Refusal is mediated by a multi-dimensional concept cone

measured in 1 paper

Wollschlager et al. find refusal in Gemma 2, Qwen 2.5, and Llama 3 8B is mediated by a polyhedral convex cone of up to 5 causally-independent directions, found via Refusal Cone Optimization (non-negative coefficients, re-orthogonalized) [wollschlager-etal-2025] Orthogonality between directions is not sufficient for independence; only ablating one and testing whether the others still reproduce the behavior establishes it [wollschlager-etal-2025] Cone dimensionality varies with model and scale, plateauing around 4D for Gemma 2 2B [wollschlager-etal-2025] This is the most geometrically elaborate of three competing accounts of refusal, versus the single-direction and affine-function accounts [wollschlager-etal-2025]

Structure

Cone

Context

refusal, safety, jailbreak, refusal geometry debate, representational independence

Confirmed in models

Gemma-2-2B-it · Gemma, Gemma-2-9B-it · Gemma, Qwen2.5-1.5B-Instruct · Qwen, Qwen2.5-14B-Instruct · Qwen, Llama-3-8B-Instruct · Llama

Method

Difference-in-means direction, Causal interventions (steering), Supervised direction search (gradient-based optimization)

Papers

The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independence — Wollschläger, T., Elstner, J., Geisler, S., Cohen-Addad, V., Günnemann, S., Gasteiger, J.2025 · arXiv:2502.17420