LoRA-GA$^2$: Low Rank Adaptation with Multi-step Gradient Adaptive Alignment

• URL: http://arxiv.org/abs/2608.19800v1
• Date: Thu, 20 Aug 2026 08:55:05 GMT
• Title: LoRA-GA$^2$: Low Rank Adaptation with Multi-step Gradient Adaptive Alignment
• Abstract summary: Low-Rank Adaptation (LoRA) is a prominent fine-tuning method for large models.<n>LoRA-GA$2$ is an effective fine-tuning algorithm that fully leverages multi-step gradient information.
• Score: 3.934797837010563
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Low-Rank Adaptation (LoRA) is a prominent fine-tuning method for large models, achieving competitive performance with reduced memory overhead. However, a persistent performance gap remains between LoRA and full fine-tuning. Recent studies have sought to narrow this gap by employing one-step gradient approximations of pretrained weights to align LoRA updates with the principal directions or intrinsic dimensionalities of full fine-tuning updates. Nevertheless, these approaches fail to capture the full dynamics of the gradients. In this paper, we propose LoRA-GA$^2$, an effective fine-tuning algorithm that fully leverages multi-step gradient information. Specifically, we introduce a lightweight probe for multi-step gradients of pretrained weights that incurs no additional GPU memory cost and only marginal time overhead. We further employ a spectrum-aware, importance-based rank allocation and optimal initialization derived from multi-step gradients. Extensive experimental results demonstrate that LoRA-GA$^2$ consistently outperforms existing LoRA variants while preserving the efficiency advantages of vanilla LoRA. For instance, LoRA-GA$^2$ surpasses the leading baseline by an average of 0.66 points on the GLUE benchmark, and outperforms the strongest baseline by 1.03 points on GSM8K and 0.87 points on HumanEval, respectively.

Related papers

• LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates [48.87937677659571]
  Low-rank adaptation (LoRA) is the standard way to finetune large models.<n>We introduce LoRA-TSD, an adapter that treats every LoRA step as a tangent to the fixed-rank matrix manifold.<n>We give the first global convergence guarantees for both LoRA-Pro and LoRA-TSD, with rates that drive the factor-gradient norms to zero.
  arXiv  Detail & Related papers  (2026-09-02T15:41:45Z)
• SOS-LoRA: Static Orthogonal-Subspace Low-Rank Adaptation with Fixed Multi-Scale Scaling [17.873016968298483]
  Low-Rank Adaptation (LoRA) is a widely used parameter-efficient fine-tuning (PEFT) method for large language models.<n>We propose Static Orthogonal Subspace LoRA (SOS-LoRA), a drop-in extension that re parameterizes a rank-rtot update as a sum of K static experts.
  arXiv  Detail & Related papers  (2026-06-27T03:25:36Z)
• Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation [85.89510825889168]
  We introduce LoRA-Pre, a novel low-rank system for efficient pre-training.<n>LoRA-Pre decomposing the momentum matrix into a compact low-rank subspace within the online linear learner.<n>We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family.
  arXiv  Detail & Related papers  (2026-02-27T18:57:06Z)
• Beyond SGD, Without SVD: Proximal Subspace Iteration LoRA with Diagonal Fractional K-FAC [50.36542772932594]
  Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights.<n>In this work, we address the gap between training with full steps with low-rank projections (SVDLoRA) and LoRA fine-tuning.<n>We propose LoRSum, a memory-efficient subroutine that closes this gap for gradient descent.
  arXiv  Detail & Related papers  (2026-02-18T13:41:41Z)
• Faster Than SVD, Smarter Than SGD: The OPLoRA Alternating Update [50.36542772932594]
  Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights.<n>There is still a gap between full training with low-rank projections (SVDLoRA) and LoRA fine-tuning, indicating that LoRA steps can be further improved.
  arXiv  Detail & Related papers  (2025-09-24T10:32:50Z)
• AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projections [42.88697930464368]
  Low-Rank Adaptation (LoRA) has emerged as an effective technique for reducing memory overhead in fine-tuning large language models.<n>It often suffers from sub-optimal performance compared with full fine-tuning since the update is constrained in the low-rank space.<n>We propose AltLoRA, an alternating projection method that avoids the difficulties in gradient approximation brought by the joint update design.
  arXiv  Detail & Related papers  (2025-05-18T15:10:38Z)
• Flat-LoRA: Low-Rank Adaptation over a Flat Loss Landscape [52.98187034726091]
  We introduce Flat-LoRA, which aims to identify a low-rank adaptation situated in a flat region of the full parameter space.<n>We show that Flat-LoRA improves both in-domain and out-of-domain generalization.
  arXiv  Detail & Related papers  (2024-09-22T11:24:10Z)
• LoRA-Pro: Are Low-Rank Adapters Properly Optimized? [121.0693322732454]
  Low-rank adaptation, also known as LoRA, has emerged as a prominent method for parameter-efficient fine-tuning of foundation models.<n>Despite its computational efficiency, LoRA still yields inferior performance compared to full fine-tuning.<n>We introduce LoRA-Pro, a method that enhances LoRA's performance by strategically adjusting the gradients of low-rank matrices.
  arXiv  Detail & Related papers  (2024-07-25T17:57:12Z)
• LoRA-GA: Low-Rank Adaptation with Gradient Approximation [5.685201910521295]
  Fine-tuning large-scale pretrained models is prohibitively expensive in terms of computational and memory costs. LoRA offers a cost-effective alternative by fine-tuning an auxiliary low-rank model that has significantly fewer parameters. LoRA converges at a considerably slower rate compared to full fine-tuning, leading to increased overall compute and often worse test performance.
  arXiv  Detail & Related papers  (2024-07-06T08:37:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.