# Tangent Model Composition for Ensembling and Continual Fine-tuning

arXiv: https://arxiv.org/abs/2307.08114 · HTML: https://mlsanity.com/paper/2307.08114/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 65 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [OFA: Unifying Architectures, Tasks, and Modalities Through a Simple Sequence-to-Sequence Learning Framework](https://mlsanity.com/paper/2202.03052/) (2022)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [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)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Co2L: Contrastive Continual Learning](https://mlsanity.com/paper/2106.14413/) (2021)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)

## Built on by (most cited first, 25 of 25)

- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [Deep Model Fusion: A Survey](https://mlsanity.com/paper/2309.15698/) (2023)
- [Parameter Efficient Multi-task Model Fusion with Partial Linearization](https://mlsanity.com/paper/2310.04742/) (2023)
- [Learning from models beyond fine-tuning](https://mlsanity.com/paper/2310.08184/) (2023)
- [Diffusion Soup: Model Merging for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2406.08431/) (2024)
- [A Second-Order Perspective on Model Compositionality and Incremental Learning](https://mlsanity.com/paper/2405.16350/) (2024)
- [MINGLE: Mixture of Null-Space Gated Low-Rank Experts for Test-Time Continual Model Merging](https://mlsanity.com/paper/2505.11883/) (2025)
- [FusionBench: A Unified Library and Comprehensive Benchmark for Deep Model Fusion](https://mlsanity.com/paper/2406.03280/) (2024)
- [Null-Space Filtering for Data-Free Continual Model Merging: Preserving Stability, Promoting Plasticity](https://mlsanity.com/paper/2509.21413/) (2025)
- [Towards Diverse Device Heterogeneous Federated Learning via Task Arithmetic Knowledge Integration](https://mlsanity.com/paper/2409.18461/) (2024)
- [Is Multiple Object Tracking a Matter of Specialization?](https://mlsanity.com/paper/2411.00553/) (2024)
- [PICASO: Permutation-Invariant Context Composition with State Space Models](https://mlsanity.com/paper/2502.17605/) (2025)
- [Balancing Speciality and Versatility: A Coarse to Fine Framework for Mitigating Catastrophic Forgetting in Large Language Models](https://mlsanity.com/paper/2404.10306/) (2024)
- [Learning Scalable Model Soup on a Single GPU: An Efficient Subspace Training Strategy](https://mlsanity.com/paper/2407.03641/) (2024)
- [Modular Embedding Recomposition for Incremental Learning](https://mlsanity.com/paper/2508.16463/) (2025)
- [Dataless Weight Disentanglement in Task Arithmetic via Kronecker-Factored Approximate Curvature](https://mlsanity.com/paper/2602.17385/) (2026)
- [RADIN: Souping on a Budget](https://mlsanity.com/paper/2401.17790/) (2024)
- [Merging without Forgetting: Continual Fusion of Task-Specific Models via Optimal Transport](https://mlsanity.com/paper/2511.19561/) (2025)
- [Linear Model Merging Unlocks Simple and Scalable Multimodal Data Mixture Optimization](https://mlsanity.com/paper/2602.04937/) (2026)
- [Distilling Linearized Behavior into Non-Linear Fine-Tuning for Effective Task Arithmetic](https://mlsanity.com/paper/2605.18993/) (2026)
- [Closing the Oracle Gap: Increment Vector Transformation for Class Incremental Learning](https://mlsanity.com/paper/2509.21898/) (2025)
- [A Unified Generalization Framework for Model Merging: Trade-offs, Non-Linearity, and Scaling Laws](https://mlsanity.com/paper/2601.21690/) (2026)
- [Multimodal Structure Learning: Disentangling Shared and Specific Topology via Cross-Modal Graphical Lasso](https://mlsanity.com/paper/2604.03953/) (2026)
- [SAFE-Merge: Data-Free Continual Model Merging with General Knowledge Preservation](https://mlsanity.com/paper/2608.01184/) (2026)
- [Text-Guided Visual Dependency Graph Learning with Cross-Modal Attention Priors](https://mlsanity.com/paper/2608.21443/) (2026)

## Abstract (arXiv)

Tangent Model Composition (TMC) is a method to combine component models independently fine-tuned around a pre-trained point. Component models are tangent vectors to the pre-trained model that can be added, scaled, or subtracted to support incremental learning, ensembling, or unlearning. Component models are composed at inference time via scalar combination, reducing the cost of ensembling to that of a single model. TMC improves accuracy by 4.2% compared to ensembling non-linearly fine-tuned models at a 2.5x to 10x reduction of inference cost, growing linearly with the number of component models. Each component model can be forgotten at zero cost, with no residual effect on the resulting inference. When used for continual fine-tuning, TMC is not constrained by sequential bias and can be executed in parallel on federated data. TMC outperforms recently published continual fine-tuning methods almost uniformly on each setting -- task-incremental, class-incremental, and data-incremental -- on a total of 13 experiments across 3 benchmark datasets, despite not using any replay buffer. TMC is designed for composing models that are local to a pre-trained embedding, but could be extended to more general settings. The code is available at: https://github.com/tianyu139/tangent-model-composition