# FREE-Merging: Fourier Transform for Efficient Model Merging

arXiv: https://arxiv.org/abs/2411.16815 · HTML: https://mlsanity.com/paper/2411.16815/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 58 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 30 of 44)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [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)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [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)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)

## Built on by (most cited first, 13 of 13)

- [Model Merging in the Essential Subspace](https://mlsanity.com/paper/2602.20208/) (2026)
- [ACE-Merging: Data-Free Model Merging with Adaptive Covariance Estimation](https://mlsanity.com/paper/2603.02945/) (2026)
- [Model Merging with Functional Dual Anchors](https://mlsanity.com/paper/2510.21223/) (2025)
- [Label-Free Cross-Task LoRA Merging with Null-Space Compression](https://mlsanity.com/paper/2603.26317/) (2026)
- [Stay Unique, Stay Efficient: Preserving Model Personality in Multi-Task Merging](https://mlsanity.com/paper/2512.01461/) (2025)
- [Preference-Aligned LoRA Merging: Preserving Subspace Coverage and Addressing Directional Anisotropy](https://mlsanity.com/paper/2603.26299/) (2026)
- [SyMerge: From Non-Interference to Synergistic Merging via Single-Layer Adaptation](https://mlsanity.com/paper/2412.19098/) (2024)
- [Dynamic Model Merging Made Slim](https://mlsanity.com/paper/2605.18904/) (2026)
- [Data-Aware Model Merging in the Essential Subspace for Multi-Task Knowledge Aggregation](https://mlsanity.com/paper/2606.19164/) (2026)
- [FREE-Switch: Frequency-based Dynamic LoRA Switch for Style Transfer](https://mlsanity.com/paper/2604.10023/) (2026)
- [View-Consistent 3D Scene Editing via Dual-Path Structural Correspondense and Semantic Continuity](https://mlsanity.com/paper/2604.17801/) (2026)
- [Saliency-Aware Model Merging](https://mlsanity.com/paper/2606.00511/) (2026)
- [UniMergeTrack: Hierarchical Model Merging for General RGB-X Visual Object Tracking](https://mlsanity.com/paper/2610.13053/) (2026)

## Abstract (arXiv)

With the rapid growth of deep learning, there is an increasing availability of open-source models for various tasks. However, single fine-tuned models often fall short of meeting the diverse needs of users. Model merging has thus emerged as an efficient method to integrate the capabilities of existing models into a unified model. Nevertheless, existing model merging methods face challenging trade-offs between performance and deployment costs, primarily due to task interference. For the first time, we reveal that task interference is evident in the frequency domain of model parameters, yet current efforts only focus on spatial domain solutions, which are largely ineffective in addressing frequency domain interference. To mitigate the impact of frequency domain interference, we propose FR-Merging, an innovative method that effectively filters harmful frequency domain interference on the backbone with minimal computational overhead. Since performance loss is inevitable with cost-free methods, we propose a lightweight task-specific expert module that dynamically compensates for information loss during merging. This proposed framework, FREE-Merging (FR-Merging with experts), strikes a balanced trade-off between training cost, inference latency, storage requirements, and performance. We demonstrate the effectiveness of both FR-Merging and FREE-Merging on multiple tasks across CV, NLP, and Multi-Modal domains and show that they can be flexibly adapted to specific needs.