# ProDiGy: Proximity- and Dissimilarity-Based Byzantine-Robust Federated Learning

arXiv: https://arxiv.org/abs/2509.09534 · HTML: https://mlsanity.com/paper/2509.09534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [FLTrust: Byzantine-robust Federated Learning via Trust Bootstrapping](https://mlsanity.com/paper/2012.13995/) (2020)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [A Little Is Enough: Circumventing Defenses For Distributed Learning](https://mlsanity.com/paper/1902.06156/) (2019)
- [Mitigating Sybils in Federated Learning Poisoning](https://mlsanity.com/paper/1808.04866/) (2018)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Fall of Empires: Breaking Byzantine-tolerant SGD by Inner Product Manipulation](https://mlsanity.com/paper/1903.03936/) (2019)
- [Learning from History for Byzantine Robust Optimization](https://mlsanity.com/paper/2012.10333/) (2020)
- [Byzantine-Robust Learning on Heterogeneous Datasets via Bucketing](https://mlsanity.com/paper/2006.09365/) (2020)
- [Survey on Federated Learning Threats: concepts, taxonomy on attacks and defences, experimental study and challenges](https://mlsanity.com/paper/2201.08135/) (2022)
- [Fixing by Mixing: A Recipe for Optimal Byzantine ML under Heterogeneity](https://mlsanity.com/paper/2302.01772/) (2023)
- [Distributed Statistical Machine Learning in Adversarial Settings: Byzantine Gradient Descent](https://mlsanity.com/paper/1705.05491/) (2017)
- [Byzantine-Resilient Non-Convex Stochastic Gradient Descent](https://mlsanity.com/paper/2012.14368/) (2020)
- [Challenges and Approaches for Mitigating Byzantine Attacks in Federated Learning](https://mlsanity.com/paper/2112.14468/) (2021)
- [An Experimental Study of Byzantine-Robust Aggregation Schemes in Federated Learning](https://mlsanity.com/paper/2302.07173/) (2023)
- [FedGT: Identification of Malicious Clients in Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2305.05506/) (2023)
- [Adaptive Gradient Clipping for Robust Federated Learning](https://mlsanity.com/paper/2405.14432/) (2024)
- [Byzantine-robust Federated Learning through Spatial-temporal Analysis of Local Model Updates](https://mlsanity.com/paper/2107.01477/) (2021)

## Abstract (arXiv)

Federated Learning (FL) emerged as a widely studied paradigm for distributed learning. Despite its many advantages, FL remains vulnerable to adversarial attacks, especially under data heterogeneity. We propose a new Byzantine-robust FL algorithm called ProDiGy. The key novelty lies in evaluating the client gradients using a joint dual scoring system based on the gradients' proximity and dissimilarity. We demonstrate through extensive numerical experiments that ProDiGy outperforms existing defenses in various scenarios. In particular, when the clients' data do not follow an IID distribution, while other defense mechanisms fail, ProDiGy maintains strong defense capabilities and model accuracy. These findings highlight the effectiveness of a dual perspective approach that promotes natural similarity among honest clients while detecting suspicious uniformity as a potential indicator of an attack.