# Analysis on the Nonlinear Dynamics of Deep Neural Networks: Topological Entropy and Chaos

arXiv: https://arxiv.org/abs/1804.03987 · HTML: https://mlsanity.com/paper/1804.03987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Deep limits and cut-off phenomena for neural networks](https://mlsanity.com/paper/2104.10727/) (2021)

## Abstract (arXiv)

The theoretical explanation for deep neural network (DNN) is still an open problem. In this paper DNN is considered as a discrete-time dynamical system due to its layered structure. The complexity provided by the nonlinearity in the dynamics is analyzed in terms of topological entropy and chaos characterized by Lyapunov exponents. The properties revealed for the dynamics of DNN are applied to analyze the corresponding capabilities of classification and generalization.