# FuRA: Full-Rank Parameter-Efficient Fine-Tuning with Spectral Preconditioning

arXiv: https://arxiv.org/abs/2605.22869 · HTML: https://mlsanity.com/paper/2605.22869/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 50 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 30 of 41)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)

## Abstract (arXiv)

Both full fine-tuning (Full FT) and parameter-efficient fine-tuning methods such as LoRA introduce weight updates without accounting for the spectral structure established during pretraining. As a result, noisy gradients from limited fine-tuning data can perturb robust pretrained features. We identify spectral preconditioning as the missing ingredient: reparameterizing each weight matrix through its full-rank singular value decomposition (SVD) and freezing one singular basis constrains updates to the pretrained column space, yielding a preconditioned optimization scheme that outperforms unconstrained Full FT at the same trainable parameter count. Building on this insight, we propose FuRA (Full-Rank Adaptation), an efficient full-rank adaptation framework based on a block tensor-train factorization W = LSR, where the large core L is fixed to the pretrained block-wise SVD basis, while only the compact core R and the block-wise singular values S are optimized. This design simultaneously provides full-rank spectral preconditioning, preserves full-rank update expressivity, and achieves parameter, memory, and step-time efficiency comparable to LoRA. FuRA consistently outperforms Full FT across multiple settings, including LLM fine-tuning (+1.37 on LLaMA-3-8B commonsense reasoning), LLM reinforcement learning for mathematical reasoning, and visual instruction tuning for VLMs. Furthermore, the 4-bit quantized variant, QFuRA, also surpasses QLoRA. Code is available at https://github.com/olokevin/FuRA-NIPS