Fed-Equilibrium Framework for Topological Pareto Control in Robust and Fair Clinical Federated Learning

The deployment of Federated Learning (FL) in multi-center clinical networks faces the challenge of "knowledge dominance," where high-volume hubs naturally overwhelm minority community nodes, implicitly treating the distinct clinical patterns of smaller cohorts as outliers. Existing geometric defenses provide a security baseline but leave this efficiency-fairness dilemma unresolved. To bridge this gap, we propose Fed-Equilibrium, a framework that advances the paradigm from simple defense to topological equilibrium. Unlike traditional aggregators, Fed-Equilibrium implements a sequential architectural synergy. It utilizes a two-stage gradient control cascade: Stage I (geometric quality assurance) enforces directional consistency via a cosine similarity funnel to filter malicious noise, creating a stabilized manifold; Stage II (topological Pareto control) then actively modulates verified contributions by identifying the optimal Pareto knee point. We validated this framework on a bi-national simulation integrating Canadian (CNODES) and U.S. (SyntheticMass) registries. Experimental results demonstrate that the system simultaneously secures the network against adversarial divergence while accommodating underrepresented signals. Notably, the minority U.S. spoke (representing less than 3% of data volume) achieved deep convergence comparable to the data-rich Canadian hub. This confirms that Fed-Equilibrium effectively counters "knowledge dominance," establishing a true "knowledge commons" where global generalizability does not come at the cost of local clinical representation.