IDyOT: A Computational Theory of Creativity as Everyday Reasoning from Learned Information - Computational Creativity Research: Towards Creative Machines - page 126

is used to select the combination that is actually used; we return to this issue below.
Nevertheless, the idea is promising, demonstrating musical behaviour that we might
expect: as the model is exposed to more music, it quickly discovers that relative pitch
representations are preferable to absolute ones, and thence that scalar and modal rep-
resentations, where relative pitch is expressed relative to a tonal centre (key note) are
more efficient still. The former of these two effects is exhibited by human infants [ 43 ];
a strong informal argument can be made for the latter by reference to the dominance
of tonal music in the West, and the commonly attested need for Western-enculturated
listeners to deliberately enter a different mode of listening to appreciate non-tonal
music [ 27 ].
Furthermore, to admit creativity beyond mere re-ordering of symbol sequences, it
is necessary to use continuous representations of meaning. Categorical perception of
pitch, timbre and colour give a clear indication that mind/brains 3 are able to maintain
dual simultaneous representations that have both discrete (symbolic) and continuous
properties. One theory that admits such a representation is that of Gärdenfors [ 17 ], in
which conceptual spaces are composed of perceptual dimensions, whose existence
is motivated by the need to make distinctions as an organism understands the world.
For example, hue, saturation and luminance are three dimensions that define colour
space, and they are integral in the sense that they cannot exist separately. Discrete
symbolic concepts such as “red” exist in correspondence with regions in the space,
with all the geometrical reasoning that this implies. Gärdenfors shows in detail how
this idea can extend to very complicated observations, such as the movement of a
human arm. Finally, the geometry of the conceptual spaces may be adjusted with
weights, changing the relative distances between concepts, allowing us to model
(aspects of) salience.
We propose that Gärdenfors' theory is an appropriate mathematical background
to support a model which is capable of optimising both the representation of the per-
ceptual content and the learned sequence, by inferring meaningful and information-
theoretically efficient conceptual spaces in context of sequences of stimuli. This
approach is comparable with the deep learning proposed by Hinton et al. [ 20 ] and
Bengio [ 2 ], in that it allows stacked hierarchies of successively more abstract repre-
sentation and decreasing dimensionality. However, our approach has the advantage of
being theoretically driven, methodologically top-down, and is therefore more readily
amenable to post-hoc analysis. A particular feature of both Gärdenfors' theory and
deep learning that is important here is the ability to learn representations over time,
each one being learned in terms of those that are already available; this is in contrast
with the usual methods of statistical linguistics, where the entire high-dimensional
space is approximated in a single operation, giving all dimensions equal precedence.
A different, but wholly compatible, notion of conceptual space was introduced by
Boden [ 3 ] in one of the seminal works of Computational Creativity. This conceptual
space is conceived with respect not to an internal representation, but to an abstract
notion of the artefact itself. For example, one can have a conceptual space of post
3 We wish to avoid arguments over where the brain ends and the mind begins, so we use this epithet
to refer to the whole assembly.