$C$-$\Delta\Theta$: Circuit-Restricted Weight Arithmetic for Selective Refusal

Abstract

Modern deployments require LLMs to enforce safety policies at scale, yet many controls rely on inference-time interventions that add recurring compute cost and serving complexity. Activation steering is widely used, but it requires runtime hooks and scales cost with the number of generations; conditional variants improve selectivity by gating when steering is applied but still retain an inference-time control path. We ask whether selective refusal can be moved entirely offline: can a mechanistic understanding of category-specific refusal be distilled into a circuit-restricted weight update that deploys as a standard checkpoint? We propose C-{\Delta}{\theta} Circuit Restricted Weight Arithmetic}, which (i) localizes refusal-causal computation as a sparse circuit using EAP-IG and (ii) computes a constrained weight update {\Delta}{\theta}C supported only on that circuit (typically <5% of parameters). Applying {\Delta}{\theta}C yields a drop-in edited checkpoint with no inference-time hooks, shifting cost from per request intervention to a one-time offline update. We evaluate category-targeted selectivity and capability retention on refusal and utility benchmarks.