# Modular Delta Merging with Orthogonal Constraints: A Scalable Framework for Continual and Reversible Model Composition

arXiv: https://arxiv.org/abs/2507.20997 · HTML: https://mlsanity.com/paper/2507.20997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 28 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent](https://mlsanity.com/paper/2006.11942/) (2020)

## Abstract (arXiv)

In real-world machine learning deployments, models must be continually updated, composed, and when required, selectively undone. However, existing approaches to model merging and continual learning often suffer from task interference, catastrophic forgetting, or lack of reversibility. We propose Modular Delta Merging with Orthogonal Constraints (MDM-OC), a novel framework that enables scalable, interference-free, and reversible composition of fine-tuned models. Each task-specific model is encoded as a delta from a shared base and projected into an orthogonal subspace to eliminate conflict. These projected deltas are then merged via gradient-based optimization to form a unified model that retains performance across tasks. Our approach supports continual integration of new models, structured unmerging for compliance such as GDPR requirements, and model stability via elastic weight consolidation and synthetic replay. Extensive experiments on vision and natural language processing benchmarks demonstrate that MDM-OC outperforms prior baselines in accuracy, backward transfer, and unmerge fidelity, while remaining memory-efficient and computationally tractable. This framework offers a principled solution for modular and compliant AI system design.