# Decouple and Orthogonalize: A Data-Free Framework for LoRA Merging

arXiv: https://arxiv.org/abs/2505.15875 · HTML: https://mlsanity.com/paper/2505.15875/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 51 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 30 of 45)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [BBQ: A Hand-Built Bias Benchmark for Question Answering](https://mlsanity.com/paper/2110.08193/) (2021)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks](https://mlsanity.com/paper/2312.06795/) (2023)
- [Model merging with SVD to tie the Knots](https://mlsanity.com/paper/2410.19735/) (2024)
- [Twin-Merging: Dynamic Integration of Modular Expertise in Model Merging](https://mlsanity.com/paper/2406.15479/) (2024)
- [EMR-Merging: Tuning-Free High-Performance Model Merging](https://mlsanity.com/paper/2405.17461/) (2024)
- [Parameter Competition Balancing for Model Merging](https://mlsanity.com/paper/2410.02396/) (2024)

## Built on by (most cited first, 18 of 18)

- [The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants](https://mlsanity.com/paper/2505.19797/) (2025)
- [Beyond GPT-5: Making LLMs Cheaper and Better via Performance-Efficiency Optimized Routing](https://mlsanity.com/paper/2508.12631/) (2025)
- [MergeVLA: Cross-Skill Model Merging Toward a Generalist Vision-Language-Action Agent](https://mlsanity.com/paper/2511.18810/) (2025)
- [ThanoRA: Task Heterogeneity-Aware Multi-Task Low-Rank Adaptation](https://mlsanity.com/paper/2505.18640/) (2025)
- [Towards Reversible Model Merging For Low-rank Weights](https://mlsanity.com/paper/2510.14163/) (2025)
- [Compress then Merge: From Multiple LoRAs into One Low-Rank Adapter](https://mlsanity.com/paper/2606.03723/) (2026)
- [Preference-Aligned LoRA Merging: Preserving Subspace Coverage and Addressing Directional Anisotropy](https://mlsanity.com/paper/2603.26299/) (2026)
- [M2A: Synergizing Mathematical and Agentic Reasoning in Large Language Models](https://mlsanity.com/paper/2605.09879/) (2026)
- [Online Data Selection Is Implicit Alignment](https://mlsanity.com/paper/2607.07023/) (2026)
- [Efficient Modular Learning through Naive LoRA Summation: Leveraging Orthogonality in High-Dimensional Models](https://mlsanity.com/paper/2508.11985/) (2025)
- [A Diffusion-Driven Fine-Grained Nodule Synthesis Framework for Enhanced Lung Nodule Detection from Chest Radiographs](https://mlsanity.com/paper/2603.01659/) (2026)
- [SSAM: Singular Subspace Alignment for Merging Multimodal Large Language Models](https://mlsanity.com/paper/2603.21584/) (2026)
- [FREE-Switch: Frequency-based Dynamic LoRA Switch for Style Transfer](https://mlsanity.com/paper/2604.10023/) (2026)
- [Training-Free Multi-Concept LoRA Composition with Prompt-Aware Weighting](https://mlsanity.com/paper/2606.03792/) (2026)
- [Co-Adaptive Multi-Task LoRA: Transfer-Aware, Label-Free Control of Domain Participation](https://mlsanity.com/paper/2607.03522/) (2026)
- [MED-DSLC: Multi-Expert-Domain Classification via Domain Supervision and Logit Calibration](https://mlsanity.com/paper/2607.10985/) (2026)
- [Not All Ranks Are Equal: Budget-Aware LoRA Merging Across Tasks](https://mlsanity.com/paper/2609.22237/) (2026)
- [From Task Mixtures to Specialized Experts](https://mlsanity.com/paper/2610.00580/) (2026)

## Abstract (arXiv)

With more open-source models available for diverse tasks, model merging has gained attention by combining models into one, reducing training, storage, and inference costs. Current research mainly focuses on model merging for full fine-tuning, overlooking the popular LoRA. However, our empirical analysis reveals that: a) existing merging methods designed for full fine-tuning perform poorly on LoRA; b) LoRA modules show much larger parameter magnitude variance than full fine-tuned weights; c) greater parameter magnitude variance correlates with worse merging performance. Considering that large magnitude variances cause deviations in the distribution of the merged parameters, resulting in information loss and performance degradation, we propose a Decoupled and Orthogonal merging approach(DO-Merging). By separating parameters into magnitude and direction components and merging them independently, we reduce the impact of magnitude differences on the directional alignment of the merged models, thereby preserving task information. Furthermore, we introduce a data-free, layer-wise gradient descent method with orthogonal constraints to mitigate interference during the merging of direction components. We provide theoretical guarantees for both the decoupling and orthogonal components. And we validate through extensive experiments across vision, language, and multi-modal domains that our proposed DO-Merging can achieve significantly higher performance than existing merging methods at a minimal cost. Notably, each component can be flexibly integrated with existing methods, offering near free-lunch improvements across tasks.