# Model Merging via Data-Free Covariance Estimation

arXiv: https://arxiv.org/abs/2604.01329 · HTML: https://mlsanity.com/paper/2604.01329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 54 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 30 of 39)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [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)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [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)
- [PAWS: Paraphrase Adversaries from Word Scrambling](https://mlsanity.com/paper/1904.01130/) (2019)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [QASC: A Dataset for Question Answering via Sentence Composition](https://mlsanity.com/paper/1910.11473/) (2019)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Model merging with SVD to tie the Knots](https://mlsanity.com/paper/2410.19735/) (2024)
- [No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces](https://mlsanity.com/paper/2502.04959/) (2025)

## Abstract (arXiv)

Model merging provides a way of cheaply combining individual models to produce a model that inherits each individual's capabilities. While some merging methods can approach the performance of multitask training, they are often heuristically motivated and lack theoretical justification. A principled alternative is to pose model merging as a layer-wise optimization problem that directly minimizes interference between tasks. However, this formulation requires estimating per-layer covariance matrices from data, which may not be available when performing merging. In contrast, many of the heuristically-motivated methods do not require auxiliary data, making them practically advantageous. In this work, we revisit the interference minimization framework and show that, under certain conditions, covariance matrices can be estimated directly from difference matrices, eliminating the need for data while also reducing computational costs. We validate our approach across vision and language benchmarks on models ranging from 86M parameters to 7B parameters, outperforming previous data-free state-of-the-art merging methods