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

TL;DR

This paper introduces C-Δθ, a method for offline, circuit-restricted weight updates that enable selective refusal in language models without inference-time interventions, reducing runtime costs.

Contribution

The paper presents a novel offline weight update technique, C-Δθ, which localizes refusal behavior into a sparse circuit and applies constrained updates for improved efficiency.

Findings

Effective category-specific refusal achieved

Significant reduction in inference-time overhead

Maintains model utility after updates

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.