AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projections

TL;DR

AltLoRA introduces an alternating projection approach for low-rank adaptation that improves gradient approximation, integrates momentum efficiently, and achieves better performance and stability in fine-tuning large language models.

Contribution

The paper proposes AltLoRA, a novel alternating projection method that enhances gradient approximation and momentum integration in low-rank adaptation, with theoretical guarantees and improved empirical results.

Findings

AltLoRA outperforms LoRA and variants across multiple tasks.

It narrows the performance gap toward full fine-tuning.

AltLoRA maintains memory efficiency while improving stability.

Abstract

Low-Rank Adaptation (LoRA) has emerged as an effective technique for reducing memory overhead in fine-tuning large language models. However, it often suffers from sub-optimal performance compared with full fine-tuning since the update is constrained in the low-rank space. Recent variants such as LoRA-Pro attempt to mitigate this by adjusting the gradients of the low-rank matrices to approximate the full gradient. However, LoRA-Pro's solution is not unique, and different solutions can lead to significantly varying performance in ablation studies. Besides, to incorporate momentum or adaptive optimization design, approaches like LoRA-Pro must first compute the equivalent gradient, causing a higher memory cost close to full fine-tuning. A key challenge remains in integrating momentum properly into the low-rank space with lower memory cost. In this work, we propose AltLoRA, an alternating projection method that avoids the difficulties in gradient approximation brought by the joint update design, meanwhile integrating momentum without higher memory complexity. Our theoretical analysis provides convergence guarantees and further shows that AltLoRA enables stable feature learning and robustness to transformation invariance. Extensive experiments across multiple tasks demonstrate that AltLoRA outperforms LoRA and its variants, narrowing the gap toward full fine-tuning while preserving superior memory efficiency.