SHARE: Rectified Half-Space Preservation for Balancing Concept Erasure and Retention

Editing-based concept erasure removes specified concepts from text-to-image diffusion models while preserving non-target behavior. However, strict preservation constraints in closed-form parameter editing can excessively restrict the available edit space. We formulate editing-based erasure as a constrained optimization problem and show that equality-based preservation limits the feasible degrees of freedom. We then introduce a rectified half-space relaxation that makes retained representations inactive without requiring their preactivations to vanish. Based on this formulation, we propose Set-aware Half-space with Analytic Readouts for Erasure (SHARE). SHARE learns a shared rectified selector and computes layer-specific residual readouts in closed form, enabling concept-dependent updates without jointly optimizing the selector and readouts. Experiments across multiple concept scales, prompt types, and model architectures demonstrate favorable trade-offs between target erasure and non-target retention.