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.
DOI
https://doi.org/10.57709/17478039
Recommended Citation
Castro Lopez Vaal, Rodrigo Ivan, "A Category-Theoretic Compositional Framework of Perceptron-Based Neural Networks plus an Architecture for Modeling Sequences Conditioned to Time-Structured Context: An Implementation of a Generative Model of Jazz Solo Improvisations." Dissertation, Georgia State University, 2020.
doi: https://doi.org/10.57709/17478039
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