Hopfield Model on Incomplete Graphs
(2019) MASK01 20182Mathematical 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:
http://lup.lub.lu.se/student-papers/record/8982568
- author
- Oldehed, Henrik
- supervisor
- organization
- course
- MASK01 20182
- year
- 2019
- 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}}, language = {{eng}}, note = {{Student Paper}}, title = {{Hopfield Model on Incomplete Graphs}}, year = {{2019}}, }