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Hopfield Model on Incomplete Graphs

Mathematical Statistics
Abstract
We consider the Hopfield model on graphs. Specifically we compare five
different incomplete graphs on 4 or 5 vertices’s including a cycle, a path
and a star. Provided is a proof of the Hamiltonian being monotonically
decreasing under asynchronous network dynamics. This result is applied
to the treated incomplete graphs to derive exact values for the incre-
mental drop in energy on pattern sizes 2, 4, and an arbitrary m under
restriction. Special cases provided includes evaluating the network on a
graph as a union of two independent components, and additionally one
example using a deterministic dilute variable. Furthermore we study the
stability of patterns considering a Hopfield model with synchronous net-
work dynamics for two... (More)
We consider the Hopfield model on graphs. Specifically we compare five
different incomplete graphs on 4 or 5 vertices’s including a cycle, a path
and a star. Provided is a proof of the Hamiltonian being monotonically
decreasing under asynchronous network dynamics. This result is applied
to the treated incomplete graphs to derive exact values for the incre-
mental drop in energy on pattern sizes 2, 4, and an arbitrary m under
restriction. Special cases provided includes evaluating the network on a
graph as a union of two independent components, and additionally one
example using a deterministic dilute variable. Furthermore we study the
stability of patterns considering a Hopfield model with synchronous net-
work dynamics for two different incomplete graphs using simulations. (Less)
Please use this url to cite or link to this publication:
author
supervisor
organization
course
year
type
M2 - Bachelor Degree
subject
keywords
Neural Network, Hopfield Model, Incomplete Graph
language
English
id
8982568
date added to LUP
2019-06-12 15:37:31
date last changed
2019-06-12 15:37:31
@misc{8982568,
abstract     = {We consider the Hopfield model on graphs. Specifically we compare five
different incomplete graphs on 4 or 5 vertices’s including a cycle, a path
and a star. Provided is a proof of the Hamiltonian being monotonically
decreasing under asynchronous network dynamics. This result is applied
to the treated incomplete graphs to derive exact values for the incre-
mental drop in energy on pattern sizes 2, 4, and an arbitrary m under
restriction. Special cases provided includes evaluating the network on a
graph as a union of two independent components, and additionally one
example using a deterministic dilute variable. Furthermore we study the
stability of patterns considering a Hopfield model with synchronous net-
work dynamics for two different incomplete graphs using simulations.},
author       = {Oldehed, Henrik},
keyword      = {Neural Network,Hopfield Model,Incomplete Graph},
language     = {eng},
note         = {Student Paper},
title        = {Hopfield Model on Incomplete Graphs},
year         = {2019},
}