Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP
A new paper compares Diff-in-Means (DiM) and Iterative Nullspace Projection (INLP) for steering refusal in safety fine-tuned chat models. The study finds that INLP counterfactual flipping matches DiM directional ablation in refusal suppression, while nullspace projection is weaker. Restricting INLP to leading directions preserves suppression with near-baseline perplexity, and the two interventions land in different activation regions, suggesting distinct representations for absence versus opposite of a concept.
[2606.13720] Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP
[Submitted on 11 Jun 2026]
Title:Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP
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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.
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Artificial Intelligence (cs.AI)
Cite as: arXiv:2606.13720 [cs.AI]
(or arXiv:2606.13720v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.13720
arXiv-issued DOI via DataCite
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From: Elisabetta Rocchetti [view email] [v1] Thu, 11 Jun 2026 06:58:33 UTC (3,289 KB)
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