The safety mechanisms of large language models (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 Low-Rank Safety Subspace Fusison. 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 on downstream tasks.

Catastrophic Forgetting (CF) means models forgetting previously acquired knowledge when learning new data. It compromises the effectiveness of large language models (LLMs) during fine-tuning, yet the underlying causes have not been thoroughly investigated. This paper takes the first step to reveal the direct link between the flatness of the model loss landscape and the extent of CF in the field of LLMs. Based on this, we introduce the sharpness-aware minimization to mitigate CF by flattening the loss landscape. Experiments on three widely-used fine-tuning datasets, spanning different model scales, demonstrate the effectiveness of our method in alleviating CF. Analyses show that we nicely complement the existing anti-forgetting strategies, further enhancing the resistance of LLMs to CF.