# Learning Rate Scaling across LoRA Ranks and Transfer to Full Finetuning

arXiv: https://arxiv.org/abs/2602.06204 · HTML: https://mlsanity.com/paper/2602.06204/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 85 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 30 of 58)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)

## Built on by (most cited first, 9 of 9)

- [LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold](https://mlsanity.com/paper/2606.12921/) (2026)
- [PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer](https://mlsanity.com/paper/2607.17620/) (2026)
- [Subtitle-Aligned Fine-Tuning of Whisper for Swiss German ASR: Benchmark Contamination, Convention Mismatch, and an Honest Baseline at 25.6% WER (13.8% cWER)](https://mlsanity.com/paper/2606.07608/) (2026)
- [PreFT: Prefill-only finetuning for efficient inference](https://mlsanity.com/paper/2605.14217/) (2026)
- [Learning When to Adapt](https://mlsanity.com/paper/2605.19028/) (2026)
- [The Hidden Power of Scaling Factor in LoRA Optimization](https://mlsanity.com/paper/2606.12883/) (2026)
- [One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning](https://mlsanity.com/paper/2609.05885/) (2026)
- [Behavior Quotient Learning for Low-Rank Adaptation of LLM Agents](https://mlsanity.com/paper/2609.12896/) (2026)
- [LoRA's Second Descent Extends Beyond Parameter Parity](https://mlsanity.com/paper/2610.04507/) (2026)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) is a standard tool for parameter-efficient finetuning of large models. While it induces a small memory footprint, its training dynamics can be surprisingly complex as they depend on several hyperparameters such as initialization, adapter rank, and learning rate. In particular, it is unclear how the optimal learning rate scales with adapter rank, which forces practitioners to re-tune the learning rate whenever the rank is changed. In this paper, we introduce Maximal-Update Adaptation (μA), a theoretical framework that characterizes how the "optimal" learning rate should scale with model width and adapter rank to produce stable, non-vanishing feature updates under standard configurations. μA is inspired from the Maximal-Update Parametrization (μP) in pretraining. Our analysis leverages techniques from hyperparameter transfer and reveals that the optimal learning rate exhibits different scaling patterns depending on initialization and LoRA scaling factor. Specifically, we identify two regimes: one where the optimal learning rate remains roughly invariant across ranks, and another where it scales inversely with rank. We further identify a configuration that allows learning rate transfer from LoRA to full finetuning, drastically reducing the cost of learning rate tuning for full finetuning. Experiments across language, vision, vision--language, image generation, and reinforcement learning tasks validate our scaling rules and show that learning rates tuned on LoRA transfer reliably to full finetuning.