Date of Award
2017
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
McDonald, Patrick
Area of Concentration
Mathematics
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.
Recommended Citation
Corning, Wiley, "Topology of Neural Networks" (2017). Theses & ETDs. 5329.
https://digitalcommons.ncf.edu/theses_etds/5329