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

arXiv: https://arxiv.org/abs/2606.13720 · HTML: https://mlsanity.com/paper/2606.13720/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations](https://mlsanity.com/paper/2312.06674/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [A Unified Understanding and Evaluation of Steering Methods](https://mlsanity.com/paper/2502.02716/) (2025)
- [Verb Conjugation in Transformers Is Determined by Linear Encodings of Subject Number](https://mlsanity.com/paper/2310.15151/) (2023)

## Built on by (most cited first, 1 of 1)

- [Extracting Persona Subspaces Through Iterative Nullspace Projection For Modulation](https://mlsanity.com/paper/2610.04676/) (2026)

## Abstract (arXiv)

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 weaker on most models. Applying each method at the layer selected by the other shows that flipping's competitiveness is robust to this change while directional ablation's is not, suggesting that DiM's apparent edge is partly a property of its own selection procedure. 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 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 opposit--an intriguing distinction that warrants further investigation in future work.