# HM3: Hierarchical Multi-Objective Model Merging for Pretrained Models

arXiv: https://arxiv.org/abs/2409.18893 · HTML: https://mlsanity.com/paper/2409.18893/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 102 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 30 of 62)

- [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)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [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)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [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)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [XNLI: Evaluating Cross-lingual Sentence Representations](https://mlsanity.com/paper/1809.05053/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [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)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [VisionLLM: Large Language Model is also an Open-Ended Decoder for Vision-Centric Tasks](https://mlsanity.com/paper/2305.11175/) (2023)
- [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, 8 of 8)

- [Diversity-Aware Policy Optimization for Large Language Model Reasoning](https://mlsanity.com/paper/2505.23433/) (2025)
- [Decouple and Orthogonalize: A Data-Free Framework for LoRA Merging](https://mlsanity.com/paper/2505.15875/) (2025)
- [AMoPO: Adaptive Multi-objective Preference Optimization without Reward Models and Reference Models](https://mlsanity.com/paper/2506.07165/) (2025)
- [Stay Unique, Stay Efficient: Preserving Model Personality in Multi-Task Merging](https://mlsanity.com/paper/2512.01461/) (2025)
- [Unified Prediction and Planning via Conflict-Aware Disjoint Parameter Training](https://mlsanity.com/paper/2607.19971/) (2026)
- [Fine-Grained Model Merging via Modular Expert Recombination](https://mlsanity.com/paper/2602.06552/) (2026)
- [Towards Adaptive Continual Model Merging via Manifold-Aware Expert Evolution](https://mlsanity.com/paper/2604.22464/) (2026)
- [A Unified Model for Cross-Domain Clone Detection via Model Merging](https://mlsanity.com/paper/2608.04215/) (2026)

## Abstract (arXiv)

Model merging is a technique that combines multiple large pretrained models into a single model with enhanced performance and broader task adaptability. It has gained popularity in large pretrained model development due to its ability to bypass the need for original training data and further training processes. However, most existing model merging approaches focus solely on exploring the parameter space, merging models with identical architectures. Merging within the architecture space, despite its potential, remains in its early stages due to the vast search space and the challenges of layer compatibility. This paper marks a significant advance toward more flexible and comprehensive model merging techniques by modeling the architecture-space merging process as a reinforcement learning task. We train policy and value networks using offline sampling of weight vectors, which are then employed for the online optimization of merging strategies. Moreover, a multi-objective optimization paradigm is introduced to accommodate users' diverse task preferences, learning the Pareto front of optimal models to offer customized merging suggestions. Experimental results across multiple tasks, including text translation, mathematical reasoning, and code generation, validate the effectiveness and superiority of the proposed framework in model merging. The code will be made publicly available after the review process.