Causal Unlearning in Collaborative Optimization: Exact and Approximate Influence Reversal under Adversarial Contributions

Computer Science > Machine Learning [Submitted on 19 May 2026] Causal Unlearning in Collaborative Optimization: Exact and Approximate Influence Reversal under Adversarial Contributions Ali Mahdavi, Azadeh Zamanifar, Amirfarhad Farhadi, Omid Kashefi Federated learning systems must support data deletion requests to comply with privacy regulations, yet retraining from scratch after each deletion is computationally prohibitive. We present HF-KCU, a method that removes a client's contribution by approximating the influence function through conjugate gradient iterations in Krylov subspaces, reducing complexity from O(d^3) to O(kd) where k<<d.A causal weighting mechanism ensures that only clients holding the deleted data receive parameter updates, preventing spurious changes to unaffected clients. Our method is designed to handle bounded adversarial perturbations to the Hessian and gradient, providing graceful degradation under realistic threat models. We validate HF-KCU across convolutional (ResNet-18, SimpleCNN) and transformer (ViT-Lite) architectures on CIFAR-10, MNIST, and Fashion-MNIST. On CIFAR-10 under Dirichlet (alpha=0.5) partitioning, HF-KCU achieves 47.75 times speedup over retraining while maintaining test accuracy within 0.60% of the rational baseline(71.16 vs 71.76 %). Membership inference attacks on the forget set yield success rates of 0.499 matching the retrained model and confirming effective privacy restoration. We provide convergence guarantees showing that the Krylov approximation error decreases as O((k ^1/2-1)/(k^1/2+1)) where k is the Hessian condition number. The causal weighting mechanism ensures surgical updates, where only clients holding deleted data are modified, preserving model quality for unaffected participants and avoiding the instability of gradient-based approaches in asynchronous federated settings. This design provides interpretability as each update is directly traceable to the influence of the deleted data. The method's efficiency and precision make it suitable for production federated systems where deletion requests arrive asynchronously and computational budgets are constrained. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Cryptography and Security (cs.CR); Performance (cs.PF) Cite as: arXiv:2605.20341 [cs.LG]   (or arXiv:2605.20341v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2605.20341 Focus to learn more Submission history From: Azadeh Zamanifar [view email] [v1] Tue, 19 May 2026 18:00:39 UTC (32 KB) Access Paper: HTML (experimental) view license Current browse context: cs.LG < prev   |   next > new | recent | 2026-05 Change to browse by: cs cs.AI cs.CR cs.PF References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)