Evaluation of Differentially-Private Federated Distillation for Computer Agriculture Crop-Yield Prediction Under Cross-Silo Heterogeneity: An Artificial Intelligence Privacy-Utility Bound for Cooperative Data Sharing

Cross-silo crop-yield prediction in computer agriculture requires cooperative learning across farms, cooperatives and extension agencies whose data cannot be pooled because of privacy regulation, commercial sensitivity and heterogeneous sensing regimes. Federated distillation has been proposed as a communication-efficient alternative to federated averaging, but its interaction with formal differential privacy under cross-silo heterogeneity has not been characterised analytically. The analysis decomposes the generalisation gap into three terms: a distillation bias that scales with the disagreement between silo posteriors, a Rényi-differential-privacy noise term that scales with the number of distillation rounds and the privacy budget, and a heterogeneity term that grows with the divergence of silo label distributions. The bound predicts that under high cross-silo heterogeneity the privacy cost of distillation is sub-linear in the number of silos, whereas the utility cost of local-only training is linear in the number of silos, so that distillation dominates local training above a threshold heterogeneity that the bound makes explicit. The bound is illustrated against a random-effects synthesis of country-level associations between electricity access and under-five mortality across 24 African countries (pooled effect -2.19361, standard error 0.26513, 95% CI [-2.71326, -1.67395], I-squared 99.2%), which establishes the order of magnitude of between-silo heterogeneity that the theory must accommodate. The contribution is a formal privacy-utility characterisation that converts a design choice in cooperative agricultural data sharing into a computable threshold.