# Angular Steering: Behavior Control via Rotation in Activation Space

arXiv: https://arxiv.org/abs/2510.26243 · HTML: https://mlsanity.com/paper/2510.26243/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 70 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 30 of 52)

- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [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)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [A StrongREJECT for Empty Jailbreaks](https://mlsanity.com/paper/2402.10260/) (2024)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)

## Built on by (most cited first, 30 of 53)

- [Spherical Steering: Geometry-Aware Activation Rotation for Language Models](https://mlsanity.com/paper/2602.08169/) (2026)
- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [Learning a Generative Meta-Model of LLM Activations](https://mlsanity.com/paper/2602.06964/) (2026)
- [COLD-Steer: Steering Large Language Models via In-Context One-step Learning Dynamics](https://mlsanity.com/paper/2603.06495/) (2026)
- [Selective Steering: Norm-Preserving Control Through Discriminative Layer Selection](https://mlsanity.com/paper/2601.19375/) (2026)
- [Concept Heterogeneity-aware Representation Steering](https://mlsanity.com/paper/2603.02237/) (2026)
- [The Unreasonable Effectiveness of Text Embedding Interpolation for Continuous Image Steering](https://mlsanity.com/paper/2603.17998/) (2026)
- [FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers](https://mlsanity.com/paper/2605.17231/) (2026)
- [Global Evolutionary Steering: Refining Activation Steering Control via Cross-Layer Consistency](https://mlsanity.com/paper/2603.12298/) (2026)
- [Steering at the Source: Style Modulation Heads for Robust Persona Control](https://mlsanity.com/paper/2603.13249/) (2026)
- [Minimizing Collateral Damage in Activation Steering](https://mlsanity.com/paper/2605.01167/) (2026)
- [The Cylindrical Representation Hypothesis for Language Model Steering](https://mlsanity.com/paper/2605.01844/) (2026)
- [The Hidden Signal of Verifier Strictness: Controlling and Improving Step-Wise Verification via Selective Latent Steering](https://mlsanity.com/paper/2605.20745/) (2026)
- [Spectral Superposition: A Theory of Feature Geometry](https://mlsanity.com/paper/2602.02224/) (2026)
- [ORBIT: Training-Free Multi-Attribute Behavioral Steering via Orthogonal Subspace Rotation](https://mlsanity.com/paper/2606.22357/) (2026)
- [Don't Lose Focus: Activation Steering via Key-Orthogonal Projections](https://mlsanity.com/paper/2605.06342/) (2026)
- [Activation Steering of Video Generation Models via Reduced-Order Linear Optimal Control](https://mlsanity.com/paper/2606.04775/) (2026)
- [Steering Robustness into World Action Models via Mechanistic Interpretability and Optimal Control](https://mlsanity.com/paper/2607.14943/) (2026)
- [Deployable Per-Instance Multi-Layer Activation Steering for Large Language Models](https://mlsanity.com/paper/2608.08829/) (2026)
- [Prototype Transformer: Towards Language Model Architectures Interpretable by Design](https://mlsanity.com/paper/2602.11852/) (2026)
- [AI Steerability 360: A Toolkit for Steering Large Language Models](https://mlsanity.com/paper/2603.07837/) (2026)
- [Inference-Time Machine Unlearning via Gated Activation Redirection](https://mlsanity.com/paper/2605.12765/) (2026)
- [Decodable Is Not Grounded: A Vision-Ablation Arbiter for VLM Spatial Reasoning](https://mlsanity.com/paper/2606.31257/) (2026)
- [How Context Shapes Truth: Geometric Transformations of Statement-level Truth Representations in LLMs](https://mlsanity.com/paper/2601.06599/) (2026)
- [Psychological Steering of Large Language Models](https://mlsanity.com/paper/2604.14463/) (2026)
- [Seeing Through Circuits: Faithful Mechanistic Interpretability for Vision Transformers](https://mlsanity.com/paper/2604.14477/) (2026)
- [Manifold-Guided Attention Steering](https://mlsanity.com/paper/2605.21770/) (2026)
- [Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering](https://mlsanity.com/paper/2605.24942/) (2026)
- [Latent Space Disentanglement via Activation Steering for Interpretable Attribute Control in Symbolic Music Generation](https://mlsanity.com/paper/2605.31295/) (2026)
- [A Geometric Account of Activation Steering through Angle-Norm Decomposition](https://mlsanity.com/paper/2606.06735/) (2026)

## Abstract (arXiv)

Controlling specific behaviors in large language models while preserving their general capabilities is a central challenge for safe and reliable artificial intelligence deployment. Current steering methods, such as vector addition and directional ablation, are constrained within a two-dimensional subspace defined by the activation and feature direction, making them sensitive to chosen parameters and potentially affecting unrelated features due to unintended interactions in activation space. We introduce Angular Steering, a novel and flexible method for behavior modulation that operates by rotating activations within a fixed two-dimensional subspace. By formulating steering as a geometric rotation toward or away from a target behavior direction, Angular Steering provides continuous, fine-grained control over behaviors such as refusal and compliance. We demonstrate this method using refusal steering emotion steering as use cases. Additionally, we propose Adaptive Angular Steering, a selective variant that rotates only activations aligned with the target feature, further enhancing stability and coherence. Angular Steering generalizes existing addition and orthogonalization techniques under a unified geometric rotation framework, simplifying parameter selection and maintaining model stability across a broader range of adjustments. Experiments across multiple model families and sizes show that Angular Steering achieves robust behavioral control while maintaining general language modeling performance, underscoring its flexibility, generalization, and robustness compared to prior approaches. Code and artifacts are available at https://github.com/lone17/angular-steering/.