# Unconstrained Model Merging for Enhanced LLM Reasoning

arXiv: https://arxiv.org/abs/2410.13699 · HTML: https://mlsanity.com/paper/2410.13699/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 32 of its 45 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 32)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [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)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks](https://mlsanity.com/paper/2312.06795/) (2023)
- [Next-Generation Database Interfaces: A Survey of LLM-based Text-to-SQL](https://mlsanity.com/paper/2406.08426/) (2024)
- [Knowledge Fusion of Large Language Models](https://mlsanity.com/paper/2401.10491/) (2024)
- [Augmenting Math Word Problems via Iterative Question Composing](https://mlsanity.com/paper/2401.09003/) (2024)
- [Transformer Fusion with Optimal Transport](https://mlsanity.com/paper/2310.05719/) (2023)
- [LLM Augmented LLMs: Expanding Capabilities through Composition](https://mlsanity.com/paper/2401.02412/) (2024)

## Built on by (most cited first, 7 of 7)

- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [InfiFPO: Implicit Model Fusion via Preference Optimization in Large Language Models](https://mlsanity.com/paper/2505.13878/) (2025)
- [Merge-of-Thought Distillation](https://mlsanity.com/paper/2509.08814/) (2025)
- [Assembly of Experts: Linear-time construction of the Chimera LLM variants with emergent and adaptable behaviors](https://mlsanity.com/paper/2506.14794/) (2025)
- [MMedExpert-R1: Strengthening Multimodal Medical Reasoning via Domain-Specific Adaptation and Clinical Guideline Reinforcement](https://mlsanity.com/paper/2601.10949/) (2026)
- [Timber: Training-free Instruct Model Refining with Base via Effective Rank](https://mlsanity.com/paper/2509.23595/) (2025)
- [Leveraging Instruction Tuning and Merging for Reasoning Model Adaptation](https://mlsanity.com/paper/2607.14895/) (2026)

## Abstract (arXiv)

Recent advancements in building domain-specific large language models (LLMs) have shown remarkable success, especially in tasks requiring reasoning abilities like logical inference over complex relationships and multi-step problem solving. However, creating a powerful all-in-one LLM remains challenging due to the need for proprietary data and vast computational resources. As a resource-friendly alternative, we explore the potential of merging multiple expert models into a single LLM. Existing studies on model merging mainly focus on generalist LLMs instead of domain experts, or the LLMs under the same architecture and size. In this work, we propose an unconstrained model merging framework that accommodates both homogeneous and heterogeneous model architectures with a focus on reasoning tasks. A fine-grained layer-wise weight merging strategy is designed for homogeneous models merging, while heterogeneous model merging is built upon the probabilistic distribution knowledge derived from instruction-response fine-tuning data. Across 7 benchmarks and 9 reasoning-optimized LLMs, we reveal key findings that combinatorial reasoning emerges from merging which surpasses simple additive effects. We propose that unconstrained model merging could serve as a foundation for decentralized LLMs, marking a notable progression from the existing centralized LLM framework. This evolution could enhance wider participation and stimulate additional advancement in the field of artificial intelligence, effectively addressing the constraints posed by centralized models.