Semantic-Constrained Federated Aggregation: Convergence Theory and Privacy-Utility Bounds for Knowledge-Enhanced Distributed Learning
Jahidul Arafat
TL;DR
SCFA introduces a principled way to incorporate domain constraints into federated learning by validating client updates against knowledge-graph encoded rules and weighting aggregation by semantic validity. The authors prove a convergence rate of $O(1/\sqrt{T} + \rho)$, derive privacy-utility bounds via hypothesis-space reduction with $\theta \approx 0.37$, and establish a linear constraint-violation impact with a critical threshold $\rho_{\text{crit}} = 0.18$. Empirical validation on a large Bosch manufacturing dataset demonstrates 22% faster convergence, 41.3% reduction in model divergence, and a 2.7× improvement in privacy-utility at $\varepsilon=10$, with results aligning closely to theory ($R^2$ around 0.93–0.94). The work shows that domain knowledge can meaningfully regularize distributed learning, enabling faster, safer, and more private collaborative modeling across industrial settings and beyond.
Abstract
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.