# Controlling Refusal Behavior of LLMs via Stiefel-Constrained Rotation Steering

arXiv: https://arxiv.org/abs/2608.30986 · HTML: https://mlsanity.com/paper/2608.30986/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Steering and probing for LLM safety, one of 13 directions in Mechanistic interpretability.
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Placed in

- Mechanistic interpretability / [Steering and probing for LLM safety](https://mlsanity.com/mechinterp/steering-and-probing-for-llm-safety/)

## Builds on (most cited first, 25 of 25)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations](https://mlsanity.com/paper/2312.06674/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [SALAD-Bench: A Hierarchical and Comprehensive Safety Benchmark for Large Language Models](https://mlsanity.com/paper/2402.05044/) (2024)
- [Qwen3Guard Technical Report](https://mlsanity.com/paper/2510.14276/) (2025)
- [Personalized Steering of Large Language Models: Versatile Steering Vectors Through Bi-directional Preference Optimization](https://mlsanity.com/paper/2406.00045/) (2024)
- [The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independence](https://mlsanity.com/paper/2502.17420/) (2025)
- [LLMs Encode Harmfulness and Refusal Separately](https://mlsanity.com/paper/2507.11878/) (2025)
- [Eight Things to Know about Large Language Models](https://mlsanity.com/paper/2304.00612/) (2023)
- [Angular Steering: Behavior Control via Rotation in Activation Space](https://mlsanity.com/paper/2510.26243/) (2025)
- [AlphaSteer: Learning Refusal Steering with Principled Null-Space Constraint](https://mlsanity.com/paper/2506.07022/) (2025)
- [Refusal in LLMs is an Affine Function](https://mlsanity.com/paper/2411.09003/) (2024)
- [Householder Pseudo-Rotation: A Novel Approach to Activation Editing in LLMs with Direction-Magnitude Perspective](https://mlsanity.com/paper/2409.10053/) (2024)
- [Spherical Steering: Geometry-Aware Activation Rotation for Language Models](https://mlsanity.com/paper/2602.08169/) (2026)
- [Beyond I'm Sorry, I Can't: Dissecting Large Language Model Refusal](https://mlsanity.com/paper/2509.09708/) (2025)
- [SOM Directions are Better than One: Multi-Directional Refusal Suppression in Language Models](https://mlsanity.com/paper/2511.08379/) (2025)
- [Selective Steering: Norm-Preserving Control Through Discriminative Layer Selection](https://mlsanity.com/paper/2601.19375/) (2026)
- [Minimizing Collateral Damage in Activation Steering](https://mlsanity.com/paper/2605.01167/) (2026)

## Abstract (arXiv)

Activation steering has emerged as a lightweight approach for controlling model refusal at inference time. A growing line of research explores trainable rotations of activations to develop geometrically principled intervention mechanisms. However, existing techniques rely on auxiliary constructs, such as refusal vectors, to define these rotations. In our work, we develop a self-contained methodology for learning parameter-efficient rotational transformations based on Riemannian optimization. We empirically validate the proposed scheme, demonstrating its superiority in intervention efficiency. An extensive ablation study highlights the importance of key design choices in our method. Our results identify the proposed rotation-based steering scheme as a promising direction for more reliable control over the behavior of LLMs.