Interpretable Client Contribution Evaluation in Federated Learning via Partial Information Decomposition

In federated learning (FL), multiple clients collaboratively train a shared model without sharing their raw data. Understanding how much each client contributes to the global model is central to fair incentive design, principled client selection, and the detection of unreliable or harmful participants. Yet client contribution is typically summarised by a single scalar utility, which conflates fundamentally different sources of value: information that is unique to a client, information that is duplicated elsewhere in the federation, and information that emerges only when several clients are combined. We propose FedPID, an information-theoretic framework for client contribution evaluation based on Partial Information Decomposition (PID), characterising each client's value in terms of these three components rather than a single number. FedPID builds class-conditioned PIDs for each client from predictions on a shared server-side validation set, producing round-wise profiles of unique, redundant, and synergistic information that can be inspected directly as a diagnostic, used to compare clients, or converted into contribution-guided aggregation weights. Across heterogeneous client settings on CIFAR-10, Fed-ISIC, and ImageNet-100, FedPID recovers expected contribution orderings from first-round profiles, identifies specialist clients that other scalar methods undervalue, and separates useful clients from noisy ones. As one downstream use, PID-derived aggregation weights improve performance in noisy-client settings compared with baselines. FedPID thus reframes client contribution as an informational composition rather than a single opaque score, providing both an interpretable diagnostic and a control signal for aggregation.