# Thesis

As part of my degree work at New College of Florida, I completed an undergratuate thesis, entitled *Topology of Neural Networks*.
In this work, I derived theoretical and experimental results about a widely used machine learning model.

#### Abstract

Although neural networks are currently used in many applications and research environments, they remain poorly understood as mathematical objects. In this thesis, we investigate the topological and algebraic properties of neural networks. We develop an understanding of algebraic structure of neural networks and produce a novel distance metric on the parameter space. We derive a backpropagation algorithm to compute the Hessian matrix of a deep rectifier network. We perform a synthetic data experiment to explore the error landscape of simple networks, and, using our distance metric, find clear patterns in the spatial distributions of learned parameters.The full document is available in PDF form.