# Enhanced Byzantine-Robust Federated Learning Via Truncated-Quadratic Loss for Heterogeneous Data

arXiv: https://arxiv.org/abs/2607.10970 · HTML: https://mlsanity.com/paper/2607.10970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [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)
- [RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets](https://mlsanity.com/paper/1811.03761/) (2018)
- [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)
- [Byzantine-Resilient Secure Federated Learning](https://mlsanity.com/paper/2007.11115/) (2020)
- [Federated Variance-Reduced Stochastic Gradient Descent with Robustness to Byzantine Attacks](https://mlsanity.com/paper/1912.12716/) (2019)
- [FedBiOT: LLM Local Fine-tuning in Federated Learning without Full Model](https://mlsanity.com/paper/2406.17706/) (2024)
- [Fixing by Mixing: A Recipe for Optimal Byzantine ML under Heterogeneity](https://mlsanity.com/paper/2302.01772/) (2023)
- [Byzantine Machine Learning Made Easy by Resilient Averaging of Momentums](https://mlsanity.com/paper/2205.12173/) (2022)
- [Byzantine-Resilient Non-Convex Stochastic Gradient Descent](https://mlsanity.com/paper/2012.14368/) (2020)
- [DETOX: A Redundancy-based Framework for Faster and More Robust Gradient Aggregation](https://mlsanity.com/paper/1907.12205/) (2019)
- [A Huber Loss Minimization Approach to Byzantine Robust Federated Learning](https://mlsanity.com/paper/2308.12581/) (2023)
- [Data Encoding for Byzantine-Resilient Distributed Optimization](https://mlsanity.com/paper/1907.02664/) (2019)
- [Byzantine-Robust Distributed Online Learning: Taming Adversarial Participants in An Adversarial Environment](https://mlsanity.com/paper/2307.07980/) (2023)
- [BOBA: Byzantine-Robust Federated Learning with Label Skewness](https://mlsanity.com/paper/2208.12932/) (2022)
- [Mean Aggregator is More Robust than Robust Aggregators under Label Poisoning Attacks on Distributed Heterogeneous Data](https://mlsanity.com/paper/2404.13647/) (2024)
- [Near-Optimal Resilient Aggregation Rules for Distributed Learning Using 1-Center and 1-Mean Clustering with Outliers](https://mlsanity.com/paper/2312.12835/) (2023)
- [Federated Learning Resilient to Byzantine Attacks and Data Heterogeneity](https://mlsanity.com/paper/2403.13374/) (2024)
- [Rethinking Byzantine Robustness in Federated Recommendation from Sparse Aggregation Perspective](https://mlsanity.com/paper/2501.03301/) (2025)
- [Byzantine-Robust Loopless Stochastic Variance-Reduced Gradient](https://mlsanity.com/paper/2303.04560/) (2023)
- [Fault Tolerant ML: Efficient Meta-Aggregation and Synchronous Training](https://mlsanity.com/paper/2405.14759/) (2024)

## Abstract (arXiv)

Federated learning distributes data among n clients, making it vulnerable to malicious attacks and data heterogeneity, which together pose challenges for robust learning. To tackle this issue, centered clipping and Huber aggregators have been exploited for Byzantine robustness. In this paper, we first demonstrate their equivalence via convex conjugate theory, and show that they can yield biased solutions in the presence of outliers, leading to failure under high data heterogeneity and a substantial fraction of outliers. Next, we propose a new robust aggregation rule that utilizes the truncated-quadratic (TQ) loss, effectively mitigating the biases of existing methods, such as centered clipping and Huber aggregators. We show that our aggregator achieves order-optimal Byzantine-robust learning under nonconvex loss functions and heterogeneous data, ultimately enhancing the reliability of federated learning systems. Additionally, we provide a robust deviation estimation strategy for TQ, demonstrating its effectiveness. Furthermore, we show that TQ maintains robustness even when only an estimate of the number of Byzantine clients is available. Finally, experimental results on MNIST, Fashion-MNIST, and CIFAR-10, indicate that our aggregator provides better robustness performance than the competing techniques.