# Phocas: dimensional Byzantine-resilient stochastic gradient descent

arXiv: https://arxiv.org/abs/1805.09682 · HTML: https://mlsanity.com/paper/1805.09682/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 13 of 13)

- [Differential Privacy and Byzantine Resilience in SGD: Do They Add Up?](https://mlsanity.com/paper/2102.08166/) (2021)
- [Backdoor Attacks in Peer-to-Peer Federated Learning](https://mlsanity.com/paper/2301.09732/) (2023)
- [Byzantine-Robust Distributed Online Learning: Taming Adversarial Participants in An Adversarial Environment](https://mlsanity.com/paper/2307.07980/) (2023)
- [Byzantine Fault-Tolerance in Federated Local SGD under 2f-Redundancy](https://mlsanity.com/paper/2108.11769/) (2021)
- [zPROBE: Zero Peek Robustness Checks for Federated Learning](https://mlsanity.com/paper/2206.12100/) (2022)
- [Combining Differential Privacy and Byzantine Resilience in Distributed SGD](https://mlsanity.com/paper/2110.03991/) (2021)
- [Privacy-Preserving Aggregation for Decentralized Learning with Byzantine-Robustness](https://mlsanity.com/paper/2404.17970/) (2024)
- [Stochastic Alternating Direction Method of Multipliers for Byzantine-Robust Distributed Learning](https://mlsanity.com/paper/2106.06891/) (2021)
- [Find a Scapegoat: Poisoning Membership Inference Attack and Defense to Federated Learning](https://mlsanity.com/paper/2507.00423/) (2025)
- [A Robust Classification Framework for Byzantine-Resilient Stochastic Gradient Descent](https://mlsanity.com/paper/2301.07498/) (2023)
- [Flag Aggregator: Scalable Distributed Training under Failures and Augmented Losses using Convex Optimization](https://mlsanity.com/paper/2302.05865/) (2023)
- [Coded Robust Aggregation for Distributed Learning under Byzantine Attacks](https://mlsanity.com/paper/2506.01989/) (2025)
- [Byzantine-Robust and Communication-Efficient Distributed Training: Compressive and Cyclic Gradient Coding](https://mlsanity.com/paper/2603.28780/) (2026)

## Abstract (arXiv)

We propose a novel robust aggregation rule for distributed synchronous Stochastic Gradient Descent~(SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server~(PS) architecture. We prove the Byzantine resilience of the proposed aggregation rules. Empirical analysis shows that the proposed techniques outperform current approaches for realistic use cases and Byzantine attack scenarios.