# CSULoRA: Closest Safe Update Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2605.30640 · HTML: https://mlsanity.com/paper/2605.30640/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 14 of 14)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [Shadow Alignment: The Ease of Subverting Safely-Aligned Language Models](https://mlsanity.com/paper/2310.02949/) (2023)
- [Language Models are Homer Simpson! Safety Re-Alignment of Fine-tuned Language Models through Task Arithmetic](https://mlsanity.com/paper/2402.11746/) (2024)
- [SafeMERGE: Preserving Safety Alignment in Fine-Tuned Large Language Models via Selective Layer-Wise Model Merging](https://mlsanity.com/paper/2503.17239/) (2025)
- [Safe Delta: Consistently Preserving Safety when Fine-Tuning LLMs on Diverse Datasets](https://mlsanity.com/paper/2505.12038/) (2025)
- [Safe Pruning LoRA: Robust Distance-Guided Pruning for Safety Alignment in Adaptation of LLMs](https://mlsanity.com/paper/2506.18931/) (2025)

## Abstract (arXiv)

Low-rank adaptation has become a standard method for parameter-efficient fine-tuning of large language models, but even small amounts of unsafe or adversarial fine-tuning data can substantially weaken the safety behavior of aligned models. Existing safety-preserving LoRA methods often rely on hard interventions such as projection, pruning, thresholding, or additional training objectives. While these methods can suppress unsafe update directions, they may also remove task-relevant information or require extra tuning. We introduce CSULoRA, a post-hoc method for correcting trained LoRA adapters through closest safe update estimation. CSULoRA estimates a safety-aligned subspace from the weight displacement between a safety-aligned model and its corresponding base checkpoint. It then decomposes each LoRA update into fully aligned, partially aligned, and off-subspace components. Instead of discarding components outside the estimated safety subspace, CSULoRA solves a closed-form penalized minimum-change problem that preserves the fully aligned component while smoothly attenuating potentially unsafe directions according to their relative energy. In adversarial fine-tuning experiments, CSULoRA substantially reduces attack success rate while preserving most of the utility gains obtained from standard LoRA fine-tuning.