# Parameter Competition Balancing for Model Merging

arXiv: https://arxiv.org/abs/2410.02396 · HTML: https://mlsanity.com/paper/2410.02396/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 99 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 30 of 68)

- [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)
- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [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)
- [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)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [DailyDialog: A Manually Labelled Multi-turn Dialogue Dataset](https://mlsanity.com/paper/1710.03957/) (2017)
- [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)

## Built on by (most cited first, 30 of 72)

- [No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces](https://mlsanity.com/paper/2502.04959/) (2025)
- [Whoever Started the Interference Should End It: Guiding Data-Free Model Merging via Task Vectors](https://mlsanity.com/paper/2503.08099/) (2025)
- [Modeling Multi-Task Model Merging as Adaptive Projective Gradient Descent](https://mlsanity.com/paper/2501.01230/) (2025)
- [RobustMerge: Parameter-Efficient Model Merging for MLLMs with Direction Robustness](https://mlsanity.com/paper/2502.17159/) (2025)
- [Efficient and Effective Weight-Ensembling Mixture of Experts for Multi-Task Model Merging](https://mlsanity.com/paper/2410.21804/) (2024)
- [CAT Merging: A Training-Free Approach for Resolving Conflicts in Model Merging](https://mlsanity.com/paper/2505.06977/) (2025)
- [Unraveling LoRA Interference: Orthogonal Subspaces for Robust Model Merging](https://mlsanity.com/paper/2505.22934/) (2025)
- [Decouple and Orthogonalize: A Data-Free Framework for LoRA Merging](https://mlsanity.com/paper/2505.15875/) (2025)
- [MergeVLA: Cross-Skill Model Merging Toward a Generalist Vision-Language-Action Agent](https://mlsanity.com/paper/2511.18810/) (2025)
- [Keeping Yourself is Important in Downstream Tuning Multimodal Large Language Model](https://mlsanity.com/paper/2503.04543/) (2025)
- [FREE-Merging: Fourier Transform for Efficient Model Merging](https://mlsanity.com/paper/2411.16815/) (2024)
- [Task Arithmetic in Trust Region: A Training-Free Model Merging Approach to Navigate Knowledge Conflicts](https://mlsanity.com/paper/2501.15065/) (2025)
- [Multi-objective Large Language Model Alignment with Hierarchical Experts](https://mlsanity.com/paper/2505.20925/) (2025)
- [Towards Minimizing Feature Drift in Model Merging: Layer-wise Task Vector Fusion for Adaptive Knowledge Integration](https://mlsanity.com/paper/2505.23859/) (2025)
- [SurgeryV2: Bridging the Gap Between Model Merging and Multi-Task Learning with Deep Representation Surgery](https://mlsanity.com/paper/2410.14389/) (2024)
- [MedSynapse-V: Bridging Visual Perception and Clinical Intuition via Latent Memory Evolution](https://mlsanity.com/paper/2604.26283/) (2026)
- [Beyond Task Vectors: Selective Task Arithmetic Based on Importance Metrics](https://mlsanity.com/paper/2411.16139/) (2024)
- [From Task-Specific Models to Unified Systems: A Review of Model Merging Approaches](https://mlsanity.com/paper/2503.08998/) (2025)
- [Knowledge Fusion of Large Language Models Via Modular SkillPacks](https://mlsanity.com/paper/2505.18502/) (2025)
- [DC-Merge: Improving Model Merging with Directional Consistency](https://mlsanity.com/paper/2603.06242/) (2026)
- [OrthAlign: Orthogonal Subspace Decomposition for Non-Interfering Multi-Objective Alignment](https://mlsanity.com/paper/2509.24610/) (2025)
- [Model Merging in the Essential Subspace](https://mlsanity.com/paper/2602.20208/) (2026)
- [To See a World in a Spark of Neuron: Disentangling Multi-task Interference for Training-free Model Merging](https://mlsanity.com/paper/2503.05320/) (2025)
- [MoORE: SVD-based Model MoE-ization for Conflict- and Oblivion-Resistant Multi-Task Adaptation](https://mlsanity.com/paper/2506.14436/) (2025)
- [Rethinking Layer-wise Model Merging through Chain of Merges](https://mlsanity.com/paper/2508.21421/) (2025)
- [When Shared Knowledge Hurts: Spectral Over-Accumulation in Model Merging](https://mlsanity.com/paper/2602.05536/) (2026)
- [Model Merging with Functional Dual Anchors](https://mlsanity.com/paper/2510.21223/) (2025)
- [Merging Smarter, Generalizing Better: Enhancing Model Merging on OOD Data](https://mlsanity.com/paper/2506.09093/) (2025)
- [MedSAMix: A Training-Free Model Merging Approach for Medical Image Segmentation](https://mlsanity.com/paper/2508.11032/) (2025)
- [Purifying Task Vectors in Knowledge-Aware Subspace for Model Merging](https://mlsanity.com/paper/2510.14697/) (2025)

## Abstract (arXiv)

While fine-tuning pretrained models has become common practice, these models often underperform outside their specific domains. Recently developed model merging techniques enable the direct integration of multiple models, each fine-tuned for distinct tasks, into a single model. This strategy promotes multitasking capabilities without requiring retraining on the original datasets. However, existing methods fall short in addressing potential conflicts and complex correlations between tasks, especially in parameter-level adjustments, posing a challenge in effectively balancing parameter competition across various tasks. This paper introduces an innovative technique named PCB-Merging (Parameter Competition Balancing), a lightweight and training-free technique that adjusts the coefficients of each parameter for effective model merging. PCB-Merging employs intra-balancing to gauge parameter significance within individual tasks and inter-balancing to assess parameter similarities across different tasks. Parameters with low importance scores are dropped, and the remaining ones are rescaled to form the final merged model. We assessed our approach in diverse merging scenarios, including cross-task, cross-domain, and cross-training configurations, as well as out-of-domain generalization. The experimental results reveal that our approach achieves substantial performance enhancements across multiple modalities, domains, model sizes, number of tasks, fine-tuning forms, and large language models, outperforming existing model merging methods. The code is publicly available at: urlhttps://github.com/duguodong7/pcb-merging.