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

Abstract: The safety mechanisms of 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 \underline{L}ow-Rank \underline{S}afety \underline{S}ubspace \underline{F}usion. 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.