# Stable-LoRA: Stabilizing Feature Learning of Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2603.05204 · HTML: https://mlsanity.com/paper/2603.05204/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [On the Impact of the Activation Function on Deep Neural Networks Training](https://mlsanity.com/paper/1902.06853/) (2019)
- [The Impact of Initialization on LoRA Finetuning Dynamics](https://mlsanity.com/paper/2406.08447/) (2024)
- [Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models](https://mlsanity.com/paper/2402.02347/) (2024)
- [LoRA Done RITE: Robust Invariant Transformation Equilibration for LoRA Optimization](https://mlsanity.com/paper/2410.20625/) (2024)
- [On the infinite-depth limit of finite-width neural networks](https://mlsanity.com/paper/2210.00688/) (2022)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) is a widely adopted parameter-efficient method for fine-tuning Large Langauge Models. It updates the weight matrix as W=W0+sBA, where W0 is the original frozen weight, s is a scaling factor and A,B are trainable low-rank matrices. Despite its robust empirical effectiveness, the theoretical foundations of LoRA remain insufficiently understood, particularly with respect to feature learning stability. In this paper, we first establish that, LoRA can, in principle, naturally achieve and sustain stable feature learning (i.e., be self-stabilized) under appropriate hyper-parameters and initializations of A and B. However, we also uncover a fundamental limitation that the necessary non-zero initialization of A compromises self-stability, leading to suboptimal performances. To address this challenge, we propose Stable-LoRA, a weight-shrinkage optimization strategy that dynamically enhances stability of LoRA feature learning. By progressively shrinking A during the earliest training steps, Stable-LoRA is both theoretically and empirically validated to effectively eliminate instability of LoRA feature learning while preserving the benefits of the non-zero start. Experiments show that Stable-LoRA consistently outperforms other baselines across diverse models and tasks, with no additional memory usage and only negligible computation overheads. The code is available at https://github.com/Yize-Wu/Stable-LoRA.