# Task Arithmetic Through The Lens Of One-Shot Federated Learning

arXiv: https://arxiv.org/abs/2411.18607 · HTML: https://mlsanity.com/paper/2411.18607/

## Key facts

- Cited by 12 papers in the map (data through 7 Oct 2026).
- Builds on 81 of its 91 references that are in the map.
- First posted on arXiv 27 Nov 2024.

## Builds on (most cited first, 30 of 81)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [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)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)

## Built on by (most cited first, 12 of 12)

- [Unraveling LoRA Interference: Orthogonal Subspaces for Robust Model Merging](https://mlsanity.com/paper/2505.22934/) (2025)
- [Merge to Mix: Mixing Datasets via Model Merging](https://mlsanity.com/paper/2505.16066/) (2025)
- [FedMerge: Federated Personalization via Model Merging](https://mlsanity.com/paper/2504.06768/) (2025)
- [Towards One-shot Federated Learning: Advances, Challenges, and Future Directions](https://mlsanity.com/paper/2505.02426/) (2025)
- [Model Merging via Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2512.21288/) (2025)
- [Statistical Deficiency for Task Inclusion Estimation](https://mlsanity.com/paper/2503.05491/) (2025)
- [FedRPCA: Enhancing Federated LoRA Aggregation Using Robust PCA](https://mlsanity.com/paper/2506.01194/) (2025)
- [Symphony-MoE: Harmonizing Disparate Pre-trained Models into a Coherent Mixture-of-Experts](https://mlsanity.com/paper/2509.18542/) (2025)
- [Federated Independent Component Analysis via Spectral Alignment and Robust Aggregation](https://mlsanity.com/paper/2505.20532/) (2025)
- [Bi-level Personalization for Federated Foundation Models: A Task-vector Aggregation Approach](https://mlsanity.com/paper/2509.12697/) (2025)
- [Ecologically-Constrained Task Arithmetic for Multi-Taxa Bioacoustic Classifiers Without Shared Data](https://mlsanity.com/paper/2605.03914/) (2026)
- [Spherical Interpolation for Backward-Compatible Multimodal Representations](https://mlsanity.com/paper/2609.39836/) (2026)

## Abstract (arXiv)

Task Arithmetic is a model merging technique that enables the combination of multiple models' capabilities into a single model through simple arithmetic in the weight space, without the need for additional fine-tuning or access to the original training data. However, the factors that determine the success of Task Arithmetic remain unclear. In this paper, we examine Task Arithmetic for multi-task learning by framing it as a one-shot Federated Learning problem. We demonstrate that Task Arithmetic is mathematically equivalent to the commonly used algorithm in Federated Learning, called Federated Averaging (FedAvg). By leveraging well-established theoretical results from FedAvg, we identify two key factors that impact the performance of Task Arithmetic: data heterogeneity and training heterogeneity. To mitigate these challenges, we adapt several algorithms from Federated Learning to improve the effectiveness of Task Arithmetic. Our experiments demonstrate that applying these algorithms can often significantly boost performance of the merged model compared to the original Task Arithmetic approach. This work bridges Task Arithmetic and Federated Learning, offering new theoretical perspectives on Task Arithmetic and improved practical methodologies for model merging.