arXiv Machine Learning
A Riemannian Geometry for Low-rank Adaptation
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv Machine Learning
Jul 30
Between Gradient and Natural Gradient: A Continuum of LoRA Initializations
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.
arXiv AI
Jun 16
SDS-LoRA: Overcoming Anisotropic Gradient Scaling in Low-Rank Adaptation
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.
arXiv Machine Learning
Jul 27
\k{appa}-LoRA: Condition Numbers Reveal Which LoRA Matrices Worth Updating
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.
arXiv Machine Learning
Sep 3
LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates
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.
Hugging Face Trending Papers
Sep 2
LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates
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 Machine Learning
Sep 21
Stiefel-AdamW: Geometry-Aware AdamW for Linear Factorization Blocks
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...