Learning from Disagreement: Conflict-Compiled Routing Networks for Heterogeneous Federated Learning

Federated learning usually treats disagreement between client updates as optimization noise to average, shrink, or project away. We ask whether structured disagreement can instead supervise where model capacity should be allocated. We introduce FedCRN, a conflict-compiled routing network that converts consensus-centered update directions into addresses for low-rank residual experts inside one shared model. Each expert is aggregated only within its conflict group. To extend these compiled addresses beyond client identity, a detached router learns per-example relative expert competence. This supports address-free unseen-client routing, while a confidence gate attenuates uncertain residuals and exactly recovers the consensus predictor under uniform routing. Our analysis shows how routing overlap changes cross-client interference, gives a separation condition for persistent compiler addresses, and derives a nonconvex bound governed by post-routing heterogeneity; it explains the mechanism rather than asserting universal superiority. Across five image federations, five paired seeds, and 12 methods, FedCRN attains the best mean rank and leads accuracy on two benchmarks. On 50-client CIFAR-100, it improves over a parameter-matched raw-update ClusterMoE by 0.24 points; after transferring clean-selected hyperparameters to CIFAR-100-C without retuning, it retains the best mean but the 0.20-point gap is not significant. Multi-mode clients, address-free inference, paired tests, and compiler/routing ablations probe the claimed round-to-sample routing path. These results support a different view of heterogeneity: incompatible updates can supervise conditional capacity allocation.