# Anchoring Refusal Direction: Mitigating Safety Risks in Tuning via Projection Constraint

arXiv: https://arxiv.org/abs/2509.06795 · HTML: https://mlsanity.com/paper/2509.06795/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 51 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 30 of 45)

- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (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)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [Jailbreaking Black Box Large Language Models in Twenty Queries](https://mlsanity.com/paper/2310.08419/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (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)
- [AutoDAN: Generating Stealthy Jailbreak Prompts on Aligned Large Language Models](https://mlsanity.com/paper/2310.04451/) (2023)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [A Survey on Large Language Model (LLM) Security and Privacy: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2312.02003/) (2023)
- [Exploiting Programmatic Behavior of LLMs: Dual-Use Through Standard Security Attacks](https://mlsanity.com/paper/2302.05733/) (2023)
- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [COLD-Attack: Jailbreaking LLMs with Stealthiness and Controllability](https://mlsanity.com/paper/2402.08679/) (2024)
- [Latent Adversarial Training Improves Robustness to Persistent Harmful Behaviors in LLMs](https://mlsanity.com/paper/2407.15549/) (2024)
- [Removing RLHF Protections in GPT-4 via Fine-Tuning](https://mlsanity.com/paper/2311.05553/) (2023)
- [Safety Layers in Aligned Large Language Models: The Key to LLM Security](https://mlsanity.com/paper/2408.17003/) (2024)
- [Safe LoRA: the Silver Lining of Reducing Safety Risks when Fine-tuning Large Language Models](https://mlsanity.com/paper/2405.16833/) (2024)
- [Vaccine: Perturbation-aware Alignment for Large Language Models against Harmful Fine-tuning Attack](https://mlsanity.com/paper/2402.01109/) (2024)
- [Explore, Establish, Exploit: Red Teaming Language Models from Scratch](https://mlsanity.com/paper/2306.09442/) (2023)
- [Language Models are Homer Simpson! Safety Re-Alignment of Fine-tuned Language Models through Task Arithmetic](https://mlsanity.com/paper/2402.11746/) (2024)

## Built on by (most cited first, 7 of 7)

- [Unified Defense for Large Language Models against Jailbreak and Fine-Tuning Attacks in Education](https://mlsanity.com/paper/2511.14423/) (2025)
- [Do Activation Monitors Survive Model Updates? Benchmarking, Predicting, and Repairing Activation-Monitor Staleness](https://mlsanity.com/paper/2606.15980/) (2026)
- [S3-CoT: Self-Sampled Succinct Reasoning Enables Efficient Chain-of-Thought LLMs](https://mlsanity.com/paper/2602.01982/) (2026)
- [Surgery: Mitigating Harmful Fine-Tuning for Large Language Models via Attention Sink](https://mlsanity.com/paper/2602.05228/) (2026)
- [Dynamic Adversarial Fine-Tuning Reorganizes Refusal Geometry](https://mlsanity.com/paper/2604.27019/) (2026)
- [From Refusal Geometry to Safety Geometry: Harmfulness--Refusal Coupling under Dynamic Adversarial Fine-Tuning](https://mlsanity.com/paper/2606.16349/) (2026)
- [How Narrative Wrapping Affects LLM Refusal: A Cross-Language Benchmark and Defense](https://mlsanity.com/paper/2610.11005/) (2026)

## Abstract (arXiv)

Instruction Fine-Tuning (IFT) has been widely adopted as an effective post-training strategy to enhance various abilities of Large Language Models (LLMs). However, prior studies have shown that IFT can significantly compromise LLMs' safety, particularly their ability to refuse malicious instructions, raising significant concerns. Recent research into the internal mechanisms of LLMs has identified the refusal direction (r-direction) in the hidden states, which plays a pivotal role in governing refusal behavior. Building on this insight, our study reveals that the r-direction tends to drift during training, which we identify as one of the causes of the associated safety risks. To mitigate such drift, our proposed ProCon method introduces a projection-constrained loss term that regularizes the projection magnitude of each training sample's hidden state onto the r-direction. Our initial analysis shows that applying an appropriate constraint can effectively mitigate the refusal direction drift and associated safety risks, but remains limited by overall performance barriers. To overcome this barrier, informed by our observation of early-stage sharp drift and a data-driven perspective, we introduce a warm-up strategy that emphasizes early-stage strong constraints and broaden the data distribution to strengthen constraint signals, leading to an enhanced ProCon method. Experimental results under various datasets, scenarios, and LLMs demonstrate that our method can significantly mitigate safety risks posed by IFT while preserving task performance gains. Even compared with strong baselines, our method consistently delivers superior overall performance. Crucially, our analysis indicates that ProCon can contribute to stabilizing the r-direction during training, while such an interpretability-driven exploration of LLMs' internal mechanisms lays a solid foundation for future safety research.