Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP

2026-06-11

AI Summary

This study investigates whether the refusal behavior of language models in response to harmful requests is governed by a single linear direction and systematically compares the efficacy of various intervention techniques. Across five open-source chat models, the authors analyze residual stream activations and visualize subspace geometry using methods including activation addition, directional ablation, nullspace projection, and counterfactual flipping. They find that INLP-based counterfactual flipping achieves refusal suppression performance comparable to mean-difference (DiM) approaches, whereas standard nullspace projection is notably less effective. Constraining the primary INLP direction enables high controllability while preserving baseline perplexity. Furthermore, the representations of “concept absence” and “concept opposition” exhibit distinct geometric structures, revealing intrinsic architectural characteristics underlying refusal mechanisms.

Abstract

Arditi et al. (2024) has shown that refusal in safety fine-tuned chat models is mediated by a single linear direction in the residual stream, recoverable by a difference-in-means (DiM) of harmful and harmless activations. We compare DiM-based interventions (activation addition and directional ablation) with two interventions derived from Iterative Nullspace Projection (INLP) -- nullspace projection and counterfactual flipping -- on five open-weight chat models, asking whether INLP can match DiM at steering refusal and whether its richer parameterisation yields more tweakable interventions. INLP counterfactual flipping is competitive with DiM directional ablation on refusal suppression, while nullspace projection is consistently weaker. Restricting INLP to the leading directions of the extracted subspace preserves most of the suppression effect at near-baseline perplexity, giving a tunable capability. Geometrically, the two INLP interventions land in qualitatively different regions of activation space: nullspace projection collapses transformed activations \emph{between} the harmful and harmless clusters, while counterfactual flipping moves them into the opposite cluster, suggesting that the model encodes the absence of a concept differently from its opposite -- an intriguing distinction that warrants further investigation in future work.

Problem

• refusal
• safety fine-tuning
• linear direction
• activation space
• language models

Innovation

• directional intervention
• Iterative Nullspace Projection
• refusal steering
• activation geometry
• counterfactual flipping