Neighbor Averaging as Perturbation: Risk-Aware Decentralized Federated Learning via Noise-Probed Sensitivity

Decentralized federated learning (DFL) enables collaborative training by repeatedly exchanging and averaging locally updated models. Under heterogeneous data, however, an update beneficial to its local client may not benefit a receiving neighbor when averaged. Existing topology-driven or learning-adaptive schemes regulate collaboration structure or influence, while the state-dependent effect of a specific averaging operation on the receiving model remains insufficiently characterized. We introduce a perturbation view of neighbor averaging, treating each candidate average as a finite parameter perturbation along the neighbor-model difference. We derive a local output-drift bound showing that the resulting effect depends jointly on the receiving model's sensitivity and the induced displacement. Motivated by this bound, we propose NoRA (Noise-Probed Risk-Aware Averaging) and the NPAR score, which combines noise-probed sensitivity with pairwise model displacement to estimate averaging risk. NoRA attenuates high-risk interactions with only one additional scalar per client beyond standard model exchange. NoRA preserves symmetric doubly stochastic mixing under state-dependent, time-varying weights and retains the standard $\mathcal{O}(1/\sqrt{KT})$ leading convergence rate under finite-window spectral contraction. Experiments across diverse datasets, heterogeneity settings, and network topologies validate its effectiveness. On CIFAR-10 with Dirichlet $\alpha =0.3$, NoRA improves mean global test accuracy by 1.7% over the strongest baseline and reaches the target accuracy with 29.3% fewer communication rounds than the fastest competing method.