# Spherical Steering: Geometry-Aware Activation Rotation for Language Models

arXiv: https://arxiv.org/abs/2602.08169 · HTML: https://mlsanity.com/paper/2602.08169/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 58 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 30 of 49)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [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)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [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)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [A Corpus and Evaluation Framework for Deeper Understanding of Commonsense Stories](https://mlsanity.com/paper/1604.01696/) (2016)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Programming Refusal with Conditional Activation Steering](https://mlsanity.com/paper/2409.05907/) (2024)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [Emergent Misalignment: Narrow finetuning can produce broadly misaligned LLMs](https://mlsanity.com/paper/2502.17424/) (2025)

## Built on by (most cited first, 21 of 21)

- [Beyond Steering Vector: Flow-based Activation Steering for Inference-Time Intervention](https://mlsanity.com/paper/2605.05892/) (2026)
- [The Hidden Signal of Verifier Strictness: Controlling and Improving Step-Wise Verification via Selective Latent Steering](https://mlsanity.com/paper/2605.20745/) (2026)
- [ICA Lens: Interpreting Language Models Without Training Another Dictionary](https://mlsanity.com/paper/2606.11722/) (2026)
- [ORBIT: Training-Free Multi-Attribute Behavioral Steering via Orthogonal Subspace Rotation](https://mlsanity.com/paper/2606.22357/) (2026)
- [Conceptors for Semantic Steering](https://mlsanity.com/paper/2605.04980/) (2026)
- [Where Steering Signals Come From: Activation Source Selection in Activation Steering](https://mlsanity.com/paper/2607.25270/) (2026)
- [Inference-Time Machine Unlearning via Gated Activation Redirection](https://mlsanity.com/paper/2605.12765/) (2026)
- [Conditional Optimal Bridge for Riemannian Activation Steering](https://mlsanity.com/paper/2607.10517/) (2026)
- [A Geometric Account of Activation Steering through Angle-Norm Decomposition](https://mlsanity.com/paper/2606.06735/) (2026)
- [BarrierSteer: LLM Safety via Learning Barrier Steering](https://mlsanity.com/paper/2602.20102/) (2026)
- [Temporal Preference Concepts and their Functions in a Large Language Model](https://mlsanity.com/paper/2606.05194/) (2026)
- [RepBench: Compiling Benchmarks into Capability Representations for Large Language Models](https://mlsanity.com/paper/2607.28008/) (2026)
- [Controlling Refusal Behavior of LLMs via Stiefel-Constrained Rotation Steering](https://mlsanity.com/paper/2608.30986/) (2026)
- [Steering Geometry: Validating Human Value Geometry in LLM Steering Space](https://mlsanity.com/paper/2609.06289/) (2026)
- [GEOSTEER: Geodesic Optimization for Activation Steering in Large Language Models](https://mlsanity.com/paper/2609.10658/) (2026)
- [MAxBench: A Multinomial Concept Recovery Benchmark](https://mlsanity.com/paper/2609.13072/) (2026)
- [How to Tame a Multi-Headed Hydra? Adaptive Multi-Category Safety Steering for Large Language Models](https://mlsanity.com/paper/2609.34514/) (2026)
- [HeadEdit: Calibrating Language Model Behavior Through the Frozen Unembedding Matrix](https://mlsanity.com/paper/2610.01170/) (2026)
- [Hesitation Has a Geometry: Entropy-Trained Hyperbolic Probes for Sparse Activation Steering](https://mlsanity.com/paper/2610.02391/) (2026)
- [One Token Can Be Enough: Bridging Prompting and Activation Steering with Prefix Steering](https://mlsanity.com/paper/2610.04967/) (2026)
- [TRACESTEER: Trace Driven Activation Steering for Hallucination Mitigation in Diffusion Language Models](https://mlsanity.com/paper/2610.18173/) (2026)

## Abstract (arXiv)

Inference-time steering offers a promising way to control language models (LMs) without retraining. However, standard approaches typically rely on activation addition, which inevitably alters the hidden-state magnitudes raising concerns about representation collapse and degraded open-ended generation. In this work, we explore Spherical Steering, a training-free primitive that resolves this trade-off through activation rotation. Rather than shifting activations with a fixed vector, our method rotates them along a geodesic toward a target direction, preserving signal integrity while steering toward the target concept. To further enhance adaptivity, we incorporate a confidence gate that dynamically modulates steering strength based on input uncertainty. Extensive experiments across multiple-choice benchmarks demonstrate that Spherical Steering significantly outperforms addition-based baselines (notably by +10% on TruthfulQA, COPA, and Storycloze), while simultaneously maintaining the model's general open-ended generation quality. This work highlights the value of geometric consistency, suggesting that norm-preserving rotation is a robust and effective primitive for precise inference-time control. The code is available at: https://github.com/chili-lab/Spherical-Steering.