# Byzantine-Tolerant Machine Learning

arXiv: https://arxiv.org/abs/1703.02757 · HTML: https://mlsanity.com/paper/1703.02757/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2017.

## Built on by (most cited first, 19 of 19)

- [OmniLytics: A Blockchain-based Secure Data Market for Decentralized Machine Learning](https://mlsanity.com/paper/2107.05252/) (2021)
- [Linear Speedup in Personalized Collaborative Learning](https://mlsanity.com/paper/2111.05968/) (2021)
- [Byzantine-Robust Aggregation for Securing Decentralized Federated Learning](https://mlsanity.com/paper/2409.17754/) (2024)
- [SafeNet: The Unreasonable Effectiveness of Ensembles in Private Collaborative Learning](https://mlsanity.com/paper/2205.09986/) (2022)
- [LEGATO: A LayerwisE Gradient AggregaTiOn Algorithm for Mitigating Byzantine Attacks in Federated Learning](https://mlsanity.com/paper/2107.12490/) (2021)
- [Escaping Saddle Points in Distributed Newton's Method with Communication Efficiency and Byzantine Resilience](https://mlsanity.com/paper/2103.09424/) (2021)
- [Data Poisoning Vulnerabilities Across Healthcare AI Architectures: A Security Threat Analysis](https://mlsanity.com/paper/2511.11020/) (2025)
- [On the Security and Privacy of Federated Learning: A Survey with Attacks, Defenses, Frameworks, Applications, and Future Directions](https://mlsanity.com/paper/2508.13730/) (2025)
- [DSFL: A Dual-Server Byzantine-Resilient Federated Learning Framework via Group-Based Secure Aggregation](https://mlsanity.com/paper/2509.08449/) (2025)
- [Collaborative Learning of Discrete Distributions under Heterogeneity and Communication Constraints](https://mlsanity.com/paper/2206.00707/) (2022)
- [FedBChain: A Blockchain-enabled Federated Learning Framework for Improving DeepConvLSTM with Comparative Strategy Insights](https://mlsanity.com/paper/2407.21282/) (2024)
- [Robust Bayesian Optimisation with Unbounded Corruptions](https://mlsanity.com/paper/2511.15315/) (2025)
- [Byzantine-Robust Clustered Federated Learning](https://mlsanity.com/paper/2306.00638/) (2023)
- [DISBELIEVE: Distance Between Client Models is Very Essential for Effective Local Model Poisoning Attacks](https://mlsanity.com/paper/2308.07387/) (2023)
- [FL-CLEANER: byzantine and backdoor defense by CLustering Errors of Activation maps in Non-iid fedErated leaRning](https://mlsanity.com/paper/2501.12123/) (2025)
- [CO-DEFEND: Continuous Decentralized Federated Learning for Secure DoH-Based Threat Detection](https://mlsanity.com/paper/2504.01882/) (2025)
- [GRANITE : a Byzantine-Resilient Dynamic Gossip Learning Framework](https://mlsanity.com/paper/2504.17471/) (2025)
- [FedDetox: Robust Federated SLM Alignment via On-Device Data Sanitization](https://mlsanity.com/paper/2604.06833/) (2026)
- [Byzantine-Resilient Federated Large Language Model via Hypergraph Message Passing](https://mlsanity.com/paper/2610.12711/) (2026)

## Abstract (arXiv)

The growth of data, the need for scalability and the complexity of models used in modern machine learning calls for distributed implementations. Yet, as of today, distributed machine learning frameworks have largely ignored the possibility of arbitrary (i.e., Byzantine) failures. In this paper, we study the robustness to Byzantine failures at the fundamental level of stochastic gradient descent (SGD), the heart of most machine learning algorithms. Assuming a set of n workers, up to f of them being Byzantine, we ask how robust can SGD be, without limiting the dimension, nor the size of the parameter space. We first show that no gradient descent update rule based on a linear combination of the vectors proposed by the workers (i.e, current approaches) tolerates a single Byzantine failure. We then formulate a resilience property of the update rule capturing the basic requirements to guarantee convergence despite f Byzantine workers. We finally propose Krum, an update rule that satisfies the resilience property aforementioned. For a d-dimensional learning problem, the time complexity of Krum is O(n2 · (d + log n)).