The paper introduces ISO-LoRA, an optimizer that improves rank utilization in Low‑Rank Adaptation (LoRA) by coupling factor updates through spectral descent on the induced tangent perturbation in weight space. Experiments on GPT‑2 adaptation show that standard optimizers like AdamW concentrate updates in a few singular directions, whereas ISO-LoRA distributes energy more evenly, leading to higher effective rank and better downstream performance across 0.1B‑7B models. The authors provide theoretical guarantees under a stylized spiked‑gradient model and demonstrate that ISO-LoRA consistently outperforms factor‑wise optimizers, especially at moderate‑to‑large LoRA ranks.
By Zihan Zhu, Zhehang Du, Xuyang Chen, Tim Tsz-Kit Lau, Jiayuan Wu, X. Y. Han, Qi Long, Weijie Su
arXiv:2607. 26247v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) fine-tunes large pretrained models at a fraction of the cost of full fine-tuning, but its performance depends strongly on how the adapters are initialized.
By Dianze Liu, Farshid Ghezelbash
arXiv:2605.07111v3 Announce Type: replace-cross
Abstract: Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides greater represe...
By Haozhan Tang, Xiuqi Zhu, Xinyin Zhang, Boxun Li, Virginia Smith, Kevin Kuo
arXiv:2602. 05988v2 Announce Type: replace Abstract: Pre-training Large Language Models (LLMs) on web-scale datasets becomes fundamental for advancing general-purpose AI.
By Keith Ando Ogawa, Bruno Lopes Yamamoto, Lucas Lauton de Alcantara, Lucas Pellicer, Rosimeire Pereira Costa, Edson Bollis, Anna Helena Reali Costa, Artur Jordao
LoRA-TSD introduces a new optimizer for low‑rank adaptation (LoRA) that treats each update as a tangent vector on the fixed‑rank matrix manifold and applies a Muon‑style spectral‑norm steepest‑descent step within that tangent space. The method avoids costly full‑matrix operations and offers a retraction that is up to 2.8× cheaper than previous manifold approaches. The authors prove that their surrogate recovers LoRA‑Pro, identify the Riemannian gradient as the natural stationarity measure, and provide the first global convergence guarantees for both LoRA‑Pro and LoRA‑TSD, achieving superior performance across multiple benchmarks with Llama and Qwen models.
By Dmitrii Andriianov, Andrey Veprikov, Aleksandr Beznosikov
arXiv:2609.37027v1 Announce Type: new
Abstract: Low-Rank Adaptation (LoRA) is a widely used approach to parameter-efficient fine-tuning (PEFT), yet a performance gap can remain relative to full fine-...
By Yihao Ouyang, Shiwei Li, Haozhao Wang, Xiandi Luo, Zhuoqi Hu, Jinglun Yu, Yichen Li, Ruixuan Li
Low-rank adaptation (LoRA) is the standard way to fine-tune large models, yet when its two factors are trained independently, the update ignores the geometry of the low-rank weight change it induces. We introduce LoRA-TSD, an optimizer that treats every LoRA step as a tangent vector of the fixed-rank matrix manifold and takes the spectral-norm steepest-descent step of Muon inside that tangent space, mapping the result back to the factors through a retraction native to the LoRA parametrization.
arXiv:2607. 22489v1 Announce Type: new Abstract: Low-Rank Adaptation (LoRA) has become a widely adopted technique for efficient neural network fine-tuning, decomposing model updates into low-rank matrices.
By Jianghui Wang, Silong Yong, Francesco Orabona, Marco Canini, Katia P. Sycara, Yaqi Xie
arXiv:2608. 19800v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) is a prominent fine-tuning method for large models, achieving competitive performance with reduced memory overhead.
By Haonan He, Xinyue Fan
arXiv:2606. 16454v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) enables efficient adaptation of large pre-trained models to downstream tasks by parameterizing weight updates with low-rank matrices.
By Junghun Oh, Sungyong Baik, Kyoung Mu Lee
arXiv:2510. 24561v3 Announce Type: replace-cross Abstract: LoRA has become a widely adopted method for PEFT, and its initialization methods have attracted increasing attention.
By Qingyue Zhang, Chang Chu, Tianren Peng, Qi Li, Xiangyang Luo, Zhihao Jiang, Shao-Lun Huang
arXiv:2607. 27680v1 Announce Type: new Abstract: Low-Rank Adaptation (LoRA) has become the standard mechanism for fine-tuning large pretrained models, yet its statistical properties remain only partially understood.
By Arunan J