Low-Rank Adaptation (LoRA) is widely used for parameter-efficient fine-tuning of large language models, but it is notably ineffective at removing backdoor behaviors from poisoned pretrained models when fine-tuning on clean dataset. Contrary to the common belief that this weakness is caused primarily by low rank, we show that LoRA’s vulnerability is fundamentally spectral. Our analysis identifies two key factors: LoRA updates (i) possess insufficient spectral strength, with singular values far below those of pretrained weights, and (ii) exhibit unfavorable spectral alignment, weakly matching clean-task directions while retaining overlap with trigger-sensitive subspaces. We further establish a critical scaling threshold beyond which LoRA can theoretically suppress trigger-induced activations, and we show empirically that standard LoRA rarely reaches this regime. We introduce Regularized Low-Rank Adaptation (RoRA), which improves forgetting by increasing spectral strength and correcting alignment through clean-strengthened regularization, trigger-insensitive constraints, and post-training spectral rescaling. Experiments across multiple NLP benchmarks and attack settings show that RoRA substantially reduces attack success rates while maintaining clean accuracy.

Reverse Kullback–Leibler (RKL) divergence is widely favored over forward KL (FKL) in large language models (LLM) distillation, yet this preference is largely based on comparisons that omit the temperature 𝜏, overlooking its central role in softening teacher distributions and improving knowledge transfer. In this work, we revisit temperature in LLM distillation and show that it fundamentally changes the comparison between FKL and RKL. Our analysis reveals an asymmetric effect: temperature substantially enriches FKL with non-dominant token signals, whereas it mainly rescales RKL gradients, causing FKL to benefit much more from 𝜏 scaling than RKL. This asymmetry overturns the standard empirical conclusion: although RKL outperforms FKL at 𝜏=1, FKL consistently surpasses RKL at higher temperatures across instruction-following benchmarks. Moreover, the impact of temperature is not limited to FKL; it improves a broader family of distillation objectives, enabling simple KL-based methods to achieve competitive performance against recent state-of-the-art LLM distillation approaches.