# Jailbreaking the Matrix: Nullspace Steering for Controlled Model Subversion

arXiv: https://arxiv.org/abs/2604.10326 · HTML: https://mlsanity.com/paper/2604.10326/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Jailbreaking, one of 12 directions in LLM safety and security.
- Builds on 42 of its 47 references that are in the map.
- First posted on arXiv 11 Apr 2026.

## Placed in

- LLM safety and security / [Jailbreaking](https://mlsanity.com/safety/jailbreaking/)

## Builds on (most cited first, 30 of 42)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [AutoDAN: Generating Stealthy Jailbreak Prompts on Aligned Large Language Models](https://mlsanity.com/paper/2310.04451/) (2023)
- [Tree of Attacks: Jailbreaking Black-Box LLMs Automatically](https://mlsanity.com/paper/2312.02119/) (2023)
- [Baseline Defenses for Adversarial Attacks Against Aligned Language Models](https://mlsanity.com/paper/2309.00614/) (2023)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)
- [SmoothLLM: Defending Large Language Models Against Jailbreaking Attacks](https://mlsanity.com/paper/2310.03684/) (2023)
- [A StrongREJECT for Empty Jailbreaks](https://mlsanity.com/paper/2402.10260/) (2024)
- [DeepInception: Hypnotize Large Language Model to Be Jailbreaker](https://mlsanity.com/paper/2311.03191/) (2023)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [CodeGeeX: A Pre-Trained Model for Code Generation with Multilingual Benchmarking on HumanEval-X](https://mlsanity.com/paper/2303.17568/) (2023)
- [ToolQA: A Dataset for LLM Question Answering with External Tools](https://mlsanity.com/paper/2306.13304/) (2023)
- [Pretraining Language Models with Human Preferences](https://mlsanity.com/paper/2302.08582/) (2023)
- [SafeDecoding: Defending against Jailbreak Attacks via Safety-Aware Decoding](https://mlsanity.com/paper/2402.08983/) (2024)
- [LLM Self Defense: By Self Examination, LLMs Know They Are Being Tricked](https://mlsanity.com/paper/2308.07308/) (2023)
- [AmpleGCG: Learning a Universal and Transferable Generative Model of Adversarial Suffixes for Jailbreaking Both Open and Closed LLMs](https://mlsanity.com/paper/2404.07921/) (2024)
- [Robust Prompt Optimization for Defending Language Models Against Jailbreaking Attacks](https://mlsanity.com/paper/2401.17263/) (2024)
- [LLM Defenses Are Not Robust to Multi-Turn Human Jailbreaks Yet](https://mlsanity.com/paper/2408.15221/) (2024)
- [Tensor Trust: Interpretable Prompt Injection Attacks from an Online Game](https://mlsanity.com/paper/2311.01011/) (2023)
- [AutoDAN: Interpretable Gradient-Based Adversarial Attacks on Large Language Models](https://mlsanity.com/paper/2310.15140/) (2023)

## Abstract (arXiv)

Large language models remain vulnerable to jailbreak attacks -- inputs designed to bypass safety mechanisms and elicit harmful responses -- despite advances in alignment and instruction tuning. We propose Head-Masked Nullspace Steering (HMNS), a circuit-level intervention that (i) identifies attention heads most causally responsible for a model's default behavior, (ii) suppresses their write paths via targeted column masking, and (iii) injects a perturbation constrained to the orthogonal complement of the muted subspace. HMNS operates in a closed-loop detection-intervention cycle, re-identifying causal heads and reapplying interventions across multiple decoding attempts. Across multiple jailbreak benchmarks, strong safety defenses, and widely used language models, HMNS attains state-of-the-art attack success rates with fewer queries than prior methods. Ablations confirm that nullspace-constrained injection, residual norm scaling, and iterative re-identification are key to its effectiveness. To our knowledge, this is the first jailbreak method to leverage geometry-aware, interpretability-informed interventions, highlighting a new paradigm for controlled model steering and adversarial safety circumvention.