# Bohdi: Heterogeneous LLM Fusion with Automatic Data Exploration

arXiv: https://arxiv.org/abs/2506.15721 · HTML: https://mlsanity.com/paper/2506.15721/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 4 Jun 2025.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (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)
- [FuseChat: Knowledge Fusion of Chat Models](https://mlsanity.com/paper/2408.07990/) (2024)
- [GenQA: Generating Millions of Instructions from a Handful of Prompts](https://mlsanity.com/paper/2406.10323/) (2024)
- [Synthesizing Post-Training Data for LLMs through Multi-Agent Simulation](https://mlsanity.com/paper/2410.14251/) (2024)
- [Condor: Enhance LLM Alignment with Knowledge-Driven Data Synthesis and Refinement](https://mlsanity.com/paper/2501.12273/) (2025)
- [Weighted-Reward Preference Optimization for Implicit Model Fusion](https://mlsanity.com/paper/2412.03187/) (2024)
- [FuseChat-3.0: Preference Optimization Meets Heterogeneous Model Fusion](https://mlsanity.com/paper/2503.04222/) (2025)

## Built on by (most cited first, 3 of 3)

- [Can Heterogeneous Language Models Be Fused?](https://mlsanity.com/paper/2604.01674/) (2026)
- [WIST: Web-Grounded Iterative Self-Play Tree for Domain-Targeted Reasoning Improvement](https://mlsanity.com/paper/2603.22352/) (2026)
- [Auto-FlexSwitch: Efficient Dynamic Model Merging via Learnable Task Vector Compression](https://mlsanity.com/paper/2604.28109/) (2026)

## Abstract (arXiv)

Heterogeneous Large Language Model (LLM) fusion integrates the strengths of multiple source LLMs with different architectures into a target LLM with low computational overhead. While promising, existing methods suffer from two major limitations: 1) reliance on real data from limited domain for knowledge fusion, preventing the target LLM from fully acquiring knowledge across diverse domains, and 2) fixed data allocation proportions across domains, failing to dynamically adjust according to the target LLM's varying capabilities across domains, leading to a capability imbalance. To overcome these limitations, we propose Bohdi, a synthetic-data-only heterogeneous LLM fusion framework. Through the organization of knowledge domains into a hierarchical tree structure, Bohdi enables automatic domain exploration and multi-domain data generation through multi-model collaboration, thereby comprehensively extracting knowledge from source LLMs. By formalizing domain expansion and data sampling proportion allocation on the knowledge tree as a Hierarchical Multi-Armed Bandit problem, Bohdi leverages the designed DynaBranches mechanism to adaptively adjust sampling proportions based on the target LLM's performance feedback across domains. Integrated with our proposed Introspection-Rebirth (IR) mechanism, DynaBranches dynamically tracks capability shifts during target LLM's updates via Sliding Window Binomial Likelihood Ratio Testing (SWBLRT), further enhancing its online adaptation capability. Comparative experimental results on a comprehensive suite of benchmarks demonstrate that Bohdi significantly outperforms existing baselines on multiple target LLMs, exhibits higher data efficiency, and virtually eliminates the imbalance in the target LLM's capabilities. Our code is available at https://github.com/gjq100/Bohdi.git.