# Intrinisic Gradient Compression for Federated Learning

arXiv: https://arxiv.org/abs/2112.02656 · HTML: https://mlsanity.com/paper/2112.02656/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 30 of 32)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Personalizing Dialogue Agents: I have a dog, do you have pets too?](https://mlsanity.com/paper/1801.07243/) (2018)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [Analyzing Federated Learning through an Adversarial Lens](https://mlsanity.com/paper/1811.12470/) (2018)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [FedML: A Research Library and Benchmark for Federated Machine Learning](https://mlsanity.com/paper/2007.13518/) (2020)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [FetchSGD: Communication-Efficient Federated Learning with Sketching](https://mlsanity.com/paper/2007.07682/) (2020)
- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization](https://mlsanity.com/paper/2002.11364/) (2020)
- [On the Intrinsic Dimensionality of Image Representations](https://mlsanity.com/paper/1803.09672/) (2018)
- [Understanding Top-k Sparsification in Distributed Deep Learning](https://mlsanity.com/paper/1911.08772/) (2019)
- [Federated Learning with Only Positive Labels](https://mlsanity.com/paper/2004.10342/) (2020)
- [Optimal Gradient Compression for Distributed and Federated Learning](https://mlsanity.com/paper/2010.03246/) (2020)

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

- [Federated Full-Parameter Tuning of Billion-Sized Language Models with Communication Cost under 18 Kilobytes](https://mlsanity.com/paper/2312.06353/) (2023)
- [Equitable Federated Learning with NCA](https://mlsanity.com/paper/2506.21735/) (2025)

## Abstract (arXiv)

Federated learning is a rapidly-growing area of research which enables a large number of clients to jointly train a machine learning model on privately-held data. One of the largest barriers to wider adoption of federated learning is the communication cost of sending model updates from and to the clients, which is accentuated by the fact that many of these devices are bandwidth-constrained. In this paper, we aim to address this issue by optimizing networks within a subspace of their full parameter space, an idea known as intrinsic dimension in the machine learning theory community. We use a correspondence between the notion of intrinsic dimension and gradient compressibility to derive a family of low-bandwidth optimization algorithms, which we call intrinsic gradient compression algorithms. Specifically, we present three algorithms in this family with different levels of upload and download bandwidth for use in various federated settings, along with theoretical guarantees on their performance. Finally, in large-scale federated learning experiments with models containing up to 100M parameters, we show that our algorithms perform extremely well compared to current state-of-the-art gradient compression methods.