# Magnitude Matters: Fixing SIGNSGD Through Magnitude-Aware Sparsification in the Presence of Data Heterogeneity

arXiv: https://arxiv.org/abs/2302.09634 · HTML: https://mlsanity.com/paper/2302.09634/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 46 references that are in the map.
- First posted on arXiv 19 Feb 2023.

## Builds on (most cited first, 30 of 36)

- [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)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [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)
- [TernGrad: Ternary Gradients to Reduce Communication in Distributed Deep Learning](https://mlsanity.com/paper/1705.07878/) (2017)
- [The Convergence of Sparsified Gradient Methods](https://mlsanity.com/paper/1809.10505/) (2018)
- [Gradient Sparsification for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1710.09854/) (2017)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [FetchSGD: Communication-Efficient Federated Learning with Sketching](https://mlsanity.com/paper/2007.07682/) (2020)
- [Federated Learning with Compression: Unified Analysis and Sharp Guarantees](https://mlsanity.com/paper/2007.01154/) (2020)
- [Revisiting Distributed Synchronous SGD](https://mlsanity.com/paper/1702.05800/) (2017)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [ATOMO: Communication-efficient Learning via Atomic Sparsification](https://mlsanity.com/paper/1806.04090/) (2018)
- [Enabling Spike-based Backpropagation for Training Deep Neural Network Architectures](https://mlsanity.com/paper/1903.06379/) (2019)
- [Distributed Learning with Compressed Gradient Differences](https://mlsanity.com/paper/1901.09269/) (2019)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [DoubleSqueeze: Parallel Stochastic Gradient Descent with Double-Pass Error-Compensated Compression](https://mlsanity.com/paper/1905.05957/) (2019)
- [Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization](https://mlsanity.com/paper/2002.11364/) (2020)
- [Error Compensated Quantized SGD and its Applications to Large-scale Distributed Optimization](https://mlsanity.com/paper/1806.08054/) (2018)
- [Understanding Clipping for Federated Learning: Convergence and Client-Level Differential Privacy](https://mlsanity.com/paper/2106.13673/) (2021)
- [Stochastic Distributed Learning with Gradient Quantization and Variance Reduction](https://mlsanity.com/paper/1904.05115/) (2019)
- [Sparse Binary Compression: Towards Distributed Deep Learning with minimal Communication](https://mlsanity.com/paper/1805.08768/) (2018)
- [Communication-Efficient Distributed Blockwise Momentum SGD with Error-Feedback](https://mlsanity.com/paper/1905.10936/) (2019)
- [Stochastic Sign Descent Methods: New Algorithms and Better Theory](https://mlsanity.com/paper/1905.12938/) (2019)
- [Bidirectional compression in heterogeneous settings for distributed or federated learning with partial participation: tight convergence guarantees](https://mlsanity.com/paper/2006.14591/) (2020)

## Built on by (most cited first, 2 of 2)

- [Convergence of Sign-based Random Reshuffling Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/2310.15976/) (2023)
- [Collaborative Compressors in Distributed Mean Estimation with Limited Communication Budget](https://mlsanity.com/paper/2601.18950/) (2026)

## Abstract (arXiv)

Communication overhead has become one of the major bottlenecks in the distributed training of deep neural networks. To alleviate the concern, various gradient compression methods have been proposed, and sign-based algorithms are of surging interest. However, SIGNSGD fails to converge in the presence of data heterogeneity, which is commonly observed in the emerging federated learning (FL) paradigm. Error feedback has been proposed to address the non-convergence issue. Nonetheless, it requires the workers to locally keep track of the compression errors, which renders it not suitable for FL since the workers may not participate in the training throughout the learning process. In this paper, we propose a magnitude-driven sparsification scheme, which addresses the non-convergence issue of SIGNSGD while further improving communication efficiency. Moreover, the local update scheme is further incorporated to improve the learning performance, and the convergence of the proposed method is established. The effectiveness of the proposed scheme is validated through experiments on Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets.