# A Unified Generalization Framework for Model Merging: Trade-offs, Non-Linearity, and Scaling Laws

arXiv: https://arxiv.org/abs/2601.21690 · HTML: https://mlsanity.com/paper/2601.21690/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 80 of its 101 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 80)

- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [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)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Florence: A New Foundation Model for Computer Vision](https://mlsanity.com/paper/2111.11432/) (2021)
- [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)
- [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)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)

## Abstract (arXiv)

Model merging efficiently aggregates capabilities from multiple fine-tuned models into a single one, operating purely in parameter space without original data or expensive re-computation. Despite empirical successes, a unified theory for its effectiveness under heterogeneous finetuning hyperparameters (e.g., varying learning rates, batch sizes) remains missing. Existing federated learning theories focus purely on optimization, which fails to explain model merging and inherently leads to theoretical paradoxes. To address this challenge, we pioneer the integration of L2-Stability theory into heterogeneous environments to rigorously decouple the excess risk of the merged model boldsymbolxavg into optimization and generalization errors. This comprehensive analysis yields three main contributions: (i) We mathematically establish the fundamental textitOptimization-Generalization Trade-off, explicitly resolving the paradox of why over-trained experts lead to catastrophic merging collapse. (ii) textitA unified theoretical framework is provided to explain not only linear merging algorithms (e.g., TA, AdaMerging) but also state-of-the-art textitnon-linear merging algorithms (e.g., TIES, DARE), proving how sparsification operators strictly tighten the generalization bound by suppressing task heterogeneity. (iii) Rather than heuristic guidelines, we derive textitQuantitative Scaling Laws that theoretically predict the precise impact of hyperparameter choices, enabling practitioners to strategically construct ``merge-friendly'' experts. Extensive experiments on the ResNet and ViT architectures across 20 visual classification tasks, involving thousands of finetuning models, robustly confirm that our theoretical scaling laws accurately predict the empirical generalization behaviors of boldsymbolxavg.