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

Computer Science > Artificial Intelligence [Submitted on 11 Jun 2026] Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP Elisabetta Rocchetti, Alfio Ferrara 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. Subjects: 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 Focus to learn more Submission history From: Elisabetta Rocchetti [view email] [v1] Thu, 11 Jun 2026 06:58:33 UTC (3,289 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)