# Foldable SuperNets: Scalable Merging of Transformers with Different Initializations and Tasks

arXiv: https://arxiv.org/abs/2410.01483 · HTML: https://mlsanity.com/paper/2410.01483/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 71 of its 88 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 30 of 71)

- [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)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [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)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [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)
- [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)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)

## Built on by (most cited first, 4 of 4)

- [NAN: A Training-Free Solution to Coefficient Estimation in Model Merging](https://mlsanity.com/paper/2505.16148/) (2025)
- [Cross-Model Transfer of Task Vectors via Few-Shot Orthogonal Alignment](https://mlsanity.com/paper/2505.12021/) (2025)
- [Merging without Forgetting: Continual Fusion of Task-Specific Models via Optimal Transport](https://mlsanity.com/paper/2511.19561/) (2025)
- [A Unified Generalization Framework for Model Merging: Trade-offs, Non-Linearity, and Scaling Laws](https://mlsanity.com/paper/2601.21690/) (2026)

## Abstract (arXiv)

Recent methods aim to merge neural networks (NNs) with identical architectures trained on different tasks into a single multi-task model. While most works focus on the simpler setup of merging NNs initialized from a common pre-trained network, we target the harder problem of merging large transformers trained on different tasks from distinct initializations. We show that traditional merging methods fail catastrophically in this setup, while Knowledge Distillation (KD) achieves much better results, though at a higher cost. However, KD is data-inefficient, as it does not exploit the original models' weights. To solve this, we introduce "Foldable SuperNet Merge" (FS-Merge), which trains a SuperNet containing the original models (with frozen weights) using a feature reconstruction objective. After training, the SuperNet is folded back to the size of a single original model. FS-Merge is simple, data-efficient, has a computational cost comparable to KD, and is proven to have superior expressiveness compared to traditional merging methods on MLP models. It achieves SOTA results when tested on MLPs and transformers across various sizes, tasks, modalities, and distribution shifts, especially in low-data scenarios.