EGGROLL replaces dense Gaussian perturbations in evolution strategies with low‑rank Gaussian products, enabling practical optimization of large language models while maintaining exactness on quadratic objectives. The paper analyzes the mean update field, error bounds, and shows that rank‑one perturbations add only a small variance penalty compared to dense ES. A new leave‑one‑out estimator, LOO‑ROLL, further reduces estimator MSE and improves post‑training performance on transformer blocks and GSM8K accuracy.
By Ege C. Kaya, Abolfazl Hashemi
arXiv:2610.23343v1 Announce Type: new
Abstract: Low-rank adaptation (LoRA) has become the standard method for parameter-efficient fine-tuning of large pretrained models, yet theoretical explanations...
By Long Nguyen-Chi, Quynh Nguyen, Thanh Nguyen-Cung, Binh T. Nguyen
arXiv:2607. 05872v1 Announce Type: new Abstract: Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked.
By Noel Thomas
arXiv:2610. 22794v1 Announce Type: new Abstract: A prominent family of low-rank LLM optimizers, pioneered by GaLore, performs gradient-subspace projection: at each step, they project the gradient into a low-dimensional subspace and map the update back to the full model.
By Xinyu Luo, Jincheng Zhou, Mengbo Wang, Zilin Shen, Nadia Atallah Lanman, Petros Drineas, Bruno Ribeiro, Brian Bullins
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:2611.07349v1 Announce Type: cross
Abstract: Parameter-efficient fine-tuning with LoRA is governed by rank, which controls parameter budget and locally accessible task updates. Existing dynamic-...
By Peng Xue, Guodong Fan, Guang-Yong Chen, Xing Chen
arXiv:2511. 13592v2 Announce Type: replace-cross Abstract: The existing method of GS-PowerOpt solves the non-convex optimization problem of the form $\max_{\boldsymbol{x} \in \mathbb{R}^d} f(\boldsymbol{x})$ through maximizing a Gaussian-smoothed surrogate $F_{N,\sigma}(\boldsymbol{\mu}) = \mathbb{E}_{\boldsymbol{x}\sim\mathcal{N}(\boldsymbol{\mu},\sigma^2 I_d)}[e^{N f(\boldsymbol{x})}]$.
By Chen Xu
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:2609.26077v1 Announce Type: new
Abstract: A Strassen-type algorithm has many realizations with the same exact product and multiplication count yet different fp8 error because basis changes resh...
By Shuxiao Xie, Shuyang Xie, Yuan Cao, Dezhi Ran, Wei Yang, Tao Xie
arXiv:2607. 21975v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) optimizes $J(B,A)=\mathcal L(W_\mathrm{base}+sBA)$ over two adapters $B \in \mathbb{R}^{m \times r}$ and $A \in \mathbb{R}^{r \times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\mathrm{base} \in \mathbb{R}^{m \times n}$.
By Ru Wang, Chengchang Liu, John C. S. Lui
arXiv:2610. 32142v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) is often highly sensitive to learning-rate (LR) choices.
By Disen Liao, Yaoliang Yu
arXiv:2609.37899v1 Announce Type: new
Abstract: Zero-order optimization (ZO) trains without backpropagation, making it relevant to forward-only hardware and non-differentiable loss, but its gradient...
By Francois Chaubard, Mykel J. Kochenderfer, Chris R\'e