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.
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: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
arXiv:2606. 00428v1 Announce Type: cross Abstract: Low-rank adapters are usually compared by sweeping a small set of ranks, but the rank also fixes the resolution of the parameter budget.
By Xinjue Wang, Xiuheng Wang, Yejun Zhang, Sergiy A. Vorobyov, Esa Ollila, Zhi-Yong Wang
ChainDoRA is a new parameter‑efficient fine‑tuning framework for large language models that replaces the dense low‑rank factorization of LoRA with a connected Tensor‑Train (TT) chain. By separating weight magnitude and direction and using a TT rank to control representation capacity, ChainDoRA achieves higher average accuracy on seven commonsense reasoning benchmarks while dramatically reducing trainable parameters—down to 5.35 M versus 56 M for LoRA and DoRA. Ablation studies show that the TT parameterization offers controllable trade‑offs between parameter cost and accuracy.
By Ashfak Yeafi, Mehedi Hasan, Md Khairul Islam
arXiv:2606. 13767v1 Announce Type: cross Abstract: Low-rank adaptation (LoRA) and its variants provide a memory- and compute-efficient alternative to full fine-tuning of pre-trained models.
By Elijah Cadenhead, Cristian McGee, Xin Li, El Houcine Bergou, Aritra Dutta
The paper introduces READ, a method for composing low‑rank adapters (LoRA) in large language models. By rewriting each adapter into a balanced canonical form and enforcing a one‑directional coupling, READ allows new skills to read but never write into the output subspaces of existing skills, eliminating interference. Experiments on four benchmark suites and two model families show that READ consistently outperforms existing baselines, improving SuperGLUE scores by over twenty points and domain suite scores by more than seven points.
By Zeyan Li, Panqi Yang, Qirong Guo, Shengda Zhuo, SIyuan Qiu, Hu Xu, Chun Li, Jianfeng Xu
arXiv:2607. 16252v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) is a widely used parameter-efficient fine-tuning (PEFT) method for large language models.
By Yupeng Chang, Yuan Wu, Yi Chang
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:2607. 17620v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices.
By Nikhil Ghosh, Tetiana Parshakova, Robert M. Gower
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
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