Information-theoretic federated learning for privacy-aware causal representation in object classification

Abstract Object classification in decentralized environments is critically hindered by data heterogeneity and privacy constraints, which cause models to learn spurious, client-specific correlations rather than generalizable, causal features. While federated learning (FL) offers a privacy-preserving training framework, standard algorithms like FedAvg lack the mechanisms to distinguish invariant causal patterns from local biases, leading to poor out-of-distribution (OOD) generalization. To bridge this gap, we propose Fed-CAFF (Federated Causal-Aware Feature Fusion), a novel framework that unifies causal representation learning and privacy-aware federated optimization within an information-theoretic objective. Our method explicitly learns a feature representation Z that maximizes mutual information with the target Y while minimizing information about client identity C given Y (i.e., max I (Y; Z) – βI (Z; C|Y)). We operationalize this objective via a server-mediated gradient anchoring mechanism that aligns client updates toward a global, causally invariant direction, effectively suppressing spurious local correlations. Furthermore, Fed-CAFF integrates differential privacy directly into the learning process, ensuring formal (ε,δ)-DP guarantees without compromising the causal objective. Extensive experiments on medical imaging (LIDC-IDRI, BraTS, INbreast) and computer vision (CIFAR-10, Caltech-101) datasets demonstrate that Fed-CAFF consistently outperforms 14 state-of-the-art methods, including recent causal (FedPIN, FedCaus), personalized (FedCPD, FedMEM), and privacy-preserving approaches, achieving gains of + 3.8 − 10.4% in global accuracy, 45% fewer critical failures in OOD settings, and 24% faster convergence while maintaining strong privacy-utility trade-offs (≤ 4% utility loss at ε < 2.0). Our work establishes that principled, information-theoretic FL can simultaneously achieve robust causal generalization, rigorous privacy, and scalable performance.