Semantic-Constrained Federated Aggregation: Convergence Theory and Privacy-Utility Bounds for Knowledge-Enhanced Distributed Learning

Federated learning enables collaborative model training across distributed data sources but suffers from slow convergence under non-IID data conditions. Existing solutions employ algorithmic modifications treating all client updates identically, ignoring semantic validity. We introduce Semantic-Constrained Federated Aggregation (SCFA), a theoretically-grounded framework incorporating domain knowledge constraints into distributed optimization. We prove SCFA achieves convergence rate O(1/sqrt(T) + rho) where rho represents constraint violation rate, establishing the first convergence theory for constraint-based federated learning. Our analysis shows constraints reduce effective data heterogeneity by 41% and improve privacy-utility tradeoffs through hypothesis space reduction by factor theta=0.37. Under (epsilon,delta)-differential privacy with epsilon=10, constraint regularization maintains utility within 3.7% of non-private baseline versus 12.1% degradation for standard federated learning, representing 2.7x improvement. We validate our framework on manufacturing predictive maintenance using Bosch production data with 1.18 million samples and 968 sensor features, constructing knowledge graphs encoding 3,000 constraints from ISA-95 and MASON ontologies. Experiments demonstrate 22% faster convergence, 41.3% model divergence reduction, and constraint violation thresholds where rho<0.05 maintains 90% optimal performance while rho>0.18 causes catastrophic failure. Our theoretical predictions match empirical observations with R^2>0.90 across convergence, privacy, and violation-performance relationships.