LoRA-Null: Low-Rank Adaptation via Null Space for Large Language Models
This addresses a key issue for practitioners fine-tuning LLMs, offering an incremental improvement to LoRA by better preserving pre-trained knowledge.
The paper tackles the problem of catastrophic forgetting of pre-trained world knowledge in Large Language Models during fine-tuning with LoRA, proposing LoRA-Null which initializes adapters from the null space of activations to preserve knowledge while maintaining performance, as validated on LLaMA models across tasks like Code, Math, and Instruction Following.
Low-Rank Adaptation (LoRA) is the leading parameter-efficient fine-tuning method for Large Language Models (LLMs). However, the fine-tuned LLMs encounter the issue of catastrophic forgetting of the pre-trained world knowledge. To address this issue, inspired by theoretical insights of null space, we propose LoRA-Null, i.e., Low-Rank Adaptation via null space, which builds adapters initialized from the null space of the pre-trained knowledge activation. Concretely, we randomly collect a few data samples and capture their activations after passing through the LLM layer. We perform Singular Value Decomposition on the input activations to obtain their null space. We use the projection of the pre-trained weights onto the null space as the initialization for adapters. Experimental results demonstrate that this initialization approach can effectively preserve the original pre-trained world knowledge of the LLMs during fine-tuning. Additionally, if we freeze the values of the down-projection matrices during fine-tuning, it achieves even better preservation of the pre-trained world knowledge. LoRA-Null effectively preserves pre-trained world knowledge while maintaining strong fine-tuning performance, as validated by extensive experiments on LLaMA series (LLaMA2, LLaMA3, LLaMA3.1, and LLaMA3.2) across Code, Math, and Instruction Following tasks. We also provide a theoretical guarantee for the capacity of LoRA-Null to retain pre-trained knowledge. Code is in https://github.com/HungerPWAY/LoRA-Null.