# Merging without Forgetting: Continual Fusion of Task-Specific Models via Optimal Transport

arXiv: https://arxiv.org/abs/2511.19561 · HTML: https://mlsanity.com/paper/2511.19561/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 64 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Builds on (most cited first, 30 of 50)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [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)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [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)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Model Fusion via Optimal Transport](https://mlsanity.com/paper/1910.05653/) (2019)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Sparse Upcycling: Training Mixture-of-Experts from Dense Checkpoints](https://mlsanity.com/paper/2212.05055/) (2022)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization](https://mlsanity.com/paper/2110.10832/) (2021)
- [Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks](https://mlsanity.com/paper/2312.06795/) (2023)

## Built on by (most cited first, 1 of 1)

- [Optimal Transport Meets Reinforcement Learning: A Survey](https://mlsanity.com/paper/2610.01413/) (2026)

## Abstract (arXiv)

Merging models fine-tuned for different tasks into a single unified model has become an increasingly important direction for building versatile, efficient multi-task systems. Existing approaches predominantly rely on parameter interpolation in weight space, which we show introduces significant distribution shift in the feature space and undermines task-specific knowledge. In this paper, we propose OTMF (Optimal Transport-based Masked Fusion), a novel model merging framework rooted in optimal transport theory to address the distribution shift that arises from naive parameter interpolation. Instead of directly aggregating features or weights, OTMF aligns the semantic geometry of task-specific models by discovering common masks applied to task vectors through optimal transport plans. These masks selectively extract transferable and task-agnostic components while preserving the unique structural identities of each task. To ensure scalability in real-world settings, OTMF further supports a continual fusion paradigm that incrementally integrates each new task vector without revisiting previous ones, maintaining a bounded memory footprint and enabling efficient fusion across a growing number of tasks. We conduct comprehensive experiments on multiple vision and language benchmarks, and results show that OTMF achieves state-of-the-art performance in terms of both accuracy and efficiency. These findings highlight the practical and theoretical value of our approach to model merging.