LoRA vs Full Fine-tuning: An Illusion of Equivalence

TL;DR

This paper compares LoRA and full fine-tuning of large language models, revealing that LoRA introduces unique high-rank singular vectors called intruder dimensions which affect model forgetting and performance.

Contribution

It demonstrates that LoRA and full fine-tuning produce fundamentally different spectral structures in weight matrices, especially regarding intruder dimensions and their impact on forgetting.

Findings

LoRA introduces high-rank intruder dimensions not present in full fine-tuning.

Intruder dimensions are causally linked to model forgetting.

Scaling down intruder dimensions improves pre-training distribution modeling with minimal performance loss.

Abstract

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to effectively fine-tune LLMs with an extreme reduction in trainable parameters. But, \emph{are their learned solutions really equivalent?} We study how LoRA and full-finetuning change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that LoRA and full fine-tuning yield weight matrices whose singular value decompositions exhibit very different structure: weight matrices trained with LoRA have new, high-ranking singular vectors, which we call \emph{intruder dimensions}, while those trained with full fine-tuning do not. Further, we extend the finding that LoRA forgets less than full fine-tuning and find its forgetting is vastly localized to the intruder dimension -- by causally intervening on the intruder dimensions by changing their associated singular values post-fine-tuning, we show that they cause forgetting. Moreover, scaling them down significantly improves modeling of the pre-training distribution with a minimal drop in downstream task performance. Given this, we should expect accumulating intruder dimensions to be harmful and lead to more forgetting. This will be amplified during continual learning because of sequentially fine-tuning, and we show that LoRA models do accumulate intruder dimensions here tend to perform worse in this setting, emphasizing the practicality of our findings.