# LSSF: Safety Alignment for Large Language Models through Low-Rank Safety Subspace Fusion

arXiv: https://arxiv.org/abs/2602.00038 · HTML: https://mlsanity.com/paper/2602.00038/

## Key facts

- Cited by 8 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 30 of its 44 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## 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 30)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [Red-Teaming Large Language Models using Chain of Utterances for Safety-Alignment](https://mlsanity.com/paper/2308.09662/) (2023)
- [Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks](https://mlsanity.com/paper/2312.06795/) (2023)
- [Language Models are Homer Simpson! Safety Re-Alignment of Fine-tuned Language Models through Task Arithmetic](https://mlsanity.com/paper/2402.11746/) (2024)
- [Model Stock: All we need is just a few fine-tuned models](https://mlsanity.com/paper/2403.19522/) (2024)
- [Low-Complexity Probing via Finding Subnetworks](https://mlsanity.com/paper/2104.03514/) (2021)
- [JAILJUDGE: A Comprehensive Jailbreak Judge Benchmark with Multi-Agent Enhanced Explanation Evaluation Framework](https://mlsanity.com/paper/2410.12855/) (2024)
- [LM-Cocktail: Resilient Tuning of Language Models via Model Merging](https://mlsanity.com/paper/2311.13534/) (2023)
- [On the Trustworthiness Landscape of State-of-the-art Generative Models: A Survey and Outlook](https://mlsanity.com/paper/2307.16680/) (2023)

## Built on by (most cited first, 8 of 8)

- [NeST: Neuron Selective Tuning for LLM Safety](https://mlsanity.com/paper/2602.16835/) (2026)
- [Structuring the Space of Sociotechnical Alignment](https://mlsanity.com/paper/2607.01250/) (2026)
- [The Geometric Price of Discrete Logic: Context-driven Manifold Dynamics of Number Representations](https://mlsanity.com/paper/2603.23577/) (2026)
- [Explaining and Breaking the Safety-Helpfulness Ceiling via Preference Dimensional Expansion](https://mlsanity.com/paper/2605.11679/) (2026)
- [Safin-1: Safety from Within through Memory-Native State Evolution](https://mlsanity.com/paper/2609.00092/) (2026)
- [Two to Tango: Coupled Task-Reference Selection for Safe LLM Fine-tuning](https://mlsanity.com/paper/2606.09866/) (2026)
- [SafeTune: A Unified Faithful Library for Auditing and Repairing Safety Drift in Fine-Tuned LLMs](https://mlsanity.com/paper/2609.22153/) (2026)
- [On Mitigation of Subliminal Learning in Large Language Models](https://mlsanity.com/paper/2609.22215/) (2026)

## Abstract (arXiv)

The safety mechanisms of large language models (LLMs) exhibit notable fragility, as even fine-tuning on datasets without harmful content may still undermine their safety capabilities. Meanwhile, existing safety alignment methods predominantly rely on the fine-tuning process, which inadvertently leads to the increased complexity and computational resources required. To address these issues, we introduce LSSF, a novel safety re-alignment framework with underlineLow-Rank underlineSafety underlineSubspace underlineFusion. Our proposed method exploits the low-rank characteristics of safety information in LLMs by constructing a low-rank projection matrix to extract the principal components of safety vectors. Notably, this projection matrix represents the low-rank safety subspace of the LLMs, which we have observed to remain stable during fine-tuning process and is isolated from the model's general capabilities. These principal components are used to effectively restore safety alignment when combined with fine-tuned LLMs through linear arithmetic. Additionally, to account for the varying encoding densities of safety information across different layers of LLMs, we propose a novel metric called safety singular value entropy. This metric quantifies the encoding density and allows for the dynamic computation of the safety-critical rank for each safety vector. Extensive experiments demonstrate that our proposed post-hoc alignment method can effectively restore the safety alignment of fine-tuned models with minimal impact on their performance in downstream tasks.