# SpectralKrum: A Spectral-Geometric Defense Against Byzantine Attacks in Federated Learning

arXiv: https://arxiv.org/abs/2512.11760 · HTML: https://mlsanity.com/paper/2512.11760/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [The Future of Digital Health with Federated Learning](https://mlsanity.com/paper/2003.08119/) (2020)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [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)
- [Can You Really Backdoor Federated Learning?](https://mlsanity.com/paper/1911.07963/) (2019)
- [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)

## Abstract (arXiv)

Federated Learning (FL) distributes model training across clients who retain their data locally, but this architecture exposes a fundamental vulnerability: Byzantine clients can inject arbitrarily corrupted updates that degrade or subvert the global model. While robust aggregation methods (including Krum, Bulyan, and coordinate-wise defenses) offer theoretical guarantees under idealized assumptions, their effectiveness erodes substantially when client data distributions are heterogeneous (non-IID) and adversaries can observe or approximate the defense mechanism. This paper introduces SpectralKrum, a defense that fuses spectral subspace estimation with geometric neighbor-based selection. The core insight is that benign optimization trajectories, despite per-client heterogeneity, concentrate near a low-dimensional manifold that can be estimated from historical aggregates. SpectralKrum projects incoming updates into this learned subspace, applies Krum selection in compressed coordinates, and filters candidates whose orthogonal residual energy exceeds a data-driven threshold. The method requires no auxiliary data, operates entirely on model updates, and preserves FL privacy properties. We evaluate SpectralKrum against eight robust baselines across seven attack scenarios on CIFAR-10 with Dirichlet-distributed non-IID partitions (alpha = 0.1). Experiments spanning over 56,000 training rounds show that SpectralKrum is competitive against directional and subspace-aware attacks (adaptive-steer, buffer-drift), but offers limited advantage under label-flip and min-max attacks where malicious updates remain spectrally indistinguishable from benign ones.