# Growing axons: greedy learning of neural networks with application to function approximation

arXiv: https://arxiv.org/abs/1910.12686 · HTML: https://mlsanity.com/paper/1910.12686/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2019.

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

- [SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs](https://mlsanity.com/paper/2102.13037/) (2021)
- [Partition of unity networks: deep hp-approximation](https://mlsanity.com/paper/2101.11256/) (2021)
- [Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine](https://mlsanity.com/paper/2204.11375/) (2022)
- [Probabilistic partition of unity networks: clustering based deep approximation](https://mlsanity.com/paper/2107.03066/) (2021)
- [Parameter-varying neural ordinary differential equations with partition-of-unity networks](https://mlsanity.com/paper/2210.00368/) (2022)
- [SUPN: Shallow Universal Polynomial Networks for Efficient Function Approximation](https://mlsanity.com/paper/2511.21414/) (2025)

## Abstract (arXiv)

We propose a new method for learning deep neural network models that is based on a greedy learning approach: we add one basis function at a time, and a new basis function is generated as a non-linear activation function applied to a linear combination of the previous basis functions. Such a method (growing deep neural network by one neuron at a time) allows us to compute much more accurate approximants for several model problems in function approximation.