# MoD: A Distribution-Based Approach for Merging Large Language Models

arXiv: https://arxiv.org/abs/2411.00406 · HTML: https://mlsanity.com/paper/2411.00406/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 27 of 27)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [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)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Aligning AI With Shared Human Values](https://mlsanity.com/paper/2008.02275/) (2020)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [BioMistral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains](https://mlsanity.com/paper/2402.10373/) (2024)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [LLaMA Pro: Progressive LLaMA with Block Expansion](https://mlsanity.com/paper/2401.02415/) (2024)
- [Model Ratatouille: Recycling Diverse Models for Out-of-Distribution Generalization](https://mlsanity.com/paper/2212.10445/) (2022)
- [Optimizing Mode Connectivity via Neuron Alignment](https://mlsanity.com/paper/2009.02439/) (2020)
- [Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning](https://mlsanity.com/paper/2306.02408/) (2023)

## Abstract (arXiv)

Large language models (LLMs) have enabled the development of numerous specialized, task-specific variants. However, the maintenance and deployment of these individual models present substantial challenges in terms of resource utilization and operational efficiency. In this work, we propose the textitMixture of Distributions (MoD) framework, a novel approach for merging LLMs that operates directly on their output probability distributions, rather than on model weights. Unlike traditional weight-averaging methods, MoD effectively preserves the specialized capabilities of individual models while enabling efficient knowledge sharing across tasks. Through extensive experimentation on mathematical reasoning benchmarks using Qwen2.5 models, we demonstrate that MoD significantly outperforms existing model merging techniques across multiple benchmarks. All code, data, and experimental materials are published at https://github.com/knovel-eng/mod.