Conceptualizing Creativity: From Distributional Semantics to Conceptual Spaces
Kat Agres, Stephen McGregor, Matthew Purver, and Geraint Wiggins
School of Electronic Engineering and Computer Science
Queen Mary University of London
London E1 4NS UK
kathleen.agres, s.e.mcgregor, m.purver, geraint.wiggins (@qmul.ac.uk)
Abstract
This paper puts forth a method for discovering
computationally-derived conceptual spaces that reflect
human conceptualization of musical and poetic creativity.
We describe a lexical space that is defined through
co-occurrence statistics, and compare the dimensions of
this space with human responses on a word association
task. Participants’ responses serve as external validation
of our computational findings, and frequent terms
are also used as input dimensions for creating mappings
from the linguistic to the conceptual domain. This novel
method finds low-dimensional subspaces that represent
particular conceptual regions within a vector space
model of distributional semantics. Word-vectors from
these discovered conceptual spaces are considered, and
argued to be useful for the evaluation of creativity and
creative artifacts within computational creativity.
Introduction
This paper presents a computational-linguistic model for
mapping lexical spaces populated by statistical representations
of words to conceptual spaces defined in terms of feature
dimensions of conceptual representations. This research
has three main goals. The first is to compare the features of
a distributional semantic vector space with the results of an
empirical word-association task completed by human subjects.
This empirical corroboration serves to demonstrate
that the model can capture meaningful aspects of human
conceptualizations of queried topics, which are “musical
creativity” and “poetic creativity” in the present study. The
second goal is to use novel methods inspired by computational
linguistics to map terms from the linguistic domain
to representations in the conceptual domain. To this end,
the terms generated by participants are used as input parameters
for our computational model that uses co-occurrence
statistics and linear algebraic metrics to quantify conceptual
proximity. The third motivation of this work concerns the
evaluation of creativity. In the field of computational creativity
(CC), the evaluation of creative output is often either
subjective on the part of the developer/researcher or unsystematic.
We offer our own fundamentally computational approach
as a means of identifying facets of the investigated
concept or domain. Put another way, our model can generate
terms within a conceptual space that may be used to query
different aspects of creative output or creative behavior.
Vector space models of distributional semantics are currently
a popular approach for quantifying linguistic similarity,
but many contemporary studies need grounding and external
validation. Much of the work in this area compares
model performance to semantic databases, but does not directly
relate results to the cognitive performance of humans,
or uses very restricted tasks, such as similarity judgments,
rather than imploring subjects to elaborate on concepts. Because
our aim is to elucidate how humans conceptualize
creativity, sampling from people’s own formulation of conceptual
spaces is essential. Therefore, in the present work,
our ground truth is derived from human responses stemming
from direct queries about creative concepts. Because human
response data is a limited and expensive resource, we hope
that our comparison to human data will inform how conceptual
spaces may be discovered as autonomously as possible
in the future (that is, without the requirement of subjective
user-input or parameter-tweaking). We also believe
that this multidisciplinary and externally validated approach
produces a more robust system.
In order to pinpoint the relationship between the output
of our computational model and the results of our empirical
study, we take the human-generated terms and investigate
their situation within the multidimensional space of our
distributional semantics model. We then determine the characteristic
co-occurrence dimensions of sets of words associated
with concepts, and apply appropriate methods to reduce
the dimensionality of the space in order to map broader
clusters of linguistic terms to conceptual regions. We argue
that the online generation of a reduced lexical space corresponds
to the contextualization inherent in the momentary
way in which concepts are necessarily formed in response
to situations in a cognitive environment. We expect that this
methodology will be a useful applied approach to formalizing
the geometrical representation of conceptual spaces.
Our research explores two related concepts: musical creativity
and poetic creativity. There are several reasons for
this choice. First, we are interested in computational creativity,
and in particular in the evaluation of creative systems
and their output. In order to evaluate creativity, it is necessary
to characterize features of this concept using the expressive
affordances of language. Our computational methods
seek to capture these features of the conceptual space. Our
model may also be used to discover conceptually-related
terms that a human might not necessarily immediately conProceedings
of the Sixth International Conference on Computational Creativity June 2015 118
sider. We hope this approach may be used to elaborate abstract
concepts by elucidating an extensive set of terms that
correspond to the queried conceptual spaces. We therefore
offer this methodology as a novel approach for exploring
and elaborating concepts, both for the evaluation of creative
systems and for potentially contributing to creative pursuits
themselves (such as poetry generation). Furthermore, we
apply our method to a more concrete domain, extending a
small subset of terms relating to the concept WILD ANIMALS
in order to indicate the anticipated generality of our model.
The organization of the paper is as follows: first we offer
a summary of computational approaches to conceptual creativity,
situating our research within the field. This overview
leads into a discussion of computational approaches to the
topics of conceptual spaces and geometric representations
of concepts. An explanation of our computational model
is then provided, including a description of how we have
modeled a lexical space populated by word-vectors. This
is followed by a description of our empirical study with human
participants, and findings from this questionnaire-based
study are reported. Given this context, we then discuss
two ways in which the participants’ responses contribute
to our computational approach. The first is a comparison
of computationally-derived terms with human-generated
terms. The second contribution will be to treat the salient
features of the word-vectors corresponding to the most frequently
reported human terms as an indication of the dimensions
of a vastly reduced subspace of our distributional semantic
model. We then discuss how terms that fall near the
centroid of the positively valued surface of the discovered
lexical spaces may be used for the evaluation of creativity.
CC and Concept Discovery
Computational approaches to creative conceptualization
have provided a target that is both elusive and essential to
the identity of a field that incorporates a particularly diverse
range of topics. Creativity itself has been interpreted
by Koestler (1964) as a kind of meshing of disparate conceptual
schemes, by which expectations are violated in favor
of interesting new combinations of frames of reference.
Presciently, Koestler has couched his model of creativity in
terms of vector spaces and transformations, an idea which is
broadly shared by the model presented in the present paper.
In the same spirit of conceptual exploration, Hesse (1963)
argued that the formation of creative analogies is the essence
of scientific discovery, an idea demonstrated by the primacy
of analogical modeling in fields such as physics, where there
is no realistic way to literally conceive of phenomena that
occur on obscurely minuscule or vast scales.
In the specifically computational domain, Veale (2006)
has proposed a system for the dynamic generation of new,
non-literal conceptual categories based on a computational
analysis of a taxonomical database such as WordNet. Likewise,
other researchers are developing formal models of
conceptual blending (Fauconnier and Turner, 2008) that
seek to discover novel combinations of familiar ideas, targeting
domains such as mathematical reasoning and story
generation (Ontanon, Zhu, and Plaza, 2012). These ap- ´
proaches make clever and effective use of heuristics to pick
out interesting new conceptual representations based on preconceived
patterns identified by programmers. As such, the
output of these methods is compelling and valid, but the conceptualization
itself is arguably handed to the system in the
prepackaged form of externally grounded symbols.
Elsewhere, Heath et al. (2013) have taken a more connectionist
approach to conceptual creativity, combining human
based word associations with statistical models of distributional
semantics to design a system that infers conceptual
categories from lists of terms, and likewise generates lists of
terms from linguistic input that is interpreted conceptually.
In a similar vein, Jager (2009) has performed a statistical ¨
analysis on a set of human reported color terms and used
this analysis to generate a geometric representation of certain
consistencies in the ways that color is conceptualized
across cultural linguistic boundaries. In their commitment
to building models based on low level, non-symbolic observations
about the world, these statistical approaches to
creative conceptualization are in the same spirit as the work
presented in the present paper.
The model described here has been designed to engage
with the field of computational creativity on two different
planes. Principally, our method seeks to implement a low
level approach to the delineation of conceptual regions based
on the geometry of a distributed semantic space. By viewing
concepts as momentary and pragmatic phenomena, we are
able to use ad hoc reductions of a high dimensional lexical
space to map concepts creatively based on situational contexts
which do not have to be preformulated in the design of
the model. Furthermore, our target domains of musical and
poetic creativity play nicely into a salient issue in the field
of computational creativity: the analysis of creativity itself,
a difficult procedure that necessarily involves some degree
of conceptualization about creativity. This secondary aspect
of the work, the potential for meta-analysis inherent in the
question of whether our model’s output will be useful for
guiding an evaluative discussion of creative work elsewhere,
is intended to give the work its own pragmatic grounding, in
that this suggests a practical application for the creative output
described in the following pages.
Spaces of Meanings
This project uses computational methods as a platform for
exploring the relationships between words and concepts
within the context of a cognitive system. In the pragmatic
spirit of Wittgenstein (1953) and Grice (1969), language is
presented as a system defined by its own functionality, with
meaning emerging from the use of words in the course of
accomplishing communicative goals. To the extent that language
is used to communicate ideas, statements are formed
contextually, with reference to expectations about how relationships
between words will suggest hierarchies of categorization
relative to a particular situation. Barsalou (1993)
characterizes the relationship between words and concepts
in terms of the linguistic vagary inherent in the application
of names to ideas: words represent concepts in a way that
is fleeting and mutable. Fundamentally, words stand as indices
to concepts, and the relationship between language and
ideas is best understood as a mapping between two separate
domains. The project presented in this paper is therefore
motivated by a desire to model the relationship between two
Proceedings of the Sixth International Conference on Computational Creativity June 2015 119
different spaces, one of words and one of concepts, and to
explore the ways in which these spaces might be aligned in
terms of the computationally tractable elements of their geometries.
Gardenfors (2000) has presented a spatial theory of con- ¨
cepts, by which the dimensions that determine the geometric
situation of a conceptual region within a space of concepts
correspond to the attributes which characterize that particular
region. So, for instance, the concept RIPE BANANAS
would occupy a region towards the higher end of the dimensions
of curviness, yellowness, and sweetness within a conceptual
space. This literal and factual quality of dimensions
grounds conceptual spaces in low level observations about
the world, giving regions within the space a geometric dynamism
that lends itself to doing higher level work with the
entities that emerge from the space as symbolic representations.
In particular, well defined conceptual regions are
characterized by convexity, a property that ensures that any
intermediate point between two outlying extensions of a region
will likewise belong to that domain.
Vector space models of distributional semantics, on the
other hand, offer an approach to language modeling involving
a distinctly unstructured computational analysis of linguistic
data. In the tradition of Harris (1957), the distributional
hypothesis holds that there is semantic information
inherent in the statistical comportment of language: linguistic
meaning can be found in the quantifiable contextual relationships
between words. This insight has motivated a
productive field of research, with computational analyses of
large scale corpora yielding distributional semantic models
in which the meanings of words, sentences, and documents
are rendered in terms of mathematically tractable representations
(Schutze, 1992; Landauer et al., 1997). Distributional ¨
semantic models treat words as vectors, with the dimensions
of these vectors representing, either directly or abstractly,
the likelihood of a word occurring in a given context. The
closeness of vectors in a lexical space, which reflects the tendency
of the proximal vectors to occur in similar contexts,
has been shown as an indication of lexical similarity between
the words tied to the vectors. In their most straightforward
implementation, distributed semantic spaces are constructed
by counting the frequency with which each word in
the model co-occurs with all other terms in a base corpus
(see Turney and Patel, 2010; Clark, 2015, for an overview).
There is an important difference between lexical spaces
and conceptual spaces: the dimensionally regimented quality
of coherent domains within a conceptual space is not
reflected in the distribution of vectors in a lexical space,
where the dimensions of word-vectors correspond simply to
the context in which those words are likely to occur, and
therefore capture all the flexibility and uncertainty of language
in use—the linguistic vagary of Barsalou’s system
of conceptual symbols. So, for instance, the other vectors
in the proximity of the word-vector !!pet in a distributed semantic
model cannot be expected to contain only terms corresponding
to domesticated animals, not least because the
word “pet” itself has other uses. In this sense, where conceptual
spaces are marked by a tidy taxonomy facilitated by
the clarity of a region’s dimensional substrate, distributed semantic
spaces embody the pragmatic messiness of language
as it is encountered in its natural, operational environment.
Therefore, while lexical spaces and conceptual spaces both
utilize geometry as a vehicle for semantics, the arrangement
of a lexical space is in an essential way less ordered.
An example of the difficulty of delineating conceptual regions
within a lexical space is illustrated in Figure 1a. In
the rudimentary distribution of words presented here, concepts
are required to stretch and overlap in order to maintain
their lexical constituencies. This simplified depiction of
the potential uncertainty of conceptual membership doesn’t
demonstrate the even more fundamental problem of picking
out salient words in regions that are littered with noise:
in practice, in the densely and unevenly populated territory
mapped out by a vector space model, many unwanted terms
will be discovered in the region generally between two other
terms. For instance, in the unrefined version of our model,
there are 14 terms essentially between the word-vectors !!cat
and !!dog, including such unlikely candidates as “during”,
“eventually”, and “featuring”. There is thus an inherent
patchiness to the mapping of concepts that might be read in
an unrefined vector space model of distributional semantics.
Here we propose a system for mapping lexical spaces
to conceptual spaces by considering a conceptualization as
a particular and temporary perspective on a space of distributed
semantics. The idea behind this system is that, for
any desired clustering of words corresponding to a particular
conceptualization, there is some subset of a distributional
space’s dimensions that will render a subspace in which that
clustering is realized. This intuition is illustrated in Figure
1b, where the conceptually entangled space of Figure 1a
collapses into a particular conceptual regime depending on
the axis along which the space is projected, which is to say,
the perspective from which the space is considered. The task
of our system is therefore to determine the dimensions which
should be picked out of a higher order vector space model
in order to realize a grouping of terms that is conceptually
homogeneous by virtue of the contextualization imposed by
a particular perspective on the space.
It is precisely the massive dimensionality of the space
which facilitates the method’s ability to pick out various successful
conceptual perspectives on the space in a momentary
and continuous way. With each additional contextual dimension
introduced to a vector space, there is an exponential increase
in the lower-dimensional combinations available to
map corresponding spatial relationships of words to conceptual
subspaces. Moving from the linguistic realm native
to vector spaces back to the cognitive domain targeted by
Gardenfors, these dimensional perspectives might be con- ¨
strued as corresponding to a contextualized perception of a
situation. In this respect, our system models the haphazard
quality of conceptualization described by Barsalou, as well
the ad hoc nature of concept formation discussed more recently
by Allott and Textor (2012), who suggest that meaning
is appropriated in situ to endow statements with contextually
relevant implicature. This phenomenon of conceptualization
arising from pragmatic communicative affordances
is what our method seeks to computationally model.
Proceedings of the Sixth International Conference on Computational Creativity June 2015 120
Figure 1: Conceptual Perspectives of Vector Spaces
wolf
dog cat
lion
canine
pet
feline
predator
(a) In this simplified and unrefined distributional semantic space,
the conceptual regions suggested by the spatial arrangement of
terms are indeterminate. Each word is roughly equidistant from
two other terms, either of which could be linked in a distinct linguistic
depiction of a concept. The conceptual domains which are
delineated by this arrangement of words are awkwardly elongated.
wolf
x
x
dog
x
cat x
x
x
lion
x
x
predator
o
predator
pet
o
canine
o
feline
o
species
niche
(b) If the same space illustrated above is considered from two different
perspectives, the indeterminate arrangements of words collapse
into lower dimensional spaces (one dimensional, in this simple
example) in which the clustering of terms suggests straightforward
conceptual domains. These perspectives effectively contextualize
the meanings inherent in the distributional characteristics of
the language model, and this context facilitates the mapping of the
linguistic space to sets of conceptual regions.
A Literal Lexical Space
Our lexical model has been constructed based on the distribution
of words found in the textual component of articles on
the English language Wikipedia website.1 The xml code of
the site was downloaded and then parsed into a text-only for-
1
The December 8, 2014 dump, downloaded from
http://meta.wikimedia.org/wiki/Data dump torrents on January
23, 2015, parsed into plain text using the “Wikipedia
mat, eliminating images, tables, lists, captions, and section
titles, leaving only the well formed sentences composing
the content of the site’s articles. Sentences were separated
by identifying terminal punctuation followed by whitespace,
then punctuation was removed and all characters were converted
to lower case. Articles (“a”, “an”, and “the”) were
stripped from the text. Sentences containing less than five
words were discarded. The resulting corpus consists of almost
60 million sentences, containing about 1.1 billion word
tokens (individual words) corresponding to about 7.4 million
word types (classes of words).
From this base corpus, we took the 200,000 most frequent
word types to form our system’s vocabulary. Our full lexical
space is represented as a matrix Mw,c, where rows correspond
to vectors representing words, and columns correspond
to co-occurrence terms. The cell for word w and cooccurrence
term c contains the mutual information MIw,c
as described in Equation 1. Here nw,c is the frequency with
which a term c is observed to co-occur within a context window
of two words on either side of a vocabulary word w; nw
represents the total count of w in the corpus; nc is the total
count of c; and a is a smoothing constant.
MIw,c = log2
✓ nw,c ⇥ N
nw ⇥ (nc + a) + 1◆
(1)
The constant a reduces the undesirable effect of contextual
words that occur very rarely throughout the corpus,
but with a high frequency in the context of certain target
words—we found 10,000 to be a good value for a based
on trial and error. The value 1 is added to the probabilistic
ratio in order to render all dimensions within the space positive:
this means that the logged MI value of target words
and context words that never occur together will be 0, and
the value for terms that co-occur less frequently than would
be expected in a random distribution will be between 0 and
1. Each word vector consists of a set of dimensions derived
through this calculation, and each of these vectors is normalised
to the scale of a unit vector. The result of this process
is a distributional semantic space in which each of the
200,000 vocabulary terms sits in the positive region of the
high-dimensional surface of a hypersphere.
One notable feature of our vector space is the literal correspondence
of its dimensions to co-occurrence terms. In
general, state-of-the-art systems apply some form of dimensional
reduction to the overall space, either using linear algebraic
transformations to perform a principal component
analysis (Pennington, Socher, and Manning, 2014), or by
weighted networks to train abstract lower-dimensional word
representations that predict the context in which that word is
encountered in the course of training (Mikolov et al., 2013).
While these techniques certainly make the space less expensive
to compute, and arguably improve results for a variety
of semantic tasks, our system is specifically geared
towards the identification of salient, literal co-occurrence
dimensions, and as such the space is, for the purposes of
our initial analysis, maintained in its raw high-dimensional
form. The dimensionality of our space is therefore on the
Extractor” software, downloaded on February 13, 2015 from
http://medialab.di.unipi.it/wiki/Wikipedia Extractor.
Proceedings of the Sixth International Conference on Computational Creativity June 2015 121
order of 7.4 million, as every word token in the corpus is a
potential context for the 200,000 words in our vocabulary.
Empirical Validation
In order to provide grounding and validation for our computational
model, human participants were asked to generate
terms during a word association task, and to reflect upon
how they would evaluate creativity in the musical and poetic
domains. Provided terms were analyzed for comparison
with the vector space model.
Method
Participants Twenty participants (avg age = 30 yrs, stdev
= 5.2 yrs) volunteered to take part in the study, of which 11
were female. Sixteen individuals indicated that their career
is either inherently creative or that they apply creativity to
improve their job performance, and all but two of the participants
engage in creative pursuits outside of work. Seven
currently practice or perform music, and five individuals currently
engage in creative writing.
Procedure After reading an information form and providing
informed consent, participants were given a brief questionnaire
to complete. Two of the questions consisted of
a word association task in which participants were asked
to list three terms they associate with “musical creativity”
or “poetic creativity”. The order in which musical or poetic
terms were prompted was counterbalanced across subjects.
The other two questions requested participants to write
one sentence describing how they would evaluate whether a
new piece of music or poetry sounds creative (the order of
these questions were similarly counterbalanced across subjects).
These results will only briefly be touched upon in the
current paper; although certainly of interest, due to space
constraints, an in-depth analysis of the evaluation sentences
must be saved for an expanded version of this work.
After providing their responses, participants were given
questionnaires requesting general demographic information
(age, ethnicity, etc), and information about their past and
current involvement in creative pursuits, e.g., “Do you currently
play music or engage in creative writing?” Upon completing
these, participants were debriefed as to the goals of
the experiment and paid £2 each for their participation.
Results
For both musical and poetic creativity, participants’ terms
were placed into two lists: An exhaustive list of all terms
provided for the concept, and a short list for terms cited by
more than two participants (per concept). In the case of musical
creativity, this yielded an exhaustive list of 52 distinct
terms, and for poetic creativity, a set of 42 terms. The short
list of musical terms included the following six terms: innovation,
sound, instruments, novelty, emotion, and expression.
The short list of poetic terms included these six terms:
emotion, rhythm, expression, structure, flow, and words. We
interpreted these concise lists of most frequent words to re-
flect dimensions of the concept that are more central to the
conceptual space they populate. This resulted in discarding
more peripheral terms such as ”sensitive” that are undoubtedly
related to creativity, but not cited frequently as an associated
concept. Plurals and conjugations were considered to
be the same category of term, e.g., ”emotions”, ”emotional”,
and ”emotion” were tallied together as ”emotion”. We continue
the discussion of empirical findings in the next section,
as we compare the model’s performance with human results.
Mapping Words to Concepts
We began the exploration of mappings from our space of
distributed semantics to a conceptual space with a top down
approach, investigating the way our system reacted to the
same kind of input that we presented to our human subjects.
Along these lines, we examined the vectors for the
word pairing “musical” and “creativity”, and likewise for
the pairing “poetical” and “creativity”. In each instance, we
calculated the mean value for each dimension that had a nonzero
value for both words – that is, for each dimension corresponding
to a term that co-occurred with both words at
least once in the corpus – and returned a ranked list of average
scores, running from high to low. Out of the 7.5 million
co-occurrence features across the entire model, 4,772 were
non-zero for both “musical” and “creativity”, and 2,673 for
both “poetic” and “creativity”, statistics which highlight the
sparsity of the base space. Our objective was to examine the
nature of the terms that tended to come up in the context of
our query as phrased for our human subjects. Results are
listed in Table 1.
The first thing to note about these results is that they are,
in a qualitative sense, coherent descriptions of properties
typically associated with the two concepts being explored.
To frame this more empirically, these results can be extended
in order to discover how far down the list of top mean dimensions
the terms reported by humans lie. Of the exhaustive list
of terms reported by human subjects in response to the “musical
creativity” query, 4 fall within the top 15 results generated
by our model; likewise, 4 human responses fall within
the top 15 mean dimensions for “poetic creativity” (these
terms are italicised in Table 1). Considering that 200,000
words were used as the vocabulary of the model, yielding
4 of the top 15 dimensions in common with humans’ responses
for both concepts is quite compelling. This outcome
may be interpreted as indicating that there is a high degree of
mutual information between the query words and terms that
humans would consider as conceptually descriptive of those
queries. In other words, there is a high likelihood of conceptually
relevant co-occurrence within the context of terms
that summarize these creative conceptual domains.
These positive results do not hold up, however, for more
concrete queries. For instance, when the mean dimensions
for the query pair “wild” and “animal” are explored,
top ranking results include some conceptually appropriate
terms such as “boars”, “deer”, and “feral”, but less directly
relevant words like “skins” and “vegetable”, and even
antonymic terms like “domesticated” are also returned. It
would seem that, in the case of words indexing more concrete
concepts, the likelihood of co-occurrence in the conceptual
context moves away from terms that generically describe
components of the concept in question. This distinction
is corroborated by Hill, Korhonen, and Bentz (2014),
Proceedings of the Sixth International Conference on Computational Creativity June 2015 122
“musical” & “creativity” “poetic” & “creativity”
innovation genius
imagination imaginative
inventiveness metaphors
improvisation originality
talent prose
talents creativity
experimentation artistry
versatility craftsmanship
artistic intuition
creativity imagery
ingenuity inspiration
aesthetics talents
spontaneity lyrical
individuality talent
artistry self-expression
Table 1: The top 15 dimensions with the highest mean scores
between the word-vectors for each of our queries as given
to human subjects. Terms in italics denote dimensions that
were also cited by humans.
who have used computational analyses of both corpora and
semantic graphs to illustrate a distinction between the way
that abstract and concrete concepts are arranged in a cognitive
linguistic system. It is hardly surprising, given the
inherent ambiguity of language use – replete, as it is, with
metaphor and implication – that simple co-occurrence probability
statistics do not generally map neatly on to well de-
fined conceptual spaces.
Projecting Words to Conceptual Subspaces
Motivated by this predictable shortcoming of a simple dimensional
analysis, we developed a more sophisticated approach
for delineating conceptual regions within dimensionally
reduced subspaces of our language model. Our technique
involves first hand-picking a small set of terms that
might be considered as paradigmatic descriptions of components
of a conceptual domain (in the present example,
WILD ANIMALS). We perform an analysis similar to the
one described above on these conceptual component terms,
selecting the word-vector for each term and then extracting
those features with non-zero values for all input terms. Once
again, we compute a ranked list of these mean feature values
and choose the co-occurrence dimensions which scored
highest on average. These salient dimensions for the small
set of words analyzed are again somewhat scattered: some
of the highest mean dimensions correspond to relevant animal
names, but the results also stray into the more conceptually
ambiguous territory signified by words like “sightings”,
“chases”, and “fat”. There are 827 universally non-zero dimensions
found between the word-vectors of the six input
terms describing exemplars of WILD ANIMALS listed in the
first column of Table 2.
We use these salient dimensions to define a drastically
simplified subspace of our lexical model. Specifically, we
reduce the model to the top 30 dimensions associated with
the set of sample words (we arrived at the number 30 through
trial and error; lower values tended to invite some unusual
vectors into the crucial region of the subspace). After normalizing
the new subspace, we then identify the central
point on the surface of the positively valued quadrant of the
reduced hypersphere—effectively the vector defined by 30
dimensions each with the the value 1/
p30. This positive
centroid is then taken as the epicenter of a linguistic mapping
of a new conceptual region, and we expand the region
outward concentrically from this point, returning an ordered
list of the points closest to the center of the positive surface
of our space’s low dimensional projection. Euclidean proximity
is calculated by computing the square root of the sum
of the squared feature-wise differences between the unit centroid
and each of the 200,000 vocabulary words projected
into the subspace. The top fifteen terms encountered using
this method are reported in Table 2. Please note that the input
terms for WILD ANIMALS are used as a preliminary test
of the model’s performance for concrete concepts; the input
was hand-selected by the investigators, while the collection
of terms relating to concrete concepts is the subject of ongoing
emprical study.
This same technique for expanding conceptual regions
through a dimensional reduction of a distributional language
model is applied to our target domains of musical and poetic
creativity, again with compelling outcomes. In this case we
were able to make use of our results from our survey: for
each of our two target domains, we choose all the terms that
were reported by three or more human subjects and analyze
these for their most salient dimensions of co-occurrence.
Again, the system’s output for these terms is not entirely
unexpected, but also not conceptually completely cohesive.
In the case of the highest mean dimensions for the human reported
constituents of MUSICAL CREATIVITY, a number of
predictable terms are returned, but somewhat less obvious
dimensions such as “lab”, “mere”, and “shapes” also rank
towards the top of the list.
Despite the conceptual uncertainty in the dimensional
analysis, when a new subspace is constructed based on these
dimensions, the central region of this space is replete with
terminology appropriate to the example words at the base of
the process. Interestingly, the original input words are only
partially rediscovered in this new space, at least within the
set of vectors most central to the positive surface of the new
subspace. This indicates that some of the input word-vectors
(used to select dimensions for creating the new subspace)
are, in terms of the probability of regular co-occurrence with
all the dimensions that underwrite the subspace, relative outliers
which nonetheless make an essential contribution to the
delineation of this linguistic representation of a conceptual
region. It is also notable, and perhaps even remarkable, that
in the case of the mapping of the conceptual region of poetic
creativity, quintessential new terms such as ”phrasing”
and ”inflection”, arguably more intricately associated with
the prosodic nature of the target domain than the original
human generated terms, arise independently.
When examining how well the model captures relevant
terms to a conceptual query, it is informative to cluster human
responses into semantic categories (such as emotion
and structural elements), and compare these results to apparent
categories of output vectors. For example, considering
the sentences that the 20 participants wrote about how
Proceedings of the Sixth International Conference on Computational Creativity June 2015 123
WILD ANIMALS MUSICAL CREATIVITY POETIC CREATIVITY
human input model output human input model output human input model output
lion bobcat innovation novelty emotion phrasing
wolf alligator sound liveliness rhythm intonation
coyote raccoon instruments spontaneity expression musicality
alligator opossum novelty innovation structure nuances
bear armadillo emotion expressiveness flow timbre
snake white-tailed expression refinement words sprightly
anteater nuance rhythmical
ocelot ingenuity nuance
peccary believability expressiveness
pronghorn newness rubato
cougar sophistication instinctive
cottontail dynamism bluesy
rattlesnake subtlety directness
skunk vibrancy modal
boar elusiveness inflections
Table 2: The output vectors most central to the positive regions of the subspaces reduced in terms of the salient dimensions of
a small set of conceptually exemplary input terms.
they would evaluate the creativity of a new song, many individuals
referred to the notion of novelty in musical creativity,
but used various terms to do so. In addition to explicitly
using the term “novelty”, participants made reference to
“unexpected”, “new”, and “surprising elements” that were
“like nothing else I’d heard before”, as well as “melodic
originality” and cases in which “known musical concepts or
styles [are] combined in a novel/innovative way.” Similarly,
when considering the model’s conceptual space of musical
creativity, the words “novelty”, “innovation”, “ingenuity”,
“newness”, “inventiveness”, “distinctiveness”, and “uniqueness”
are found within the top 30 model output vectors. Although
this is a qualitative assessment of the results, it does
seem clear that the precise terms from humans and the model
might not be exactly the same, but there is significant categorical
or conceptual overlap between the two.
One may also note that the output vectors for poetic creativity
appear to be rather “musical”. This may reflect the
fact that the input dimensions were provided by people who,
overall, have significant musical experience - all but three
of the participants have had musical training or have played
music informally, whereas only four of the participants have
experience with creative writing. People’s experience with
music might frame the way they think about other creative
domains, or at the very least influencing the terms used to
describe poetic creativity; consequently, this has led to a
subspace that highlights the musical nature of this sample.
In light of our model’s ability to find conceptually proximal
terms, we propose that this method has the potential
to be practically applied to the discovery of unexpected and
valuable terms for the evaluation of creative output. Importantly,
this approach may be applied to different corpora;
for example, Wikipedia pages in different languages may
be explored to address the difficult issue of identifying conceptually
similar spaces across languages. The model’s conceptual
spaces concretely delineate evaluative terms that one
person alone may not consider. For example, the terms “distinctiveness”,
“finesse”, “artistry”, and “stylization” were
not cited by humans, but were within the top 30 output vectors
discovered by the model. Future work may build on
these findings, by using the model’s discovered terms as criteria
for subjective evaluation of creative output. In addition,
discovering the geometry, flexibility, and contextual speci-
ficity of conceptual spaces may be very useful for assessing
products or systems based on specific underlying concepts
(or developed to address particular conceptual issues).
More generally, our method is presented as an implementation
of the mapping of words to concepts: this approach
charts a passage from a statistically tractable lexical space
to the abstract but natively cognitive domain of ideas. The
temporary and contextual aspect of this mapping is essential
to its success: it is the flexibility of the model that allows
for the bespoke generation of subspaces, just as it is the
pragmatic frangibility of language that permits the ready-tohand
adaptation of meaning for unfolding expressive purposes.
As can be seen in our results, the same terms arise in
different constellations of meaning depending on the contextual
perspective taken on the space. It is the strength of our
language model that it can be adapted in this way, with the
high dimensional arrangement of words allowing for their
projection as multitudinous conceptual representations.
Conclusion
We investigated the terms and concepts that individuals most
strongly associate with creativity in the musical and poetic
domains, and described a computational methodology
for modeling these conceptual relationships. Our multidisciplinary
approach employs methods inspired by computational
linguistics, as well as methods from empirical psychology.
There were several outcomes of this work: the
output from our distributional semantics vector space model
was compared with human responses on a word association
task. Human-generated terms were found within the top 15
dimensions of our model’s lexical space, despite the model’s
very large vocabulary. This served as validation that the
Proceedings of the Sixth International Conference on Computational Creativity June 2015 124
model discovers a lexical space that encapsulates the kind
of terms humans use to describe these concepts.
Subsequently, the most frequently reported human terms
were used as model input parameters for discovering conceptual
spaces of lower dimensionality. Our model was able
to find vastly reduced subspaces corresponding to MUSICAL
CREATIVITY and POETIC CREATIVITY, which again captured
semantically relevant terms, many corresponding directly
to participants’ terms, and others extending the list of
terms to insightful new dimensions. In addition, by sampling
word-vectors that fall near the centroid of the discovered
conceptual mappings, we aimed to find potentially useful
terms for the evaluation of creativity. Although computational
and AI methods have generated many systems
which aim to display creative behavior or produce creative
artefacts, the evaluation of computational creativity remains
distinctly problematic. Therefore, we offer our method and
results as a formal approach to delineating conceptuallyrelevant
criteria on which to base the evaluation of creativity
and creative artefacts in future studies.
We saw, in terms of the most common dimensions in lexical
space and the highest-mean word vectors in conceptual
space, that the model is able to discover semantic categories
and indices of concepts that are alligned to human conceptualizations.
This said, the model did not capture all of the
semantic categories cited by humans. The most noteworthy
omission is in regards to emotion, as terms relating to affect
and evoked emotional response were some of the most
frequently cited terms for both musical and poetic creativity.
Accordingly, future work will investigate why the model
does not capture this cluster of emotion-related terms.
Further directions for the future include the application of
this computational approach to other domains, such as “culinary
creativity”, both for the ontologically useful task of
elaborating concepts themselves, and to create well-tailored
terminology for the assessment of creative output from the
corresponding domains. This methodology may also be
used to approach the task of conceptual blending: rather than
specifying input vectors that belong to only one concept, one
may supply input dimensions from several. This could result
in output terms discovered at the intersection of the lexical
regions specified by the vectors’ different input dimensions.
Acknowledgments
The projects Lrn2Cre8 and ConCreTe acknowledge the
financial support of the Future and Emerging Technologies
(FET) programme within the Seventh Framework Programme
for Research of the European Commission, under
FET grants number 610859 and 611733, respectively. This
research is also supported by EPSRC grant EP/L50483X/1.
<references_biblio/>
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