LoRA is All You Need for Safety Alignment of Reasoning LLMs

Reasoning-capable LLMs have achieved major breakthroughs in solving complex problems, but recent work shows that acquiring and deploying strong reasoning can introduce significant safety risks. A common mitigation is to apply a secondary safety-alignment phase after reasoning is learned; however, safety alignment often degrades reasoning performance--a phenomenon known as the "Safety Tax". In this work, we show that a simple approach can largely bypass this trade-off: applying LoRA during SFT on refusal datasets. Despite its simplicity, this recipe achieves safety comparable to full-model alignment while preserving reasoning performance close to the original reasoning-tuned model, and the result holds across multiple model sizes and architectures, two safety benchmarks, and four reasoning benchmarks spanning mathematics, science, and code generation. We further ablate LoRA configurations and find that (1) rank-1 updates are sufficient to achieve the best safety-reasoning trade-off, (2) applying LoRA only to the MLP up-projection layers can outperform updating the full MLP, and (3) updating middle layers is more effective than updating early or late layers. Finally, we provide a theoretical analysis that helps understand when and why LoRA works, revealing that overshooting the rank budget (using a larger rank than needed for the finetuning task) induces base-task degradation at a rate inversely proportional to the intrinsic dimensionality of the base task. This suggests LoRA is most effective when the finetuning task is low-rank and the base capability is high-rank.