# Why Do More Experts Fail? A Theoretical Analysis of Model Merging

arXiv: https://arxiv.org/abs/2505.21226 · HTML: https://mlsanity.com/paper/2505.21226/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 79 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 30 of 55)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [EVA: Exploring the Limits of Masked Visual Representation Learning at Scale](https://mlsanity.com/paper/2211.07636/) (2022)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Personalized Soups: Personalized Large Language Model Alignment via Post-hoc Parameter Merging](https://mlsanity.com/paper/2310.11564/) (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)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [ZipLoRA: Any Subject in Any Style by Effectively Merging LoRAs](https://mlsanity.com/paper/2311.13600/) (2023)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)

## Built on by (most cited first, 6 of 6)

- [Model Merging Scaling Laws in Large Language Models](https://mlsanity.com/paper/2509.24244/) (2025)
- [DiMtextsuperscript3: Bridging Multilingual and Multimodal Models via Direction- and Magnitude-Aware Merging](https://mlsanity.com/paper/2605.12960/) (2026)
- [Communication-Efficient Personalized Adaptation via Federated-Local Model Merging](https://mlsanity.com/paper/2602.18658/) (2026)
- [Saliency-Aware Model Merging](https://mlsanity.com/paper/2606.00511/) (2026)
- [Model Merging to Evolution: Parameter Space Exploration for Expert Models](https://mlsanity.com/paper/2606.28373/) (2026)
- [Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging](https://mlsanity.com/paper/2609.37564/) (2026)

## Abstract (arXiv)

Model merging dramatically reduces storage and computational resources by combining multiple expert models into a single multi-task model. Although recent model merging methods have shown promising results, they struggle to maintain performance gains as the number of merged models increases. In this paper, we investigate the key obstacles that limit the scalability of model merging when integrating a large number of expert models. First, we prove that there is an upper bound on model merging. Further theoretical analysis reveals that the limited effective parameter space imposes a strict constraint on the number of models that can be successfully merged. Gaussian Width shows that the marginal benefit of merging additional models diminishes according to a strictly concave function. This implies that the effective parameter space becomes rapidly saturated as the number of merged models increases. Furthermore, using Approximate Kinematics Theory, we prove the existence of a unique optimal threshold beyond which adding more models does not yield significant performance improvements. At the same time, we introduce a straightforward Reparameterized Heavy-Tailed method (RHT) to extend the coverage of the merged model, thereby enhancing its performance. Empirical results on 12 benchmarks, including both knowledge-intensive and general-purpose tasks, validate our theoretical analysis. We believe that these results spark further research beyond the current scope of model merging. The source code is in the Github repository: https://github.com/wzj1718/ModelMergingAnalysis.