SNR-Guided Model Sizing for Differentially Private Federated Learning with LiRA Privacy Auditing

Abstract

Federated Learning (FL) enables distributed training while keeping data local, but exchanged model updates can leak information through membership inference attacks. Differential privacy mitigates this risk via noise injection; however, aggressive DP regimes with strong noise can destabilize large models. An SNR-guided framework is introduced to select model dimensionality based on the signal-to-noise ratio imposed by the privacy budget. Three optimizers, DP-FedAvg, DP-FedAvgM, and DP-FedAdam, are evaluated across six domains, including image, clinical, IoT, and network security tasks. Privacy leakage is assessed using both loss-based membership inference and the likelihood-ratio attack LiRA. DP-FedAvgM achieves 98.10% accuracy on MNIST at ε =200 with LiRA AUC near random guessing (0.491). SNR-guided models reduce communication cost by up to 66×. Sensitivity calibration experiments further show that incorrect noise allocation can reduce accuracy by up to 1.36 percentage points. These results highlight the importance of model sizing and noise calibration for reliable privacy-preserving FL under strong DP constraints.