# High-Dimensional Random Projection for Activation Steering in Language Models

arXiv: https://arxiv.org/abs/2606.15092 · HTML: https://mlsanity.com/paper/2606.15092/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Activation steering methods, one of 13 directions in Mechanistic interpretability.
- Builds on 40 of its 50 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Placed in

- Mechanistic interpretability / [Activation steering methods](https://mlsanity.com/mechinterp/activation-steering-methods/)

## Builds on (most cited first, 30 of 40)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [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)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [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)
- [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)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Breaking the Curse of Dimensionality with Convex Neural Networks](https://mlsanity.com/paper/1412.8690/) (2014)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Programming Refusal with Conditional Activation Steering](https://mlsanity.com/paper/2409.05907/) (2024)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Steering Language Model Refusal with Sparse Autoencoders](https://mlsanity.com/paper/2411.11296/) (2024)
- [Understanding Reasoning in Thinking Language Models via Steering Vectors](https://mlsanity.com/paper/2506.18167/) (2025)

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

- [Does Steering Break Your Model? A Multi-Dimensional Evaluation Suite for LLM Steering Methods](https://mlsanity.com/paper/2610.07722/) (2026)

## Abstract (arXiv)

Activation steering has emerged as a key methodology for controlling the behavior of large language models (LLMs). Existing difference-in-means based methods, however, are fundamentally limited: they capture only mean differences between class activations and fail to recover discriminative signals that naturally exist in the nonlinear feature subspace under the superposition hypothesis. Motivated by that, we propose High-Dimensional Random-projection for Activation Steering (HiDRA), a training-free approach that integrates seamlessly with existing activation steering methods. By performing activation addition in the projected high-dimensional space, HiDRA can provably capture a better discriminative structure beyond the reach of linear methods. Experiments across diverse LLM families and benchmarks demonstrate that HiDRA consistently outperforms baseline counterparts, achieving stronger behavioral control without significant computational overhead.