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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.
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...
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.
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.
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-...