# Dual Decomposition of Weights and Singular Value Low Rank Adaptation

arXiv: https://arxiv.org/abs/2505.14367 · HTML: https://mlsanity.com/paper/2505.14367/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [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)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [KronA: Parameter Efficient Tuning with Kronecker Adapter](https://mlsanity.com/paper/2212.10650/) (2022)
- [Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization](https://mlsanity.com/paper/2311.06243/) (2023)
- [Cross-lingual Prompting: Improving Zero-shot Chain-of-Thought Reasoning across Languages](https://mlsanity.com/paper/2310.14799/) (2023)
- [LoRA-XS: Low-Rank Adaptation with Extremely Small Number of Parameters](https://mlsanity.com/paper/2405.17604/) (2024)
- [Conditional Adapters: Parameter-efficient Transfer Learning with Fast Inference](https://mlsanity.com/paper/2304.04947/) (2023)
- [Parameter-Efficient Fine-Tuning without Introducing New Latency](https://mlsanity.com/paper/2305.16742/) (2023)
- [SVFT: Parameter-Efficient Fine-Tuning with Singular Vectors](https://mlsanity.com/paper/2405.19597/) (2024)
- [FACTUAL: A Benchmark for Faithful and Consistent Textual Scene Graph Parsing](https://mlsanity.com/paper/2305.17497/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Unified Study of LoRA Variants: Taxonomy, Review, Codebase, and Empirical Evaluation](https://mlsanity.com/paper/2601.22708/) (2026)

## Abstract (arXiv)

Parameter-Efficient Fine-Tuning (PEFT) has emerged as a critical paradigm for adapting Large Language Models (LLMs) to downstream tasks, among which Low-rank Adaptation (LoRA) represents one of the most widely adopted methodologies. However, existing LoRA-based approaches exhibit two fundamental limitations: unstable training dynamics and inefficient knowledge transfer from pre-trained models, both stemming from random initialization of adapter parameters. To overcome these challenges, we propose DuDe, a novel approach that decomposes weight matrices into magnitude and direction components, employing Singular Value Decomposition (SVD) for principled initialization. Our comprehensive evaluation demonstrates DuDe's superior performance and robustness, achieving up to 48.35% accuracy on MMLU and 62.53% (± 1.59) accuracy on GSM8K. Our theoretical analysis and empirical validation collectively demonstrate that DuDe's decomposition strategy enhances optimization stability and better preserves pre-trained representations, particularly for domain-specific tasks requiring specialized knowledge. The combination of robust empirical performance and rigorous theoretical foundations establishes DuDe as a significant contribution to PEFT methodologies for LLMs.