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Hopfield Model on Incomplete Graphs

Oldehed, Henrik (2019) In Bachelor's Theses in Mathematical Sciences MASK01 20182
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
Oldehed, Henrik
supervisor
organization
course
MASK01 20182
year
type
M2 - Bachelor Degree
subject
keywords
Neural Network, Hopfield Model, Incomplete Graph
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMS-4031-2019
ISSN
1654-6229
other publication id
2019:K4
language
English
id
8982568
date added to LUP
2019-06-12 15:37:31
date last changed
2024-09-27 17:03:52
@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}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{Hopfield Model on Incomplete Graphs}},
  year         = {{2019}},
}