# Classification with Runge-Kutta networks and feature space augmentation

arXiv: https://arxiv.org/abs/2104.02369 · HTML: https://mlsanity.com/paper/2104.02369/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Deep learning as optimal control problems: models and numerical methods](https://mlsanity.com/paper/1904.05657/) (2019)
- [Structure preserving deep learning](https://mlsanity.com/paper/2006.03364/) (2020)
- [Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more](https://mlsanity.com/paper/1503.04021/) (2015)

## Abstract (arXiv)

In this paper we combine an approach based on Runge-Kutta Nets considered in [Benning et al., J. Comput. Dynamics, 9, 2019] and a technique on augmenting the input space in [Dupont et al., NeurIPS, 2019] to obtain network architectures which show a better numerical performance for deep neural networks in point and image classification problems. The approach is illustrated with several examples implemented in PyTorch.