Preprints available

[Thomas H. Hildebrandt]

	My translation of the following paper is soon to appear in
Electronics, Information, and Communication in Japan (Scripta
Technica, Silver Spring, MD).  To obtain a copy in PostScript format
(sans figure), e-mail your request directly to me.  I cannot supply
hardcopy, due to budgetary constraints, so please don't ask; also, the
one figure is not necessary for understanding the paper.

				Thomas H Hildebrandt
				Visiting  Researcher
				EE and CS Department
				Room 304 Packard Lab
				19 Lehigh University
				Bethlehem, PA  18015


\title{Analysis of Neural Network Energy Functions Using Standard
Forms

\thanks{Translated from the Japanese by Thomas H.  Hildebrandt.
The original appeared in Denshi Joohoo Tsuushin Gakkai Ronbunshi
(Transactions of the Institute of Electronics, Information, and
Communication Engineers (of Japan)), V.J74-D-II, N.6, pp.804--811,
June 1991}}

\author{Masanori IZUMIDA\thanks{Information Engineering Department, 
Faculty of Engineering, Ehime University, Matsuyama-shi 790 Japan}, 
Kenji MURAKAMI$^{\dagger}$ and Tsunehiro AIBARA$^{\dagger}$}

\begin{abstract}

In this paper, we discuss a method for analyzing the energy function
of a Hopfield type neural network.  In order to analyze the energy
function which solves the given minimization problem, or simply, the
problem, we define the standard form of the energy function.  In
general, a multidimensional energy function is complex, and it is
difficult to investigate the energy functions arising in practice, but
when placed in the standard form, it is possible to compare and
contrast the forms of the energy functions themselves.  Since an
orthonormal transformation will not change the form of an energy
function, we can stipulate that the standard form represent
identically energy functions which have the same form.  Further,
according to the theory associated with standard forms, it is possible
to partition a general energy function according to the eigenvalues of
the connection weight matrix, and if we analyze each energy function,
we can investigate the properties of the actual energy function.
Using this method, we analyze the energy function given by Hopfield
for the Travelling Salesman Problem, and study how the minimization
problem is realized in the energy function.  Also, we study the mutual
effects of a linear combination of energy functions and discuss the
results.

\end{abstract} 

KEYWORDS: Neural network, energy function, eigenvalue decomposition,
travelling salesman problem, standard form.