Paper Detail

One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning

Huiyi Wang, Daijiao Liu, Lina Yao, Dong Gong

arxiv Score 12.8

Published 2026-09-05 · First seen 2026-09-09

General AI

Abstract

Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the nominal rank budget. To address this, we propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate, computed online from training-time signals and mean-normalized per module to preserve the global LR budget. AnLR-LoRA instantiates this model with two signals available during AdamW optimization, namely function-space velocity and Adam SNR, as a lightweight scheme with no extra trainable parameters. Across commonsense reasoning, natural language generation and visual instruction-tuning benchmarks, AnLR-LoRA consistently improves over LoRA while encouraging broader use of rank capacity, with gains that remain robust across a wide range of global learning rates and transfer cleanly to other LoRA variants.

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BibTeX

@article{wang2026one,
  title = {One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning},
  author = {Huiyi Wang and Daijiao Liu and Lina Yao and Dong Gong},
  year = {2026},
  abstract = {Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the },
  url = {https://arxiv.org/abs/2609.05885},
  keywords = {cs.LG},
  eprint = {2609.05885},
  archiveprefix = {arXiv},
}

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