# NGN: Learning Neural Network Size as a Differentiable Count

arXiv: https://arxiv.org/abs/2609.27291 · HTML: https://mlsanity.com/paper/2609.27291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 26 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Sparse Low-rank Adaptation of Pre-trained Language Models](https://mlsanity.com/paper/2311.11696/) (2023)
- [Variational Inference for Infinitely Deep Neural Networks](https://mlsanity.com/paper/2209.10091/) (2022)
- [Adaptive Width Neural Networks](https://mlsanity.com/paper/2501.15889/) (2025)

## Abstract (arXiv)

Neural network size is usually chosen before training, separating architecture selection from weight optimization. We introduce the Neurogenesis Network (NGN), a differentiable parameterization for learning how many ordered structural components a model should use. For each ordered component group, one learnable boundary selects an active prefix while the model parameters are trained. The boundary can grow from a compact initialization and can be deployed by discarding components beyond the learned boundary. Controlled experiments examine convergence of the learned boundary, the performance of deployed prefixes, and comparisons with fixed-size models and alternative approaches to learning capacity. We then apply the same mechanism to MLPs, convolutional and graph networks, Transformers, state-space models, LoRA, and adapters. Across these settings, deploying only the learned prefix usually changes performance little, and the selected architectures perform similarly to fixed models trained at the same size. These results show that structural capacity can be optimized directly as a count.