Specific curiosity as a cause and consequence of transformational creativity
Kazjon Grace & Mary Lou Maher
Department of Software and Information Systems
University of North Carolina at Charlotte
Charlotte, NC 28203 USA
{k.grace,m.maher}@uncc.edu
Abstract
This paper describes a framework by which creative
systems can intentionally exhibit transformational creativity.
Intentions are derived from surprising events in
a process based on specific curiosity. We argue that autonomy
of intent is achieved when a creative system directs
its generative processes based on knowledge learnt
from within its creative domain, and develop a framework
to elaborate this behaviour. The framework describes
ways that transformation of the creative domain
can arise: from learning, from a serendipitous situation,
and as a result of intentional exploration. Examples of
each of these kinds of transformation are then illustrated
through examples in the domain of recipes.
Introduction
Significant effort has been devoted to developing computational
models that can recognise creative artefacts, on the
assumption such a capability could be used to generate creative
artefacts if paired with an appropriate search algorithm.
However, generate-and-test creative systems lack any kind
of autonomous intent: they never decide to make a green
artefact, or a loud one, or a happy one, unless such qualities
are built into their externally-provided objective function.
As classically formulated, a search function does not
distinguish two points within its space in any way but by
the objective, and thus has no intent that can be defined
with the representations that define that space, only in how
the resulting artefacts perform. Search functions that can
modify their goals while searching (Gebser, Kaufmann, and
Schaub 2009), or that search based on specific past experiences
(Cully, Clune, and Mouret 2014) do exist, but, from a
computational creativity perspective, there remains an unanswered
question: under what conditions should a system decide
to modify its search?
At first this lack of autonomous intentions in our systems’
search processes may fail to seem problematic: we are not
constrained by cognitive plausibility. There is no inherent
reason why intentionality, while clearly a quality of human
creators, should be required in their digital analogue. Our
goal is systems which produce output that would be considered
creative, regardless of the processes involved. On
closer inspection, however, autonomy of intention may not
be so easily discarded from creativity. Intent is intrinsically
tied to definitions of art and creativity (Dewey 2005), where
the debated questions concern not whether an artefact’s creator
had intent, but whether that intent should be privileged
over observers’ interpretations (Best 1981). Intention is seen
among human creators as critical both to the production and
consumption of creative artefacts – evidence that argues for
its role in appreciative as well as generative computational
processes.
Autonomy of intent also provides critical information for
use in framing. A creative system’s ability to construct framing
narratives for its work – considered critical to any computationally
creative construct (Charnley, Pease, and Colton
2012) – stems from its ability to provide justification for
creative decisions. Without autonomy of intent these justifications
can only be driven by external objectives (e.g. “I
wanted to make the artefact seem brighter”), not intrinsic
motivations (e.g. “I was exploring how colour influenced
brightness”). Human creators make the decision to explore
a particular set of concepts, and follow that exploration to
its resolution by way of creative expression. Framing, as
the channel by which a creative system can convince its
audience of its creative autonomy, should explain such explorations.
Previous models of intent in framing have been
based on information extrinsic to the creative domain, such
as the day’s top news stories (Krzeczkowska et al. 2010), but
we argue that without learning how to connect such external
knowledge to the creative domain (e.g. through analogy),
then such intent cannot be autonomous.
How, then, can a creative system derive intent from its
knowledge about the creative domain? On what basis should
it transform its inspiring set and own past creations into contextual
constraints on its search process? For one possible
answer we turn to cognitive studies of how human designers
think during the process of designing, and how their search
for a creative solution affects itself. Human designers do
not sequentially analyse a problem, synthesise solutions to
it and then evaluate those solutions, but instead switch between
those processes iteratively (Schon 1983), finding new ¨
problems as frequently as they find new solutions (Weisberg
1993). This co-evolution of problem-framing alongside
problem-solving becomes more evident in expert designers
(Cross 2004), and – more critically for our purposes – has
been shown to produce more valuable output (Getzels and
Csikszentmihalyi 1976). A cognitive protocol analysis of
Proceedings of the Sixth International Conference on Computational Creativity June 2015 260
sketching architects found that not only did they regularly
unexpected discover features in their own drawings, but that
those discoveries often led to reformulation of the design
task (Suwa, Gero, and Purcell 1999). These reformulations
led in turn to more unexpected discoveries, evidence that
this cycle of intentionality and exploration is beneficial, if
not central, to human creativity. We seek to capture this cycle
in the computational model presented in this paper.
We propose that the inspiration for a computational model
of intentional creativity can come from the iterative process
of defining the creative task and solving it in parallel. We
propose that intentions are not created de novo, but that they
arise from a drive to explore what the system has observed
but not understood, both from its own output and that of
other creators. The catalyst for this exploratory behaviour
is unexpectedness: a creator being surprised by an artefact,
and forming the intention to explore some part of the design
space in return. We refer to this as a kind of specific curiosity,
after the distinction between specific and diversive
curiosity first articulated by Berlyne (1966).
We frame our model for specific curiosity as an extension
of Wiggins (2006) framework for describing exploratory and
transformational creativity. With that symbolic representation
we can then describe how transformational creativity
leads to surprise, and how surprise can in turn lead to further
creativity.
Transformational creativity, surprise and their
effects on behaviour
This paper describes a model of autonomous intent in creative
systems, drawing on theories of evaluating creativity,
psychological studies of curiosity and cognitive studies of
how designers respond to unexpected discoveries. We introduce
each of those literatures here.
Three long-lost cousins: novelty, transformational
creativity and surprise
Novelty (Newell, Shaw, and Simon 1959; Saunders and
Gero 2001), surprise (Macedo and Cardoso 2001; Grace
et al. 2014) and domain transformation (Boden 2003;
Wiggins 2006) are three core ideas around which the debate
on how to computationally recognise creative artefacts has
revolved. In Grace and Maher (2014) we outlined how each
of those three could be connected to the notion of unexpectedness,
establishing one possible way to compare them in a
common language.
Novelty was, to the authors’ knowledge, first floated
alongside value by Newell, Shaw and Simon (1959), forming
the closest thing to a broadly-accepted definition for
creativity that we have today. Novelty and value are proposed
as necessary and complementary aspects of creativity:
a solely valuable artefact is merely good, while a solely
novel artefact is merely weird. Novelty is typically conceptualised
as difference from that which is known (Sternberg
and Lubart 1999), and usually operationalised by a distance
measure between a new observation and past experiences.
An alternate view of novelty is based on the degree
to which observing an artefact helps an agent to understand
the world (Schmidhuber 2010), proponents of which criticise
the distance-based approach as attributing overly high
novelty to noise.
Boden (2003) proposed another solution to the problem
of distinguishing meaningful novelty from noise by focusing
on impact. Transformational creativity is based on the
degree to which an artefact changes the creative domain
to which it belongs. This is suggested by Boden to be a
more significant form of creativity than the combination of
“mere” novelty and value, which she considers the result of
exploratory creativity. Wiggins (2006) formalises Boden’s
definition of transformational creativity and provides a general
description of a creative system that is capable of it,
although he questions Boden’s strict hierarchical superiority
of transformation over exploration.
The authors have previously proposed unexpectedness
and surprise as an alternative formulation of novelty (Grace
et al. 2014), although we are far from the first to do so
(Macedo and Cardoso 2001). Unexpectedness is the degree
to which observing an artefact violates (i.e. opposes) an
agent’s confident predictions about the world. The flexibility
of this approach is in the source of predictions, which may
be relationships within the artefacts, trends derived from the
domain’s history, or other sources of knowledge. Novelty
can be described from this perspective as a form of unexpectedness
based on the predicting that the domain will
continue as it has in the past. Surprise is an affective response
to unexpectedness: unexpected artefacts induce surprise
in their observers. Transformational creativity can be
described as a quantification of surprise based on how much
a new artefact changed domain knowledge. This connection
was described in Baldi and Itti (2010), who used an information
theoretic perspective to connect measuring surprise
by (un-)likelihood to measuring it by impact on knowledge.
Throughout this paper we adopt the viewpoint that these
three notions are intimately connected, constituting complementary
perspectives on how a creative artefact can be
meaningfully different from those that preceded it. We argue
that the evaluative processes of creative systems should
possess the ability to detect all of the above aspects of meaningful
difference, and that any one of them – in conjunction
with value – can indicate creativity.
Curiosity and the pursuit of novelty
Curiosity is an overloaded term in psychology, referring
both to a trait possessed by different people to different degrees,
as well as to motivating state that drives its experiencers
to seek novel stimuli (Berlyne 1966). The latter definition,
curiosity as a state, has been proposed as a motivator
for computational creative systems (Saunders and Gero
2001; Merrick and Maher 2009), based on the principle that
novelty-seeking (alone or alongside value) will drive exploration
towards creative solutions.
Berlyne distinguishes state-curiosity along two axes: perceptual
vs epistemic and specific vs diversive. Perceptual
curiosity is the drive towards novel sensory stimuli, and has
been observed in a variety of animals of different cognitive
capabilities. Epistemic curiosity is the drive to acquire novel
knowledge This conceptual curiosity can be modelled by
Proceedings of the Sixth International Conference on Computational Creativity June 2015 261
systems that learn a conceptual space and measure novelty
within it, rather than measuring between artefacts at the level
of sensory input (Saunders and Gero 2001). The distinction
between creativity at the sensory and knowledge-levels has
been drawn within computational creativity by Smith and
Mateas (2011), who refer to the latter as “rational curiosity”.
The specific/diversive division has received less attention
in computational creativity. Specific curiosity is the search
for observations that explain or elaborate a particular goal
concept. Diversive curiosity, on which most computational
models of curiosity have focussed, is the search for new information
without any specific targets. While the search for
a specific concept can be modelled by search, the challenge
is how to trigger specific curiosity: when and why should a
creative system become specifically curious? This is related
to the broader issue of creative autonomy (Jennings 2010;
Saunders 2011). In this paper we develop a model of specific
curiosity that uses surprise as a way to address this challenge.
How surprises affect designing
Cognitive studies of human creators – particularly in the
field of design – have shown that surprise significantly impacts
the creative process. Designing has been described as
a “reflective conversation with the medium” (Schon 1983), ¨
meaning that designers iteratively synthesise new additions
to their emerging design and then reflect on their effects. Expressing
creative artefacts through rough yet external representations
– usually referred to as sketches in the case
of human designers – is a critical component of the creative
process as it allows designers to observe changes
they did not consciously make (Schon and Wiggins 1992;
Goldschmidt 1991). Through this externalisation a designer
may perceive an emergent shape, discover a new relationship
between components, or construct an analogy to
past designs. Several computational creativity systems have
adopted this cyclical reflective approach in whole or in part,
including the search-bias transformation in DeLeNoX (Liapis
et al. 2013), the interpretation-driven mapping of Idiom
(Grace, Gero, and Saunders 2015) and the expectation-based
reinterpretation of Kelly and Gero (Kelly and Gero 2014).
This iterative process of “seeing” (perceiving an emerging
design) and “moving” (making a change to it) allows
designers to read more off a sketch than they originally
put there (Schon and Wiggins 1992). Though the term
has since been corrupted beyond recognition, this was the
original meaning of design thinking: an iterative, reflective,
solutions-focussed strategy as opposed to a step-bystep,
analytical problem-focused one (Lawson 2006). In
a “think aloud” cognitive protocol study where architects
were observed designing, unexpected discoveries were bidirectionally
causally connected to reformulation of the design
goals, i.e.: surprises led to transformation of the problem,
and transformation of the problem led to surprises
(Suwa, Gero, and Purcell 1999). These results with human
creators suggest that surprise-triggered specific curiosity
might be useful for encouraging transformative creativity
in artificial creative systems. In the remainder of this paper
we develop a framework for how that behaviour could be
operationalised.
Unexpectedness-triggered specific curiosity: A
model of transformation-seeking behaviour
We adopt the creative systems framework from (Wiggins
2006) to describe our model of unexpectedness and specific
curiosity. Wiggins’ framework describes a creative system
in terms of a search process that traverses a conceptual space
to generate artefacts, coupled with a metacognitive search
process that traverses the space of all possible conceptual
spaces. The resulting system is capable of both exploratory
and transformational creativity, with the latter represented as
exploration at the meta-level. The following symbols define
the core of the framework, although readers are encouraged
to familiarise themselves with the original, which affords
each definition far greater depth:
U is the universe, the space of all possible distinct
concepts that make up all possible representations
of artefacts in the current creative domain.
L is the ruleset language, the set of all possible rules
that act on concepts the creative system can construct.
J.K is the definition interpreter that takes a subset of L
and acts on a set of concepts, yielding real numbers
in [0,1]. This is used to apply a rule set to a set of
concepts, assigning a value to each.
R ✓ L is a constraint ruleset, by which the system defines
the scope of the conceptual space (within U).
C is a conceptual space is the current subset of U
permitted by R. i.e., C = JRK(U).
T ✓ L is a traversal ruleset, by which the system explores
C.
E ✓ L is an evaluation ruleset, by which the system evaluates
proposed concepts.
cin is the input set, a totally ordered subset of U that
reflects the list of artefacts known to the system, in
the order of the system’s observation of them.
cout is the output set, a totally ordered subset of U that
reflects the output of the creative system after a particular
generative iteration.
hh., ., .ii is the generation interpreter that takes three subsets
of L, the rules that define the conceptual space
R, the rules that define how to traverse that space
T, and the rules that assign value to members of
that space, E and acts on the set of all previously
observed artefacts to generate a new set of artefacts.
i.e., cout = hhR,T,Eii(cin).
LL is the meta-level ruleset language, the set of all
possible rules that act on rulesets (i.e., on L) the
creative system can construct.
RL ✓ LL is a meta-level constraint ruleset, by which the system
defines the scope of the meta-conceptual space
of possible rules that can be part of L.
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TL ✓ LL is a meta-level traversal ruleset, by which the system
explores the space of possible rules for L.
EL ✓ LL is a meta-level evaluation ruleset, by which the
system evaluates proposed rulesets for their ability
to generate valuable concepts.
The differentiation of R, the rules defining the conceptual
space, from T, the rules defining the search process
which acts on that space, is a significant addition to Boden’s
notion of transformational creativity. With this distinction
Wiggins can describe two kinds of transformational
creativity: R-transformation of the space of possible concepts,
and T-transformation of the search process for generating
new concepts. R-transformation, closest to Boden’s
original conceptualisation of transformative creativity, concerns
the redefinition of what a creative system considers
possible. T-transformation concerns the redefinition of how
a creative system creates.
The definition of a creative domain – as captured by Wiggins’
R – is a socially grounded construct. While it is useful
from the perspective of defining transformation across a creative
domain to think of that construct as stable across all
members of a society, in practice this knowledge must be
learnt by each member. In Boden’s original model, the definition
of the creative domain is agreed amongst all participants,
and this knowledge is not expected to be constructed
through exposure to the domain. Wiggins hints at the social
nature of R, but does not distinguish individual and societal
transformation of the conceptual space. To model the
influence of artefacts created by others on a system’s behaviour,
we must capture this distinction: we will use R
to refer to an individual creative system’s definition of the
space, but one could imagine a broader, socially grounded
historical-R of the sort Boden describes emerging from the
cross-pollination of ideas and norms.
Our intent is to capture specific curiosity – intentional
pursuit of further transformation along a search trajectory
incited by a particular transformative example – within an
expansion of this framework. To achieve this, we need to
expand Wiggins’ formalisation in four ways:
• To enable a creator to be surprised by its own output, as
in Schon (1983), a creative system must externalise and ¨
re-perceive its creations as part of the generative process.
• To incorporate the influence of other creators, the input
to a creative system’s generative process must include all
artefacts it has observed, not just its own creations.
• To model the probabilistic nature of expectations, the conceptual
space should be a fuzzy set of probable concepts,
not a crisp set of possible concepts.
• To separate unexpectedness from inexplicability, the system
should be aware of its confidence in the predicted
likelihood of any concept being in the conceptual space.
These changes capture the situated, social, and
expectation-based nature of creative systems, allowing
us to use Wiggins’ formalisation to explore the question of
when, where and why transformative creativity occurs.
Surprise as R-transformation
We now formally describe the above expansion of the framework.
The literature on design cognition describes how creators
can be surprised by their own creations. For this to be
possible in an artificial creative system those creations must
be represented in a way that contains additional information
not used to create them. To reflect this we add a step to the
post-generation process of the creative system. First, hh., ., .ii
is used to generate a new set of outputs, cout, from the current
inputs, and then instead of those outputs being directly
appended to cin for the next iteration, they are first reified via
a function r, which maps from a concept to an externalised
representation of that concept which we call an “artefact”,
and then re-perceived by a function p, which maps from an
artefact back to a concept in U. The nature of perception,
reification and the space of possible artefacts is beyond the
scope of this paper.
To capture a society of creative systems that influence
each others’ work, we must amend the generative step of
Wiggins’ formalisation: instead of applying the interpreter
hh., ., .ii to just cin, the ordered set of that system’s own past
creations, we must apply it to all an ordered set of all concepts
the system has previously observed, regardless of their
source. We assume our creative system is part of a society
of creative systems that are all producing artefacts within
the same domain (by which we mean they share at least U).
Each creative system possesses an additional ordered set of
concepts, cobs that it has observed but did not create. Different
societies may have different structures in which creative
systems are exposed to each others’ work in more or
less selective ways, but cobs is generated by applying the
perception function p defined above to some subset of the
artefacts externalised by other creative systems. If cobs is
non-empty before a creative system has generated any concepts
of its own, then those pre-existing known artefacts are
the system’s inspiring set (Ritchie 2001). We can now describe
the generation step in our amended formalisation, applying
the interpreter to the union of creations and observations,
and afterwards reifying and re-perceiving the output,
i.e. cout = p(r(hhR,T,Eii(cin [ cobs))).
Wiggins suggests that the output of the interpretation
function for R (a real number in [0, 1]) be converted to a
boolean value indicating membership in C. We propose instead
that C be considered a fuzzy set, with the output of
the interpreter defining a membership function l :U! [0, 1]
that indicates the likelihood of observing each concept as
part of the domain. This transforms Wiggins’ space of possible
artefacts into a space of probable artefacts, and lets us
capture all the rich relationships between concepts that influence
their mutual likelihoods. We derive this interpretation
from our previous work on expectation, novelty and transformation,
see Grace and Maher (2014) for details.
We introduce into our framework a notion of confidence.
This serves to differentiate unexpectedness (a violation of
confident expectations) from ignorance (Ortony and Partridge
1987). To achieve this we replace the J.K interpreter
from Wiggins with a modified version, L.M, which differs
only in that it returns a 2-tuple of real numbers in [0,1] for
each artefact to which it is applied. The first, as in J.K, is
Proceedings of the Sixth International Conference on Computational Creativity June 2015 263
the truth value, which becomes the value of the likelihood
function l that defines the artefact’s membership in the resulting
set. The second value is the system’s confidence,
with 0 indicating a complete lack of confidence and 1 indicating
complete certainty. This confidence becomes another
function c :U! [0, 1]. We use L.M when generating the conceptual
space with R, as in:
C = LRM(U )
As a result our C is a fuzzy set of concepts with a membership
function l defining the likelihood of observing each
concept in U, as well as a similar confidence function c
defining the system’s confidence in each artefact’s likelihood.
These functions are compiled from the first and last
elements, respectively, of the tuples output by L.M. That is,
for each concept a 2 U, given LRM({a})=(al, ac) and
assuming al > 0:
a 2 C , l(a) = al, c(a) = ac
From this perspective, Wiggins’ R becomes the creative
system’s expectations about the creative domain. This connection
between conceptual space membership and expectation
allows us to describe the influence of surprise on creative
search. In our amended framework, R-transformation
is commonplace and necessary, a natural effect of creative
systems acquiring the knowledge they need to competently
model the society’s rules about the domain through their
own experience.
A creative system experiences expectation failure when
the conceptual representation of a newly observed artefact
has a low a-priori likelihood in the conceptual space. We can
then distinguish two kinds of artefact that cause expectation
failure: inexplicable ones, where the system is not confident
of its predicted low likelihood, and unexpected ones, where
it is. An unexpected artefact au is one for which:
au 2 (cin [ cobs), l(au) ⇡ 0, c(au) ⇡ 1
Complementarily, for an inexplicable artefact ai:
ai 2 (cin [ cobs), l(ai) ⇡ 0, c(ai) 6⇡ 1
Only in the first case can we say that the agent’s expectations
were violated – in the absence of a confident prediction
the system was merely ignorant. Both inexplicable and unexpected
artefacts should by rights induce a transformation
of the domain knowledge in R, as well as potentially transformations
of T. Those transformations can be considered
a result of creativity if the artefact(s) that caused them are
valuable under E. Given our definition of unexpectedness in
terms of R we can restate how our expanded formalisation
captures the dyad of novelty and value. The rules in E will
be concerned with the evaluation of artefacts’ performance,
quality, style, and other components of value, and some portion
of T will use those evaluations to direct search. Contrastingly,
some other subset of T will be concerned with
novelty seeking: evaluating the dissimilarity of new artefacts
to existing ones using measures of novelty, surprise and
transformativity. We refer to this novelty-seeking subset as
Tn ⇢ T. These latter traversal rules will be based on the
likelihoods, confidences, and transformations of L associated
with artefacts.
We do not seek to resolve the disputes surrounding the
definitions of novelty, surprise or transformation, only suggesting
that Tn could contain metrics for any or all of those,
but we do require that for any creative system Tn 6= ;.
Any artefact valued by both Tn and E can be considered
p-creative. This generative act is serendipitous if the search
process possessed no specific intent to create that artefact or
anything like it. An artefact discovered to be transformative
by Tn after its creation was not the result of a directed
search, for the system cannot know how its knowledge will
be transformed by new observations. This places limits on
a creative system’s ability to generate framing about its creative
output: serendipity defies satisfying explanation.
In the next section we use our definitions of inexplicable
and unexpected artefacts to describe different possible
kinds of transformational creativity. We also propose how
a system might adopt constraints on its future generation in
response to unexpectedness, and thereby intentionally seek
out further unexpected discoveries.
Specific curiosity as a consequence of surprise
A system that has observed inexplicable artefacts will attempt
to learn: to improve its (clearly insufficient) knowledge
of U. We consider learning to be a creative system’s
response to the inexplicable, and it is our first possible kind
of R-transformation. Learning can be expressed as the application
of TL to produce new R and/or T in response
to inexplicable artefact(s) in cin or cobs. While the mechanisms
of learning will be specific to the rules in LL, we can
describe its effects: it attempts to transform R such that the
likelihood of previously observed artefacts increases.
A system that has observed unexpected artefacts will be
surprised. We consider artefact-induced surprise to be a creative
system’s response to unexpected artefacts, and it is our
second kind of R-transformation. Artefact-induced surprise
can be expressed as the application of TL to produce new R
and/or T in response to unexpected artefact(s) in cin or cobs.
Learning occurs from unexpected objects as it does from inexplicable
ones, producing R-transformations that increase
the expected likelihood of previous observations.
Inspired by cognitive studies of reflection in human designers
by Suwa et al (1999) and others we can now consider
how surprise might affect a system’s future generative
behaviour (i.e. cause transformation of T). Specific curiosity,
as introduced earlier, is the deliberate pursuit of specific
new knowledge or stimuli through the adoption of goals or
constraints on behaviour. In the context of a creative system
this is T-transformation with the goal of exploring an unexpected
stimulus, based on the hypothesis that (as observed in
human designers), surprise begets further surprise. This can
also be considered a form of active learning (Cohn, Ghahramani,
and Jordan 1996), where the system actively tries to
fill the gaps in its knowledge through generation.
To become specifically curious about an artefact is to seek
to create more artefacts that embody the interesting things
about it. We formalise this as follows: given an unexpected
Proceedings of the Sixth International Conference on Computational Creativity June 2015 264
artefact au we can determine the subset of rules that contributed
to its confident low-likelihood prediction: Rau ✓
R. These rules embody the domain knowledge that was violated
by the perception of the new artefact, in that they produced
a confident prediction that was proven wrong. This
subset forms the basis of the system’s specific curiosity, in
that the system can use them to pursue artefacts that are unexpected
according to just those rules. To define this we
induce r, a relevance function over concepts that measures
the complement of the likelihood of a concept occurring in a
conceptual space defined exclusively by Rau . Accordingly
r(a) ⇡ 1 for any artefact a that would be considered unexpected
according to the same rules as was au, including au
itself. Conversely, any artefact that is not unexpected, or is
unexpected due to other rules not in Rau , would produce a
lower value of r. We can then define specific curiosity about
au as replacing Tn with a single rule that seeks artefacts for
which r(a) ⇡ 1. This (temporarily) redirects the system’s
general (i.e. diversive) search for novel artefacts towards
those that are unexpected according to the same rules as the
one that caused the surprise.
By constructing a relevance function from the rules violated
by the unexpected artefact we focus the system upon
the parts of its own knowledge that produced the unexpected
result. The results of this specific curiosity will vary based
on the structure of the knowledge that was violated. If the
rules define boundaries of the domain, the relevance function
will value artefacts that break the same boundaries as
the focus of curiosity. If the violated rules placed the focus in
a new or rare category, the relevance function will value artefacts
in that category. If the violated rules define an expected
relationship between components of the artefacts’ representation,
the relevance function will value artefacts that break
the same relationship in the same way as the focus. In each
case the relevance function will value artefacts that are in
some way similar to the one that caused surprise, but with
that similarity determined by the system’s knowledge.
The hypothesis driving this specific curiosity is that regions
of the conceptual space that generate one unexpected
artefact likely have the potential to generate more, and
searching nearby has a greater chance to yield further unexpected
(and therefore potentially creative) artefacts than
searching elsewhere in the space. This behaviour aligns with
the concept of creative autonomy and situational adaptation
of goals described in (Jennings 2010).
In the following section we illustrate the above kinds of
R-transformation with examples from the domain of recipe
generation.
A worked example of
unexpectedness-triggered specific curiosity
As a hypothetical example of our unexpectedness-triggered
reformulation approach, consider the creative domain of
recipes. Culinary creativity has recently attracted attention
in the computational creativity community (Morris et al.
2012; Varshney et al. 2013), and we draw upon it as a way
of illustrating our model of specific curiosity.
Assume a hypothetical recipe generation system integrated
with a large online recipe repository. The system has
access to all the recipes posted by humans, and is tasked with
supplementing that database with its own creations. Each
recipe is an artefact represented by its ingredients and their
quantities, the preparation steps, and metadata such as cooking
time and user-applied tags. This is supplemented by behavioural
information for each recipe: the full text and ratings
of its set of user reviews. The system’s task is to generate
novel and valuable recipes, and submit them for human
consumption and review. E is based on aggregated user ratings.
R is based on domain knowledge represented by a set
of predictive models that describe the likelihood of various
combinations of ingredients, quantities, tags, categories, reviews
and ratings occuring. We can now describe three ways
that this implementation of our framework could encounter
transformative creativity.
The first cause of R-transformation is encountering an
inexplicable recipe. This would be commonplace while the
system developed its knowledge about the domain (as the
pre-existing human-created recipes that form its inspiring
set were added to its database). For example, assume that
the system, early into its learning, encountered its first slowcooked
dish. The existing rules in R would assign a very
low a-priori likelihood to a recipe with an eight hour cooking
time, but having seen so few previous recipes of any kind
it would also assign a low confidence to that prediction. The
result would be learning – transforming R to incorporate the
new range of observed cooking times. No surprise or specific
curiosity would result – the system’s understanding of
the conceptual space improved as a result of observing new
kinds of artefact that had been produced by others, a necessary
and commonplace step of acquiring competency in a
creative domain.
The second cause of R-transformation is an unexpected
recipe. This occurs when the system makes confident predictions
of the likelihood of observed recipes, but is still
wrong, possibly as the result of a change in the behaviour
of the other creative systems in the society (which, in this
case, are the human submitters of recipes). Consider what
would happen to the system’s knowledge about the ingredient
“ginger” if its inspiring set (i.e. the recipes in cobs it
used to populate R before generating any artefacts of its
own) contained mostly Western recipes, and it developed
confident predictions about that ingredient before being exposed
to Eastern-inspired recipes. It would confidently expect
that ginger was found mostly in sweet baked goods,
alongside ingredients like butter, sugar and flour. Encountering
a recipe for ginger-and-soy chicken would be highly
surprising, causing it to adapt its domain knowledge to fit the
new recipe. In this case the creative system had a robust, but
incomplete model of the creative domain, and observed an
artefact that it would consider p-creative, even though that
artefact’s creator may have considered it novel.
The third cause of R-transformation is as a result of specific
curiosity caused by an earlier surprising recipe. As another
example, consider “chicken paprikash”, a Hungarianinspired
dish that combines a roux-based sauce with currylike
spices (cumin, paprika and chili). This is an incongruous
combination of ingredients and instructions, as the maProceedings
of the Sixth International Conference on Computational Creativity June 2015 265
jority of roux-based sauces are flavoured with herbs, stocks
and/or cheeses. Our creative system encounters this recipe,
becomes surprised as in the ginger-and-soy chicken example,
and uses that surprise to trigger specific curiosity. The
rules in R that confidently assign a low likelihood to a recipe
containing both the steps for a roux and the ingredients for a
curry are extracted as Rau. A relevance function is then
constructed from those rules that evaluates the degree to
which a recipe violates them, and this function replaces the
novelty-seeking rules in Tn. The system begins generating
recipes that violate these specific rules, such as a roux-based
sauce with other unexpected ingredients (such as chocolate),
or curries with unusual preparation steps (such as being
baked into a pie). The authors feel compelled to mention
that they are not chefs, but encourage readers to assume for
the sake of argument that those new recipes are both novel
and valuable. The observation of these new recipes would
lead to additional R-transformation, and this time that transformation
can be said to have a deliberate cause. These artefacts
were not created serendipitously, they were intentionally
generated as the result of a targeted exploration of a
specific region of the creative domain, and their discovery
further transformed the conceptual space.
Specific curiosity can be triggered both from a creative
system’s own creations, or from those of the other creative
systems within its society (here the human user-base of the
recipe website). In the case of the chicken paprikash above,
the specific curiosity episode was triggered by the observation
of a surprising creative artefact generated by a human –
other likely external curiosity-triggers in this domain could
include the addition of bacon to sweet foods, the inclusion
of leafy greens in smoothies, the rise of a new and novel
“superfood”, or a seasonally resurgent ingredient.
The creative system could trigger its own specific curiosity
episodes by generating recipes that, once reified and reperceived,
were considered surprising. Consider, for example,
rules in our creative system’s T that use computational
analogy-making to map between two recipes and then transfer
a new ingredient from the source to the target. An analogy
could be constructed between a calzone and an omelette,
as both consist of a base layer to which toppings are added
before the base is folded over to create a filled final product.
The rules for analogical transfer in T identify that the tomato
paste spread on the calzone is missing from the omelette, and
create a new recipe in which a tomato sauce is spread over
the omelette before folding. This would be considered unexpected
by the rules in R that pertain to omelettes, which
would make confident predictions that a tomato-based sauce
would be unlikely to be involved in an omelette recipe. The
authors again remind the reader that we are definitely not
chefs, but let us assume that the resulting sauced omelette
was also considered valuable. Specific curiosity about that
unexpected combination of ingredients and cooking methods
would result in a transformation of Tn to specifically
seek out further recipes involving unusual ingredients being
added to omelettes during cooking. Generating new artefacts
under this transformed search trajectory could lead to
the recipes with further unexpected mid-omelette additions
such as spices or fruits. These new creative artefacts would
further transform the rules in R that pertain to omelette creation,
and if they were also considered valuable according
to E then they would constitute intentional transformative
creativity.
Conclusions
We have described an extension to Wiggins’ (2006) framework
that captures the notions of unexpectedness, surprise
and specific curiosity. This approach is motivated by the
need for creative systems that can make autonomous evaluative
decisions and exhibit intentional behaviour (Jennings
2010; Saunders 2012). The solution proposed in our framework
draws on literature from design cognition which suggests
that human creators are not only capable of selfsurprise
but that it is a significant driver of creative output.
Based on this inspiration from cognition we model surprise
based on violation of a creative system’s learnt model of the
conceptual space, and describe specific curiosity behaviours
that explore surprising stimuli.
Within our framework we can distinguish three causes
of transformational creativity: inexplicable artefacts, unexpected
artefacts, and specific curiosity. If found in an artefact
that was also valuable the first would not be creative (as
the transformation resulted from a lack of sufficient knowledge
to make predictions), the second would be serendipitous
creativity (as the system stumbled upon it without any
deliberate goal), and the last would constitute intentional
creativity. Specific curiosity describes the iterative cycle between
the R-transformation that occurs when observing or
creating an unexpected artefact, the T-transformation that
facilitates the resulting search for more, similarly surprising
artefacts, and the resulting R-transformation that heralds the
success of that deliberate search. Our future work involves
the development of systems like the one presented here as
an example: creative machines capable of surprise, specific
curiosity and autonomous intent.
<references_biblio/>
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