# SortedNet: A Scalable and Generalized Framework for Training Modular Deep Neural Networks

arXiv: https://arxiv.org/abs/2309.00255 · HTML: https://mlsanity.com/paper/2309.00255/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [DynaBERT: Dynamic BERT with Adaptive Width and Depth](https://mlsanity.com/paper/2004.04037/) (2020)
- [Universally Slimmable Networks and Improved Training Techniques](https://mlsanity.com/paper/1903.05134/) (2019)

## Built on by (most cited first, 6 of 6)

- [Sorted LLaMA: Unlocking the Potential of Intermediate Layers of Large Language Models for Dynamic Inference](https://mlsanity.com/paper/2309.08968/) (2023)
- [Deep Hierarchical Learning with Nested Subspace Networks for Large Language Models](https://mlsanity.com/paper/2509.17874/) (2025)
- [SnapGen++: Unleashing Diffusion Transformers for Efficient High-Fidelity Image Generation on Edge Devices](https://mlsanity.com/paper/2601.08303/) (2026)
- [AdaPerceiver: Transformers with Adaptive Width, Depth, and Tokens](https://mlsanity.com/paper/2511.18105/) (2025)
- [Do Vision Transformers Need All-to-All Attention? Global Communication Through Elastic Learned Cores](https://mlsanity.com/paper/2605.12491/) (2026)
- [Your Transformer Is Secretly Elastic](https://mlsanity.com/paper/2610.20588/) (2026)

## Abstract (arXiv)

Deep neural networks (DNNs) must cater to a variety of users with different performance needs and budgets, leading to the costly practice of training, storing, and maintaining numerous user/task-specific models. There are solutions in the literature to deal with single dynamic or many-in-one models instead of many individual networks; however, they suffer from significant drops in performance, lack of generalization across different model architectures or different dimensions (e.g. depth, width, attention blocks), heavy model search requirements during training, and training a limited number of sub-models. To address these limitations, we propose SortedNet, a generalized and scalable training solution to harness the inherent modularity of DNNs. Thanks to a generalized nested architecture (which we refer as textitsorted architecture in this paper) with shared parameters and its novel update scheme combining random sub-model sampling and a new gradient accumulation mechanism, SortedNet enables the training of sub-models simultaneously along with the training of the main model (without any significant extra training or inference overhead), simplifies dynamic model selection, customizes deployment during inference, and reduces the model storage requirement significantly. The versatility and scalability of SortedNet are validated through various architectures and tasks, including LLaMA, BERT, RoBERTa (NLP tasks), ResNet and MobileNet (image classification) demonstrating its superiority over existing dynamic training methods. For example, we introduce a novel adaptive self-speculative approach based on sorted-training to accelerate large language models decoding. Moreover, SortedNet is able to train 160 sub-models at once, achieving at least 96% of the original model's performance.