# LoX: Low-Rank Extrapolation Robustifies LLM Safety Against Fine-tuning

arXiv: https://arxiv.org/abs/2506.15606 · HTML: https://mlsanity.com/paper/2506.15606/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Safety alignment, refusal and guardrails, one of 12 directions in LLM safety and security.
- Builds on 36 of its 41 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Placed in

- 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 36)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (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)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [The Unlocking Spell on Base LLMs: Rethinking Alignment via In-Context Learning](https://mlsanity.com/paper/2312.01552/) (2023)
- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [Safety Fine-Tuning at (Almost) No Cost: A Baseline for Vision Large Language Models](https://mlsanity.com/paper/2402.02207/) (2024)
- [What is in Your Safe Data? Identifying Benign Data that Breaks Safety](https://mlsanity.com/paper/2404.01099/) (2024)
- [Vaccine: Perturbation-aware Alignment for Large Language Models against Harmful Fine-tuning Attack](https://mlsanity.com/paper/2402.01109/) (2024)
- [Fine-tuning can cripple your foundation model; preserving features may be the solution](https://mlsanity.com/paper/2308.13320/) (2023)
- [Representation Noising: A Defence Mechanism Against Harmful Finetuning](https://mlsanity.com/paper/2405.14577/) (2024)
- [Booster: Tackling Harmful Fine-tuning for Large Language Models via Attenuating Harmful Perturbation](https://mlsanity.com/paper/2409.01586/) (2024)
- [Harmful Fine-tuning Attacks and Defenses for Large Language Models: A Survey](https://mlsanity.com/paper/2409.18169/) (2024)
- [Use of LLMs for Illicit Purposes: Threats, Prevention Measures, and Vulnerabilities](https://mlsanity.com/paper/2308.12833/) (2023)
- [Antidote: Post-fine-tuning Safety Alignment for Large Language Models against Harmful Fine-tuning](https://mlsanity.com/paper/2408.09600/) (2024)
- [How Should Pre-Trained Language Models Be Fine-Tuned Towards Adversarial Robustness?](https://mlsanity.com/paper/2112.11668/) (2021)

## Built on by (most cited first, 12 of 12)

- [Watch the Weights: Unsupervised monitoring and control of fine-tuned LLMs](https://mlsanity.com/paper/2508.00161/) (2025)
- [Antibody: Strengthening Defense Against Harmful Fine-Tuning for Large Language Models via Attenuating Harmful Gradient Influence](https://mlsanity.com/paper/2603.00498/) (2026)
- [Turning the Spell Around: Lightweight Alignment Amplification via Rank-One Safety Injection](https://mlsanity.com/paper/2508.20766/) (2025)
- [Surgery: Mitigating Harmful Fine-Tuning for Large Language Models via Attention Sink](https://mlsanity.com/paper/2602.05228/) (2026)
- [Revisiting Robustness for LLM Safety Alignment via Selective Geometry Control](https://mlsanity.com/paper/2602.07340/) (2026)
- [Preventing Safety Drift in Large Language Models via Coupled Weight and Activation Constraints](https://mlsanity.com/paper/2604.12384/) (2026)
- [Safeguarding LLM Fine-tuning via Push-Pull Distributional Alignment](https://mlsanity.com/paper/2601.07200/) (2026)
- [A Few Steps Further: Why Defenses Against Malicious Finetuning Erode Under Continued Training](https://mlsanity.com/paper/2605.14605/) (2026)
- [Open-Weight LLM Fine-Tuning Defenses are Susceptible to Simple Attacks](https://mlsanity.com/paper/2605.26526/) (2026)
- [Safety Anchor: Defending Harmful Fine-tuning via Geometric Bottlenecks](https://mlsanity.com/paper/2605.05995/) (2026)
- [Jailbreak to Protect: Buffering and Reinforcing via Temporary Jailbreaking for Safe Fine-Tuning in Large Language Models](https://mlsanity.com/paper/2605.24550/) (2026)
- [SafeTune: A Unified Faithful Library for Auditing and Repairing Safety Drift in Fine-Tuned LLMs](https://mlsanity.com/paper/2609.22153/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have become indispensable in real-world applications. However, their widespread adoption raises significant safety concerns, particularly in responding to socially harmful questions. Despite substantial efforts to improve model safety through alignment, aligned models can still have their safety protections undermined by subsequent fine-tuning - even when the additional training data appears benign. In this paper, we empirically demonstrate that this vulnerability stems from the sensitivity of safety-critical low-rank subspaces in LLM parameters to fine-tuning. Building on this insight, we propose a novel training-free method, termed Low-Rank Extrapolation (LoX), to enhance safety robustness by extrapolating the safety subspace of an aligned LLM. Our experimental results confirm the effectiveness of LoX, demonstrating significant improvements in robustness against both benign and malicious fine-tuning attacks while preserving the model's adaptability to new tasks. For instance, LoX leads to 11% to 54% absolute reductions in attack success rates (ASR) facing benign or malicious fine-tuning attacks. By investigating the ASR landscape of parameters, we attribute the success of LoX to that the extrapolation moves LLM parameters to a flatter zone, thereby less sensitive to perturbations. The code is available at github.com/VITA-Group/LoX.