Interpretability Bounds for Federated Clinical Text Classifiers Under Differential Privacy Noise Injection: A Computer Privacy-Utility Evaluation

Federated learning allows clinical text classifiers to be trained across hospitals without centralising patient records, and differential privacy (DP) noise injection is the standard mechanism for bounding what any single record can reveal. Both techniques, however, degrade the internal representations on which post hoc interpretability methods depend, and the resulting loss of explanation fidelity has not been characterised as a formal quantity. The framework is evaluated through a replication-based design study of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.640), with power estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 56 clusters are required for 80% power at a 5 percentage point effect, and that the interpretability bound tightens superlinearly as the privacy budget falls below unity. The contribution is a computable bound that lets clinical deployers reason about explanation reliability before committing to a privacy budget, rather than discovering attribution collapse after deployment.