Beyond Zero Initialization: Investigating the Impact of Non-Zero Initialization on LoRA Fine-Tuning Dynamics

TL;DR

This paper explores how initializing LoRA layers with non-zero values affects fine-tuning dynamics, revealing improved robustness and that strict starting from pretrained weights is unnecessary, supported by theoretical analysis and experiments.

Contribution

It provides the first theoretical analysis of non-zero initialization in LoRA and demonstrates its benefits for robustness and flexibility in fine-tuning.

Findings

Non-zero initialization improves robustness to learning rate choices.

Non-zero initialization generally does not harm fine-tuning performance.

Theoretical analysis supports empirical results.

Abstract

Low-rank adaptation (LoRA) is a widely used parameter-efficient fine-tuning method. In standard LoRA layers, one of the matrices, $A$ or $B$, is initialized to zero, ensuring that fine-tuning starts from the pretrained model. However, there is no theoretical support for this practice. In this paper, we investigate the impact of non-zero initialization on LoRA's fine-tuning dynamics from an infinite-width perspective. Our analysis reveals that, compared to zero initialization, simultaneously initializing $A$ and $B$ to non-zero values improves LoRA's robustness to suboptimal learning rates, particularly smaller ones. Further analysis indicates that although the non-zero initialization of $AB$ introduces random noise into the pretrained weight, it generally does not affect fine-tuning performance. In other words, fine-tuning does not need to strictly start from the pretrained model. The validity of our findings is confirmed through extensive experiments across various models and datasets. The code is available at https://github.com/Leopold1423/non_zero_lora-icml25.