An Approach to Artificial Concept Learning Based on Human Concept Learning by Using Artificial Neural Networks - Advancing Artificial Intelligence Through Biological Process Applications - page 132

INTRODUCTION

what happens with these states if the network
capacity is exceeded.
The main idea of this chapter holds that when
patterns are very close each other, or if the net
capacity is exceeded, then local minima corre-
sponding to similar patterns tend to be combined,
forming one unique local minimum. So, although
considered as a limitation of the net as associative
memory, this fact can explain the way in which
the human brain form concepts: several patterns,
all of them similar to a common typical represen-
tative, are associated and form a group in which
particular features are not distinguishable.
Obviously, enough samples are needed to
generalize and not to distinguish their particular
features in both cases: artificial and natural (hu-
man) concept learning. If there are few samples
from some class, they will still be retrieved by
the net individually, that is, as an associative
memory.

Hebb (1949) introduced a physiological learn-
ing method based on the reinforcement of the
interconnection strength between neurons. It was
explained in the following terms:

When an axon of cell A is near enough to excite
a cell B and repeatedly or persistently takes part
in firing it, some growth process or metabolic
change takes place in one or both cells such
that A's efficiency, as one of the cells firing B, is
increased.

This kind of learning method has been widely
applied to recurrent networks in order to store
and retrieve patterns in terms of their similar-
ity. Models that used this learning rule were the
bipolar model (BH) presented by J. J. Hopfield
in 1982 (Hopfield, 1982) representing a powerful
neural model for content addressable memory,
or its analogical version, among others. These
networks, although successful in solving many
combinatorial optimization problems, present two
main problems when used as content-addressable
memory: their low capacity and the apparition of
spurious patterns.
The capacity parameter α is usually defined
as the quotient between the maximum number of
patterns to load into the network and the number
of used neurons that obtains an acceptable error
probability (usually p error =0.05 or 0.01). It has
been shown that this constant is approximately
α=0.15 for BH.
This value means that, in order to load K pat-
terns, more than K/ α neurons will be needed to
achieve an error probability lower than or equal
to p error . Or equivalently, if the net is formed by N
neurons, the maximum number of patterns that
can be loaded in the net (with that error constraint)
is K< α N .
Since patterns are associated to states of the
network with minimal energy, we wonder about

NEURAL bACkGROUND

Associative memory has received much attention
for the last two decades. Though numerous models
have been developed and investigated, the most
influential is Hopfield's Associative Memory,
based on his bipolar model (Hopfield, 1982). This
kind of memory arises as a result of his studies on
collective computation in neural networks.
Hopfield's model consists in a fully-intercon-
nected series of bi-valued neurons (outputs are either
-1 or +1). Neural connection strength is expressed
in terms of weight matrix W = ( w i , j ), where w i , j rep-
resents the synaptic connection between neurons
i and j . This matrix is determined in the learning
phase by applying Hebb's postulate of learning
Hebb, and no further synaptic modification is
considered later.
Two main problems arise in this model: the
apparition of spurious patterns and its low ca-
pacity.