Rafal Latkowski
Hopfield Neural Networks --- Theory and applications (in Polish)

Bachelor thesis under supervision of Professor Andrzej Skowron.

Warsaw University, Institute of Mathematics, 1999
39 pages

Abstract
This Bachelor Thesis describes the functioning and construction of
Hopfield Neural Network based on simple application (TELE-TEXT Noise
Removal). In the first chapter the short historical introduction is
provided together with placement of Hopfield Neural Networks in history
of research on Neural Networks. The second chapter presents the idea of
Hopfield Neural Network and probabilistic proof on the network capacity
estimation. The third chapter presents an application of the HNN's to
the TELE-TEXT Noise Removal problem. Based on the experimental
evaluation the theorem on reduced network capacity and stability
condition is formulated.

Main Result
The main result of this work is a theorem with proof, that even in
spite of the well known estimation of the maximal Hopfield Neural
Network capacity (c=0.138*N), there always exits many triples of
patterns, which cannot be learned by the neural network. The proof
is constructive, i.e. it constructs the finite family of
counter-examples.