# Dual LoRA: Enhancing LoRA with Magnitude and Direction Updates

arXiv: https://arxiv.org/abs/2512.03402 · HTML: https://mlsanity.com/paper/2512.03402/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [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)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [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)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [Knowledgeable Prompt-tuning: Incorporating Knowledge into Prompt Verbalizer for Text Classification](https://mlsanity.com/paper/2108.02035/) (2021)
- [Exploring Versatile Generative Language Model Via Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2004.03829/) (2020)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Delta-LoRA: Fine-Tuning High-Rank Parameters with the Delta of Low-Rank Matrices](https://mlsanity.com/paper/2309.02411/) (2023)
- [Dynamic Prefix-Tuning for Generative Template-based Event Extraction](https://mlsanity.com/paper/2205.06166/) (2022)
- [RandLoRA: Full-rank parameter-efficient fine-tuning of large models](https://mlsanity.com/paper/2502.00987/) (2025)

## Abstract (arXiv)

Low-rank adaptation (LoRA) is one of the most popular methods among parameter-efficient fine-tuning (PEFT) methods to adapt pre-trained large language models (LLMs) to specific downstream tasks. However, the model trained based on LoRA often has an unsatisfactory performance due to its low-rank assumption. In this paper, we propose a novel method called Dual LoRA to improve the performance by incorporating an inductive bias into the original LoRA. Specifically, we separate low-rank matrices into two groups: the magnitude group to control whether or not and how far we should update a parameter and the direction group to decide whether this parameter should move forward or backward, to better simulate the parameter updating process of the full fine-tuning based on gradient-based optimization algorithms. We show that this can be simply achieved by adding a ReLU function to the magnitude group and a sign function to the direction group. We conduct several experiments over a wide range of NLP tasks, including natural language understanding (NLU) and commonsense reasoning datasets on RoBERTa, DeBERTa, and LLaMA-1/2/3 as baseline models. The results show that we consistently outperform LoRA and its state-of-the-art variants with the same number of trainable parameters.