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
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.
The paper introduces a geometry-aware Bayesian fine‑tuning method that uses Stein variational gradient descent on the Stiefel manifold. By transporting low‑rank adapter matrices along this manifold, the approach preserves orthogonality constraints and yields multiple inference solutions, enabling uncertainty quantification. Experiments demonstrate improved model calibration and higher prediction accuracy compared to Euclidean‑space SVGD and related methods.
By Quang-Duy Tran, Trung Le, Bao Duong, Phuoc Nguyen, Thin Nguyen
arXiv:2603. 29824v2 Announce Type: replace Abstract: Parameter-efficient fine-tuning methods such as LoRA enable efficient adaptation of large pretrained models, but often lag behind full fine-tuning in both convergence speed and final performance.
By Fr\'ed\'eric Zheng, Alexandre Prouti\`ere
arXiv:2510. 01878v2 Announce Type: replace Abstract: Low-rank gradient optimization for large language models is currently divided into two categories: structured methods that rigorously identify subspaces, and randomized approaches employed primarily for computational efficiency.
By Sahar Rajabi, Nayeema Nonta, Sirisha Rambhatla
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:2609.21039v1 Announce Type: new
Abstract: A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matri...
By Emanuele Zangrando, Marco Sutti, Francesco Tudisco
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:2606. 14970v1 Announce Type: new Abstract: Fine-tuning large language models (LLMs) has become a central application of modern optimization, enabling pretrained models to adapt to diverse downstream tasks and domain-specific data.
By Dmitriy Bystrov, Daniil Medyakov, Dmitry Bylinkin, Aleksandr Beznosikov
arXiv:2606. 18650v1 Announce Type: new Abstract: As Large Language Model (LLM) datasets scale to trillions of tokens, data selection has emerged as a critical frontier to filter out uninformative noise and construct adaptive learning trajectories.
By Jiaxing Wang, Deping Xiang, Jin Xu, Zirui Liu, Zicheng Zhang, Guoqiang Gong, Jun Fang, Chao Liu, Pengzhang Liu, Tongxuan Liu, Ke Zhang, Qixia Jiang
arXiv:2608. 05783v1 Announce Type: cross Abstract: Machine unlearning has become a critical capability for safely removing specific, sensitive knowledge from large language models (LLMs).
By Pawe{\l} Batorski, Przemys{\l}aw Spurek, Paul Swoboda
arXiv:2601. 04710v2 Announce Type: replace-cross Abstract: Fine-tuning large language models (LLMs) achieves strong performance but is often limited by the memory overhead of backpropagation.
By Feihu Jin, Shipeng Cen, Ying Tan