# Label-Free Cross-Task LoRA Merging with Null-Space Compression

arXiv: https://arxiv.org/abs/2603.26317 · HTML: https://mlsanity.com/paper/2603.26317/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 76 of its 109 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 30 of 76)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [DocVQA: A Dataset for VQA on Document Images](https://mlsanity.com/paper/2007.00398/) (2020)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Deep Visual-Semantic Alignments for Generating Image Descriptions](https://mlsanity.com/paper/1412.2306/) (2014)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [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)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [Efficiently Identifying Task Groupings for Multi-Task Learning](https://mlsanity.com/paper/2109.04617/) (2021)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)

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

- [From Parameters to Behaviors: A Survey of Model Fusion for Large Language Models](https://mlsanity.com/paper/2609.19553/) (2026)
- [Beyond Uniform Subspaces: Spectrum-Aware and Depth-Adaptive Fusion for Multi-Task Model Merging](https://mlsanity.com/paper/2609.24612/) (2026)
- [New LoRA Skills Should Read but Never Write](https://mlsanity.com/paper/2609.31600/) (2026)
- [Triggering Generalist Reasoning via Predictive Uncertainty for Dual-System VLA](https://mlsanity.com/paper/2610.05025/) (2026)

## Abstract (arXiv)

Model merging combines independently fine-tuned checkpoints without joint multi-task training. In the era of foundation-model, fine-tuning with Low-Rank Adaptation (LoRA) is prevalent, making LoRA merging a promising target. Existing approaches can work in homogeneous settings where all target tasks are classification but often fail when tasks span classification and regression. Approaches using entropy-based surrogates do not apply to regression and are costly for large language models due to long token sequences. We introduce Null-Space Compression (NSC) Merging, a label-free, output-agnostic method that sets merge weights from adapter geometry. Our key observation is that during LoRA finetuning the down-projection factor A in Delta W = BA compresses its null space, and the compression correlates with performance. NSC uses this as an optimization signal for merging that can generalize across classification, regression, and sequence generation. NSC achieves state-of-the-art performance across twenty heterogeneous vision tasks with balanced gains where prior methods overfit subsets of tasks. It also outperforms baselines on six NLI benchmarks and on vision-language evaluations for VQA and image captioning, demonstrating scalability and effectiveness.