
- [Optimus-CC: Efficient Large NLP Model Training with 3D Parallelism Aware Communication Compression](https://mlsanity.com/paper/2301.09830/) (2023)
- [Coordinating Momenta for Cross-silo Federated Learning](https://mlsanity.com/paper/2102.03970/) (2021)
- [E-3SFC: Communication-Efficient Federated Learning with Double-way Features Synthesizing](https://mlsanity.com/paper/2502.03092/) (2025)
- [Communication-Efficient Distributed Learning with Local Immediate Error Compensation](https://mlsanity.com/paper/2402.11857/) (2024)
- [On the Convergence of Federated Learning Algorithms without Data Similarity](https://mlsanity.com/paper/2403.02347/) (2024)
- [Contractive error feedback for gradient compression](https://mlsanity.com/paper/2312.08538/) (2023)
- [SA-PEF: Step-Ahead Partial Error Feedback for Efficient Federated Learning](https://mlsanity.com/paper/2601.20738/) (2026)

## Abstract (arXiv)

Although the distributed machine learning methods can speed up the training of large deep neural networks, the communication cost has become the non-negligible bottleneck to constrain the performance. To address this challenge, the gradient compression based communication-efficient distributed learning methods were designed to reduce the communication cost, and more recently the local error feedback was incorporated to compensate for the corresponding performance loss. However, in this paper, we will show that a new "gradient mismatch" problem is raised by the local error feedback in centralized distributed training and can lead to degraded performance compared with full-precision training. To solve this critical problem, we propose two novel techniques, 1) step ahead and 2) error averaging, with rigorous theoretical analysis. Both our theoretical and empirical results show that our new methods can handle the "gradient mismatch" problem. The experimental results show that we can even train faster with common gradient compression schemes than both the full-precision training and local error feedback regarding the training epochs and without performance loss.