# BiDoRA: Bi-level Optimization-Based Weight-Decomposed Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2410.09758 · HTML: https://mlsanity.com/paper/2410.09758/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 72 references that are in the map.
- First posted on arXiv 13 Oct 2024.

## Builds on (most cited first, 30 of 47)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [CIDEr: Consensus-based Image Description Evaluation](https://mlsanity.com/paper/1411.5726/) (2014)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Pre-trained Models for Natural Language Processing: A Survey](https://mlsanity.com/paper/2003.08271/) (2020)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Side Adapter Network for Open-Vocabulary Semantic Segmentation](https://mlsanity.com/paper/2302.12242/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [The E2E Dataset: New Challenges For End-to-End Generation](https://mlsanity.com/paper/1706.09254/) (2017)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [AdapterDrop: On the Efficiency of Adapters in Transformers](https://mlsanity.com/paper/2010.11918/) (2020)
- [Towards moderate overparameterization: global convergence guarantees for training shallow neural networks](https://mlsanity.com/paper/1902.04674/) (2019)
- [Exploring Versatile Generative Language Model Via Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2004.03829/) (2020)
- [Bilateral Multi-Perspective Matching for Natural Language Sentences](https://mlsanity.com/paper/1702.03814/) (2017)
- [Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks](https://mlsanity.com/paper/1909.12292/) (2019)

## Built on by (most cited first, 4 of 4)

- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [A First-order Generative Bilevel Optimization Framework for Diffusion Models](https://mlsanity.com/paper/2502.08808/) (2025)
- [EDoRA: Efficient Weight-Decomposed Low-Rank Adaptation via Singular Value Decomposition](https://mlsanity.com/paper/2501.12067/) (2025)
- [MAP: Revisiting Weight Decomposition for Low-Rank Adaptation](https://mlsanity.com/paper/2505.23094/) (2025)

## Abstract (arXiv)

Parameter-efficient fine-tuning (PEFT) is a flexible and efficient method for adapting large language models (LLMs) to downstream tasks. Among these methods, weight-decomposed low-rank adaptation (DoRA) is a promising approach that decomposes weight matrices into magnitude and direction components to mimic full fine-tuning (FT) better. However, DoRA's simultaneous optimization of these components makes it over-expressive, increases the risk of overfitting, and creates a coupled updating pattern that limits its learning capacity. To address these issues, we propose Bi-level Optimization-Based Weight-Decomposed Low-Rank Adaptation (BiDoRA), a novel PEFT method based on a bi-level optimization framework. BiDoRA fundamentally differs from DoRA by optimizing the magnitude and direction in two separate, asynchronous loops using distinct training and validation data splits. This decoupled optimization process effectively mitigates overfitting and allows for more flexible updates that align even more closely with FT. For instance, weight decomposition analysis shows BiDoRA achieves a magnitude-direction update correlation of -8.042, significantly closer to the FT ideal compared to -1.784 for DoRA. Evaluation of BiDoRA on diverse tasks spanning natural language understanding, generation, token classification, and extremely small biomedical datasets reveals that it consistently outperforms DoRA and a wide range of leading PEFT methods. This improvement is statistically significant, as demonstrated on the GLUE benchmark where BiDoRA surpasses DoRA with a p-value of 2.4×10-4 in terms of the Wilcoxon signed-rank test. The code for BiDoRA is available at https://github.com/t2ance/BiDoRA.