# The Blessing and Curse of Dimensionality in Safety Alignment

arXiv: https://arxiv.org/abs/2507.20333 · HTML: https://mlsanity.com/paper/2507.20333/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Safety alignment and jailbreak attacks, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 60 of its 80 references that are in the map.
- First posted on arXiv 27 Jul 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Safety alignment and jailbreak attacks](https://mlsanity.com/alignment/safety-alignment-and-jailbreak-attacks/)
- LLM safety and security / [Safety alignment, refusal and guardrails](https://mlsanity.com/safety/safety-alignment-refusal-and-guardrails/)

## Builds on (most cited first, 30 of 60)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [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)
- [Seq2SQL: Generating Structured Queries from Natural Language using Reinforcement Learning](https://mlsanity.com/paper/1709.00103/) (2017)
- [Unified Language Model Pre-training for Natural Language Understanding and Generation](https://mlsanity.com/paper/1905.03197/) (2019)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)

## Built on by (most cited first, 10 of 10)

- [Steering MoE LLMs via Expert (De)Activation](https://mlsanity.com/paper/2509.09660/) (2025)
- [Activation Steering with a Feedback Controller](https://mlsanity.com/paper/2510.04309/) (2025)
- [In-Distribution Steering: Balancing Control and Coherence in Language Model Generation](https://mlsanity.com/paper/2510.13285/) (2025)
- [Concept Heterogeneity-aware Representation Steering](https://mlsanity.com/paper/2603.02237/) (2026)
- [NeuronGuard: Robust LLM Safety Alignment via Ablation-Aware Safety Signal Redistribution](https://mlsanity.com/paper/2608.23959/) (2026)
- [One Leak Away: How Pretrained Model Exposure Amplifies Jailbreak Risks in Finetuned LLMs](https://mlsanity.com/paper/2512.14751/) (2025)
- [TrojanPraise: Jailbreak LLMs via Benign Fine-Tuning](https://mlsanity.com/paper/2601.12460/) (2026)
- [Does Less Hallucination Mean Less Creativity? An Empirical Investigation in LLMs](https://mlsanity.com/paper/2512.11509/) (2025)
- [Kernelized Activation Steering](https://mlsanity.com/paper/2610.01062/) (2026)
- [Steering by Influence: Curvature Aware Data Weighting for Activation Steering](https://mlsanity.com/paper/2610.06383/) (2026)

## Abstract (arXiv)

The focus on safety alignment in large language models (LLMs) has increased significantly due to their widespread adoption across different domains. The scale of LLMs play a contributing role in their success, and the growth in parameter count follows larger hidden dimensions. In this paper, we hypothesize that while the increase in dimensions has been a key advantage, it may lead to emergent problems as well. These problems emerge as the linear structures in the activation space can be exploited, in the form of activation engineering, to circumvent its safety alignment. Through detailed visualizations of linear subspaces associated with different concepts, such as safety, across various model scales, we show that the curse of high-dimensional representations uniquely impacts LLMs. Further substantiating our claim, we demonstrate that projecting the representations of the model onto a lower dimensional subspace can preserve sufficient information for alignment while avoiding those linear structures. Empirical results confirm that such dimensional reduction significantly reduces susceptibility to jailbreaking through representation engineering. Building on our empirical validations, we provide theoretical insights into these linear jailbreaking methods relative to a model's hidden dimensions. Broadly speaking, our work posits that the high dimensions of a model's internal representations can be both a blessing and a curse in safety alignment.