creative systems as dynamical systems

Creative Systems

as Dynamical Systems Alessandro Valitutti

University College Dublin

ICCBR-‐15

28 September 2015

Rationale

•  A conceptual space of a creative system can be decomposed in several regions called “basins of attractions”, each associated to a specific type of artefacts.

•  “Classic” CBR is “conservative”, i.e. generates solutions included in the basin of attraction containing the past examples.

• We propose two forms of similarity between artefacts, according to typicality (t-‐similarity) and value (v-‐similarity). Their combined use allows CBR to reach different basins of attractions and makes it more creative.

1 ICCBR-‐15 28 September 2015

Outline

1.  Creative Systems

2.  The Fractal Tree

3.  Analogies

4.  Key Ideas


Creative Systems

(Wiggins 2006):

•  The conceptual space is a set of artefacts (in Boden’s terms, concepts) which are in some quasi-‐syntactic sense deemed to be acceptable as examples of whatever is being created. Implicitly, the conceptual space may include partially defined artefacts too.

•  Exploratory creativity is the process of exploring a given conceptual space


Creative Systems (Wiggins 2006):

A creative system is represented by the following symbols:

•  L is a language in which to express concepts (artefacts) and rules

•  U is the (abstract) set of all possible partial and complete artefacts describable in the creative system being modelled

•  T is a set of rules which [...] describe the behaviour of a creative agent as it traverses the conceptual space from known artefacts to unknown ones [...] and possibly back again

•  R is a set of rules, expressed using the language L, which select an “acceptable” or “relevant” subset of U which corresponds with Boden’s1 conceptual space

•  ℇ is a set of rules by which value is attributed to a created artefact


Creative Systems


(Ritchie 2007):

•  set of basic items B = data types (e.g. string of words, arrays of pixels) characterising the artefacts produced by the program

•  set of results R = set of artefacts produced by the program with a specific set of setting parameters

•  inspiring set I: The construction of the program is influenced (either explicitly or implicitly) by some subset of the available basic items. This subset, which we will call the inspiring set, could be all the relevant artefacts known to the program designer, or items which the program is designed to replicate, or a knowledge base of known examples which drives the computation within the program.

Creative Systems


(Ritchie 2007):

•  typ(X) = value of typicality associated to the artefact X

•  val(X) = value of quality associated to X •  Tα,β(X) = {x ∈ X | α ≤ typ(X) ≤ β}

•  Vα,β(X) = {x ∈ X | α ≤ val(X) ≤ β}

B

Set of basic items

B

I

Inspiring set

B

I

Set of results

R

B

I R

Typical artefacts Tα,1(R) = {x ∈ R | α ≤ typ(X) ≤ 1}

Tα,1(R)

B

I R

Valuable artefacts Vγ,1(R) = {x ∈ R | γ ≤ val(X) ≤ 1}

Vγ,1(R)

The Fractal Tree


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The Fractal Tree


Observations

•  Shape types: polygon, snow flake, vegetable

•  Shape dimensions: curvature, aperture, symmetry

• Optimal configurations


Main Analogies

Creative System


Problem Solver

Dynamical System

Creative System as Dynamical System

What is a path in the “square of fractal trees”?

1.  A search in the conceptual space of a creative system

2.  A trajectory in the phase space of a dynamical system

An attractor is a set of states (i.e., elements of the state space of a dynamical system) towards which a set of dynamical paths tend to evolve.

The set of dynamical paths pointing to the attractor is called basin of attraction.


Basin Jumping and Creativity

•  The conceptual space can be decomposed in basins of attraction.

•  Starting from a set of past examples (inspiration set), a creative system can reach from which a specific basin of attraction can be explored.

•  “Classic CBR” allows a creative system to explore the basin of attraction containing the set of past examples (assumed to be the inspiration set)

•  “Creative CBR” should allows a creative system to reach basin of attractions not containing the past examples

•  In summary, if we assume the creativity as a search in the conceptual space, a higher degree of creativity is associated to the search of new basins of attraction (basin jumping).


Double Similarity •  CBR is based on the capability to recognize a new case as

similar to one of the past cases

•  Creative CBR should employ two forms of similarity: •  T-‐Similarity: degree to which two artefacts are recognised as

belonging to the same type •  V-‐Similarity: degree to which the value of two artefacts is

recognised as similar

•  T-‐similarity allows the system to explore the current basin of attraction

•  V-‐similarity allows the system to reach different basins of attraction


Types of Attraction Basins

•  Types of artefacts

•  Creative Ideation: different renderings of the same idea

•  Components of an artefact (e.g. lexical component of a text)

• Different styles or patterns


Summary of Key Ideas

• Analogies •  problem solving: state/search space •  generative system: space of configuration •  creative system: conceptual space •  dynamical system: phase space •  CBR: past examples, inspiring set and basin of

attraction

•  Multiplicity of attraction basins

• Double similarity and basin jumping


Future Work

•  Exploiting creative systems complexity (Typ vs. Val, truth inference vs. valence inference)

• Application to fictional ideation: different renderings of the same idea

• Application to linguistic creativity: parametrisation and connection of different patterns


References

•  G. Wiggins (2006). Searching for Computational Creativity. New Generation Computing, 24(3).

•  G. Ritchie (2007). Some Empirical Criteria for Attributing Creativity to a Computer Program. Minds and Machines, 17(1).

•  R. Gibbs (2012). Metaphors, snowflakes, and termite nests. How nature creates such beautiful things. Chapter published in: Metaphor in Use: Context, culture, and communication. Amsterdam: John Benjamins.


creative systems as dynamical systems

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