Mind, Body, World- Foundations of Cognitive Science, 2013a

to one point, and chords whose root belongs to the other are mapped to the other
point. Interestingly, there is no systematic relationship in the graph that maps onto
the two circles. For instance, it is not the case that the four points toward the back
of the Figure 4-12 cube all map onto the same circle of major seconds.
1.0
6th
Major7
H3
0.5
1.0
H2 0.5
Dom7
Major
0.0
1.0
0.5
H1
0.0
Figure 4-13. An example of output unit partitioning of the hidden unit space for
the chord classification network.
Figure 4-13 illustrates how the output units can partition the points in the hidden
unit space in order to classify chords. Each output unit in this network is a value
unit, which carves two parallel hyperplanes through a pattern space. To solve the
chord classification problem, the connection weights and the bias of each output
unit must take on values that permit these two planes to isolate the two points associated
with one chord type from all of the other points in the space. Figure 4-13
shows how this would be accomplished by the output unit that signals that a 6 th
chord has been detected.
4.11 Trigger Features
For more than half a century, neuroscientists have studied vision by mapping the
receptive fields of individual neurons (Hubel & Wiesel, 1959; Lettvin, Maturana,
McCulloch, & Pitts, 1959). To do this, they use a method called microelectrode
172 Chapter 4