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Abstract

Privacy regulations require data deletion in federated learning (FL). Full retraining is computationally infeasible, and existing unlearning methods either degrade accuracy or become too expensive for large neural networks. We present HF-KCU (Hessian-Free Krylov Causal Unlearning). The method removes client contributions in FL by approximating influence functions via Hessian-free conjugate gradient iterations. Complexity drops from $O(d^3)$ to $O(kd)$ with $k \ll d$. A causal weighting mechanism restricts parameter updates to clients holding deleted data, preventing unintended changes elsewhere. HF-KCU degrades predictably under bounded adversarial perturbations. On CIFAR-10, MNIST, and FashionMNIST across ResNet-18, SimpleCNN, and ViT-Lite, HF-KCU achieves a 47.75x speedup over retraining. On CIFAR-10, test accuracy stays within 0.60% of the retrained baseline (71.16% vs 71.76%). Membership inference attack success rates (0.499) match the retrained model. Convergence analysis shows exponential error decrease.