# Leveraging Submodule Linearity Enhances Task Arithmetic Performance in LLMs

arXiv: https://arxiv.org/abs/2504.10902 · HTML: https://mlsanity.com/paper/2504.10902/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 46 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 30 of 40)

- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [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)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [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)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Cosmos QA: Machine Reading Comprehension with Contextual Commonsense Reasoning](https://mlsanity.com/paper/1909.00277/) (2019)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [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)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Branch-Train-Merge: Embarrassingly Parallel Training of Expert Language Models](https://mlsanity.com/paper/2208.03306/) (2022)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Composing Parameter-Efficient Modules with Arithmetic Operations](https://mlsanity.com/paper/2306.14870/) (2023)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Knowledge Fusion of Large Language Models](https://mlsanity.com/paper/2401.10491/) (2024)
- [Branch-Train-MiX: Mixing Expert LLMs into a Mixture-of-Experts LLM](https://mlsanity.com/paper/2403.07816/) (2024)
- [Model Ratatouille: Recycling Diverse Models for Out-of-Distribution Generalization](https://mlsanity.com/paper/2212.10445/) (2022)
- [A Paradigm Shift in Machine Translation: Boosting Translation Performance of Large Language Models](https://mlsanity.com/paper/2309.11674/) (2023)

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

- [Layer-wise Swapping for Generalizable Multilingual Safety](https://mlsanity.com/paper/2601.22620/) (2026)
- [M-Loss: Quantifying Model Merging Compatibility with Limited Unlabeled Data](https://mlsanity.com/paper/2602.08564/) (2026)
- [When Model Merging Breaks Routing: Training-Free Calibration for MoE](https://mlsanity.com/paper/2606.03391/) (2026)
- [Exploring Information Seeking Agent Consolidation](https://mlsanity.com/paper/2602.00585/) (2026)

## Abstract (arXiv)

Task arithmetic is a straightforward yet highly effective strategy for model merging, enabling the resultant model to exhibit multi-task capabilities. Recent research indicates that models demonstrating linearity enhance the performance of task arithmetic. In contrast to existing methods that rely on the global linearization of the model, we argue that this linearity already exists within the model's submodules. In particular, we present a statistical analysis and show that submodules (e.g., layers, self-attentions, and MLPs) exhibit significantly higher linearity than the overall model. Based on these findings, we propose an innovative model merging strategy that independently merges these submodules. Especially, we derive a closed-form solution for optimal merging weights grounded in the linear properties of these submodules. Experimental results demonstrate that our method consistently outperforms the standard task arithmetic approach and other established baselines across different model scales and various tasks. This result highlights the benefits of leveraging the linearity of submodules and provides a new perspective for exploring solutions for effective and practical multi-task model merging.