Databases Reference
In-Depth Information
FIGURE 3.4: Abstract representation of a GN and its storage framework.
in methods such as Hebbian and incremental learning. The term used for this
collaborative learning is Collaborative-Comparison Learning (CCL) [63].
3.2.1 Bias Array Design for Pattern Memorization
In a GN-based implementation, patterns are stored as associations between
the elements of the pattern. This pattern representation is different from other
neural network approaches, which store patterns as a composition of values.
The pattern storage mechanism adopted by GN is a bias array. Figure 3.4
shows an abstract representation of a GN and its storage structure.
GN minimizes the storage required for input patterns. For one-dimensional
input patterns, the growth of the storage element of each neuron is limited by
the Index{left, right} format of a bias entry. Consider a comparison between
a GN bias entry and the storage capacity requirements of each neuron in a
feed-forward neural network, given different binary pattern sizes used in the
networks. In a feed-forward network, each neuron requires input from all of
the elements within a pattern. When given a pattern, p with n input elements
(i.e., the size) and d dimensions, each neuron must memorize d
n
combinations
of patterns. Conversely, the storage capacity required for memorization by
each neuron in a GN network is only d
2
. From this perspective, GN offers
significantly higher storage e
ciency than the feed-forward neural network.
3.2.2 Collaborative-Comparison Learning Technique
In a GN-based implementation, an adjacency comparison approach is em-
ployed in the learning scheme using simple signal/data comparisons. Each GN
holds a segment of the overall subpattern. Collectively, these neurons represent
the entire subpattern. Consider the GN subnet structure shown in Figure 3.5.
The entire “ABCDE” pattern can be stored using five GNs, each responsible
for capturing the values of its adjacent neurons. By linking these neurons into
a one-dimensional structure, we can determine the GNs that collaboratively
contain a memory of the “ABCDE” pattern.
