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

4.10 Chord Classification by a Multilayer Perceptron
Artificial neural networks provide a medium in which to explore empiricism, for
they acquire knowledge via experience. This knowledge is used to mediate an
input-output mapping and usually takes the form of a distributed representation.
Distributed representations provide some of the putative connectionist advantages
over classical cognitive science: damage resistance, graceful degradation, and so on.
Unfortunately, distributed representations are also tricky to interpret, making it
difficult for them to provide new theories for cognitive science.
However, interpreting the internal structures of multilayered networks, though
difficult, is not impossible. To illustrate this, let us consider a multilayer perceptron
trained to classify different types of musical chords. The purpose of this section is to
discuss the role of hidden units, to demonstrate that networks that use hidden units
can also be interpreted, and to introduce a decidedly connectionist notion called
the coarse code.
Chords are combinations of notes that are related to musical scales, where a
scale is a sequence of notes that is subject to certain constraints. A chromatic scale
is one in which every note played is one semitone higher than the previous note. If
one were to play the first thirteen numbered piano keys of Figure 4-7 in order, then
the result would be a chromatic scale that begins on a low C and ends on another C
an octave higher.
2 4 7 9 11 14 16 19 21 23 26 28 31 33 35
1 3 5 6 8 10 12 13 15 17 18 20 22 24 25 27 29 30 32 34 36 37
Figure 4-7. A small piano keyboard with numbered keys. Key 1 is C.
A major scale results by constraining a chromatic scale such that some of its notes
are not played. For instance, the C major scale is produced if only the white keys
numbered from 1 to 13 in Figure 4-7 are played in sequence (i.e., if the black keys
numbered 2, 4, 7, 9, and 11 are not played).
Figure 4-8. The C major scale and some of its added note chords.
162 Chapter 4