FuRA: Full-Rank Parameter-Efficient Fine-Tuning with Spectral Preconditioning
FuRA is a novel full-rank parameter-efficient fine-tuning method that preserves pretrained robust features via spectral preconditioning, outperforming full fine-tuning and LoRA on LLM and VLM fine-tuning; its 4-bit quantized variant QFuRA also surpasses QLoRA.
Article intelligence
Key points
- Existing methods like full FT and LoRA ignore pretrained spectral structure, causing noisy gradients to perturb features
- FuRA uses block tensor-train factorization, freezes pretrained SVD bases, and optimizes only compact core and singular values
- Achieves +1.37 on LLaMA-3-8B commonsense reasoning over full FT, and excels in RL for math reasoning and visual instruction tuning
- 4-bit quantized QFuRA also surpasses QLoRA
Why it matters
This matters because existing methods like full FT and LoRA ignore pretrained spectral structure, causing noisy gradients to perturb features.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.22869] FuRA: Full-Rank Parameter-Efficient Fine-Tuning with Spectral Preconditioning
[Submitted on 19 May 2026]
Title:FuRA: Full-Rank Parameter-Efficient Fine-Tuning with Spectral Preconditioning
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Abstract: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 this https URL
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2605.22869 [cs.LG]
(or arXiv:2605.22869v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.22869
arXiv-issued DOI via DataCite
Submission history
From: Yequan Zhao [view email] [v1] Tue, 19 May 2026 22:11:25 UTC (1,111 KB)
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