# Neural Networks as Geometric Chaotic Maps

arXiv: https://arxiv.org/abs/1912.05081 · HTML: https://mlsanity.com/paper/1912.05081/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2019.

## Built on by (most cited first, 3 of 3)

- [Learning a Stochastic Differential Equation Model of Tropical Cyclone Intensification from Reanalysis and Observational Data](https://mlsanity.com/paper/2601.08116/) (2026)
- [Multi-Objective Optimization for Value-Sensitive and Sustainable Basket Recommendations](https://mlsanity.com/paper/2111.05944/) (2021)
- [Multirotor Ensemble Model Predictive Control I: Simulation Experiments](https://mlsanity.com/paper/2305.12625/) (2023)

## Abstract (arXiv)

The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural networks can efficiently model chaotic dynamics by becoming structurally chaotic themselves. We first confirm neural network's efficiency in emulating chaos by showing that a parsimonious neural network trained only on few data points can reconstruct strange attractors, extrapolate outside training data boundaries, and accurately predict local divergence rates. We then posit that the trained network's map comprises sequential geometric stretching, rotation, and compression operations. These geometric operations indicate topological mixing and chaos, explaining why neural networks are naturally suitable to emulate chaotic dynamics.