Formal Logic Inference Guided Uncertainty Quantification for Personalized Federated Learning

Abstract

Federated Learning (FL) enables privacy-preserving model training across heterogeneous distributed systems, such as smartgrid forecasting or traffic-flow prediction from geographically dispersed sensors and devices. A key challenge in such settings is capturing client-specific patterns while addressing data heterogeneity and uncertainty at scale. Existing approaches, including Bayesian Neural Networks (BNNs) and clustering-based methods, struggle with scalability and consistent personalization. We propose LogiCP, a novel FL framework that integrates formal logic reasoning with uncertainty quantification (UQ) to support scalable and personalized learning with theoretical guarantees. LogiCP uses Signal Temporal Logic (STL) to extract temporal patterns and form semantically coherent client clusters, controlling intra-cluster heterogeneity. Within each cluster, LogiCP applies decentralized Conformal Prediction (CP) to produce distribution-free prediction intervals with mathematical guarantees that encompass the real value. LogiCP dynamically assigns clients to clusters at runtime without retraining, improving practicality. Evaluations on three real-world datasets—traffic, temperature, and electricity—show that LogiCP consistently outperforms BNN-, clustering-, and CP-based baselines, achieving up to a 95% improvement in client-level MSE while maintaining strong scalability.