FedSOUL: Federated Continual Unlearning via Spectral Orthogonality

As privacy, copyright, and safety requirements evolve, federated learning systems face a growing imperative to accommodate sequential unlearning requests. However, existing federated unlearning methods are designed for single-shot settings and their direct sequential application may lead to uncontrolled parameter-space overlap, causing cross-request interference that undermines prior forgetting. To address this, we propose the Spectral Orthogonality for Federated Continual unlearning (FedSOUL), a framework that reduces direct overlap among sequential unlearning updates. The core idea is to structure model updates in a shared orthonormal spectral basis, where each client is assigned a dedicated subspace in the frequency domain. Under this design, each unlearning request updates only its associated subspace, while all others remain unchanged, ensuring that sequential updates do not overlap in the allocated spectral coefficient space and thereby reducing cross-request interference. Beyond interference control, FedSOUL also improves efficiency by operating on sparse spectral coefficients, using FFT-based transforms for efficient computation and communicating only sparse coefficient updates. From a theoretical perspective, we relate continual unlearning to geometric conditions on update directions and show that our spectral construction satisfies update orthogonality by design, while functional preservation depends on bounded projected gradient leakage. Extensive experiments demonstrate that FedSOUL maintains stable unlearning–utility trade-offs across up to ten sequential requests and consistently outperforms competitive federated baselines. Our code is available at https://anonymous.4open.science/r/fedunlearning-1B92/.