SpecGate: Spectral Decomposition and LOF-Gated Aggregation for Defending Against Backdoor Attacks in Federated Learning

Federated Learning (FL) enables collaborative model training without exposing raw data; however, untrusted client updates make the system vulnerable to backdoor attacks, which inject persistent malicious behaviors while maintaining high benign accuracy. Many existing defenses are difficult to deploy in practice. Some require clean validation data or extra verification, while others rely on aggressive noise injection or strict clipping, which may reduce model utility and destabilize training, especially in Non-IID and cross-device FL settings. Meanwhile, many clustering-based defenses rely on cluster-level hard filtering, such as retaining the dominant cluster while removing or strongly down-weighting clients outside it. Such group-level decisions may mishandle borderline or minority benign clients under data heterogeneity or adaptive attacks. To address these issues, we propose SpecGate, a robust aggregation framework that models client updates through spectral decomposition. It further introduces a coordinate-wise energy difference and produces a three-dimensional feature vector consisting of residual strength, low-rank projection consistency, and parameter energy-distribution distance. We then use robust standardization and Local Outlier Factor (LOF) to generate outlier scores that reflect local neighborhood structure, and map them through temperature scaling into continuous soft weights for soft suppression rather than strict exclusion. Experiments on MNIST and CIFAR-10 under IID, Non-IID, and cross-device settings demonstrate that SpecGate consistently reduces attack success rates while maintaining strong main-task accuracy and robustness.