Autoencoders as Dynamical Systems

Artificial neural networks whose input and output have the same dimension are mathematical functions on n-dimensional space. An autoencoder is an example of such a neural network. Taking iterates of the autoencoder defines a discrete-time dynamical system. In this thesis, we study the dynamics of various types of neural networks with this property. One outcome is the discovery of a new class of functions called "nowhere coexpanding functions". This class is used to further our understanding of one dimensional dynamical systems.