The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independence

TL;DR

This paper explores the complex spatial structures behind refusal behaviors in large language models, revealing multiple independent mechanisms and proposing a new framework for understanding their representational independence.

Contribution

It introduces a gradient-based method to identify multiple independent refusal directions and concept cones, advancing understanding of LLM refusal mechanisms.

Findings

Multiple independent refusal directions identified

Refusal mechanisms governed by complex spatial structures

Functionally independent directions confirmed

Abstract

The safety alignment of large language models (LLMs) can be circumvented through adversarially crafted inputs, yet the mechanisms by which these attacks bypass safety barriers remain poorly understood. Prior work suggests that a single refusal direction in the model's activation space determines whether an LLM refuses a request. In this study, we propose a novel gradient-based approach to representation engineering and use it to identify refusal directions. Contrary to prior work, we uncover multiple independent directions and even multi-dimensional concept cones that mediate refusal. Moreover, we show that orthogonality alone does not imply independence under intervention, motivating the notion of representational independence that accounts for both linear and non-linear effects. Using this framework, we identify mechanistically independent refusal directions. We show that refusal mechanisms in LLMs are governed by complex spatial structures and identify functionally independent directions, confirming that multiple distinct mechanisms drive refusal behavior. Our gradient-based approach uncovers these mechanisms and can further serve as a foundation for future work on understanding LLMs.