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