# Model Merging as Probabilistic Inference in Fine-Tuning Parameter Space

arXiv: https://arxiv.org/abs/2607.01689 · HTML: https://mlsanity.com/paper/2607.01689/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 52 references that are in the map.
- First posted on arXiv 2 Jul 2026.

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

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [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)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [On the Challenges and Perspectives of Foundation Models for Medical Image Analysis](https://mlsanity.com/paper/2306.05705/) (2023)
- [Model merging with SVD to tie the Knots](https://mlsanity.com/paper/2410.19735/) (2024)
- [Deep Model Fusion: A Survey](https://mlsanity.com/paper/2309.15698/) (2023)
- [Model Merging by Uncertainty-Based Gradient Matching](https://mlsanity.com/paper/2310.12808/) (2023)
- [Scaling Wearable Foundation Models](https://mlsanity.com/paper/2410.13638/) (2024)
- [Modeling Multi-Task Model Merging as Adaptive Projective Gradient Descent](https://mlsanity.com/paper/2501.01230/) (2025)
- [Concrete Subspace Learning based Interference Elimination for Multi-task Model Fusion](https://mlsanity.com/paper/2312.06173/) (2023)
- [Federated Learning from Vision-Language Foundation Models: Theoretical Analysis and Method](https://mlsanity.com/paper/2409.19610/) (2024)
- [MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation](https://mlsanity.com/paper/2406.07529/) (2024)
- [Statistical Model Aggregation via Parameter Matching](https://mlsanity.com/paper/1911.00218/) (2019)
- [Mix Data or Merge Models? Optimizing for Diverse Multi-Task Learning](https://mlsanity.com/paper/2410.10801/) (2024)
- [A Re-ranker Scheme for Integrating Large Scale NLU models](https://mlsanity.com/paper/1809.09605/) (2018)

## Abstract (arXiv)

Model merging aims to combine existing single-task solutions into a multi-task solution without additional data-driven fine-tuning.~Most existing approaches achieve this using geometric properties of local solution spaces. However, such geometric views provide limited guidance for scoring how statistically useful each task-specific update direction is across tasks during merging. To address this, we formulate model merging from a new perspective of probabilistic inference under a product-of-experts (PoE) scenario where each single-task solution defines an energy-based expert model (EBM) over the merged parameters. We show that several existing model merging methods arise as special cases of our framework under energy designs that impose implicit Gaussian assumptions on directional residuals between merged and task-specific models. Empirically, we find that these residuals are often heavy-tailed which exposes a mismatch with the imposed light-tailed Gaussian structures. We address this with a heavy-tailed PoE design based on Cauchy experts, which better captures the observed residual behavior while admitting a provably convergent inference procedure. Experiments across multiple tasks and architectures show significant improvements over state-of-the-arts baselines. Our code is available at https://github.com/MinhLong210/PoE-EBM-Merging.git.