# FRoD: Full-Rank Efficient Fine-Tuning with Rotational Degrees for Fast Convergence

arXiv: https://arxiv.org/abs/2512.23485 · HTML: https://mlsanity.com/paper/2512.23485/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 21 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning](https://mlsanity.com/paper/2311.12023/) (2023)
- [SVFT: Parameter-Efficient Fine-Tuning with Singular Vectors](https://mlsanity.com/paper/2405.19597/) (2024)
- [VB-LoRA: Extreme Parameter Efficient Fine-Tuning with Vector Banks](https://mlsanity.com/paper/2405.15179/) (2024)
- [Singular Value Fine-tuning: Few-shot Segmentation requires Few-parameters Fine-tuning](https://mlsanity.com/paper/2206.06122/) (2022)
- [Make LoRA Great Again: Boosting LoRA with Adaptive Singular Values and Mixture-of-Experts Optimization Alignment](https://mlsanity.com/paper/2502.16894/) (2025)
- [SVFit: Parameter-Efficient Fine-Tuning of Large Pre-Trained Models Using Singular Values](https://mlsanity.com/paper/2409.05926/) (2024)

## Abstract (arXiv)

Parameter-efficient fine-tuning (PEFT) methods have emerged as a practical solution for adapting large foundation models to downstream tasks, reducing computational and memory costs by updating only a small subset of parameters. Among them, approaches like LoRA aim to strike a balance between efficiency and expressiveness, but often suffer from slow convergence and limited adaptation capacity due to their inherent low-rank constraints. This trade-off hampers the ability of PEFT methods to capture complex patterns needed for diverse tasks. To address these challenges, we propose FRoD, a novel fine-tuning method that combines hierarchical joint decomposition with rotational degrees of freedom. By extracting a globally shared basis across layers and injecting sparse, learnable perturbations into scaling factors for flexible full-rank updates, FRoD enhances expressiveness and efficiency, leading to faster and more robust convergence. On 20 benchmarks spanning vision, reasoning, and language understanding, FRoD matches full model fine-tuning in accuracy, while using only 1.72% of trainable parameters under identical training budgets.