Date of Award

5-4-2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Mariana Montiel

Second Advisor

Vladimir Bondarenko

Third Advisor

Martin Norgaard

Fourth Advisor

Marina Arav

Abstract

This work introduces an algebraic graphical language of perceptrons, multilayer perceptrons, recurrent neural networks, and long short-term memory neural networks, via string diagrams of a suitable hypergraph category equipped with a concatenation diagram operation by means of a monoidal endofunctor. Using this language, we introduce a neural network architecture for modeling sequential data in which each sequence is subject to a specific context with a temporal structure, that is, each data point of a sequence is conditioned to a different past, present, and future context than the other points. As proof of concept, this architecture is implemented as a generative model of jazz solo improvisations.

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