Mathematical limit theorems for computational creativity

Research output: Contribution to journalArticle

Abstract

Creativity is the generation of an idea or artifact judged to be novel and high-quality by a knowledgeable social group, and is often said to be the pinnacle of intelligence. Several computational creativity systems of various designs are now being demonstrated and deployed. These myriad design possibilities raise the natural question: Are there fundamental limits to creativity? Here, we define a mathematical abstraction to capture key aspects of combinatorial creativity and study fundamental tradeoffs between novelty and quality. The functional form of this fundamental limit resembles the capacity-cost relationship in information theory, especially when measuring novelty using Bayesian surprise - the relative entropy between the empirical distribution of an inspiration set and that set updated with the new idea or artifact. As such, we show how information geometry techniques provide insight into the limits of creativity and find that the maturity of the creative domain directly parameterizes the fundamental limit. This result is extended to the case when there is a diverse audience for creativity and when the quality function is not known but must be estimated from samples.

Original languageEnglish (US)
Article number8618382
JournalIBM Journal of Research and Development
Volume63
Issue number1
DOIs
StatePublished - Jan 1 2019

Fingerprint

Information theory
Entropy
Geometry
Costs

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Mathematical limit theorems for computational creativity. / Varshney, Lav R.

In: IBM Journal of Research and Development, Vol. 63, No. 1, 8618382, 01.01.2019.

Research output: Contribution to journalArticle

@article{06020270b5e34161adfe0a30ec64e902,
title = "Mathematical limit theorems for computational creativity",
abstract = "Creativity is the generation of an idea or artifact judged to be novel and high-quality by a knowledgeable social group, and is often said to be the pinnacle of intelligence. Several computational creativity systems of various designs are now being demonstrated and deployed. These myriad design possibilities raise the natural question: Are there fundamental limits to creativity? Here, we define a mathematical abstraction to capture key aspects of combinatorial creativity and study fundamental tradeoffs between novelty and quality. The functional form of this fundamental limit resembles the capacity-cost relationship in information theory, especially when measuring novelty using Bayesian surprise - the relative entropy between the empirical distribution of an inspiration set and that set updated with the new idea or artifact. As such, we show how information geometry techniques provide insight into the limits of creativity and find that the maturity of the creative domain directly parameterizes the fundamental limit. This result is extended to the case when there is a diverse audience for creativity and when the quality function is not known but must be estimated from samples.",
author = "Varshney, {Lav R}",
year = "2019",
month = "1",
day = "1",
doi = "10.1147/JRD.2019.2893907",
language = "English (US)",
volume = "63",
journal = "IBM Journal of Research and Development",
issn = "0018-8646",
publisher = "IBM Corporation",
number = "1",

}

TY - JOUR

T1 - Mathematical limit theorems for computational creativity

AU - Varshney, Lav R

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Creativity is the generation of an idea or artifact judged to be novel and high-quality by a knowledgeable social group, and is often said to be the pinnacle of intelligence. Several computational creativity systems of various designs are now being demonstrated and deployed. These myriad design possibilities raise the natural question: Are there fundamental limits to creativity? Here, we define a mathematical abstraction to capture key aspects of combinatorial creativity and study fundamental tradeoffs between novelty and quality. The functional form of this fundamental limit resembles the capacity-cost relationship in information theory, especially when measuring novelty using Bayesian surprise - the relative entropy between the empirical distribution of an inspiration set and that set updated with the new idea or artifact. As such, we show how information geometry techniques provide insight into the limits of creativity and find that the maturity of the creative domain directly parameterizes the fundamental limit. This result is extended to the case when there is a diverse audience for creativity and when the quality function is not known but must be estimated from samples.

AB - Creativity is the generation of an idea or artifact judged to be novel and high-quality by a knowledgeable social group, and is often said to be the pinnacle of intelligence. Several computational creativity systems of various designs are now being demonstrated and deployed. These myriad design possibilities raise the natural question: Are there fundamental limits to creativity? Here, we define a mathematical abstraction to capture key aspects of combinatorial creativity and study fundamental tradeoffs between novelty and quality. The functional form of this fundamental limit resembles the capacity-cost relationship in information theory, especially when measuring novelty using Bayesian surprise - the relative entropy between the empirical distribution of an inspiration set and that set updated with the new idea or artifact. As such, we show how information geometry techniques provide insight into the limits of creativity and find that the maturity of the creative domain directly parameterizes the fundamental limit. This result is extended to the case when there is a diverse audience for creativity and when the quality function is not known but must be estimated from samples.

UR - http://www.scopus.com/inward/record.url?scp=85064631054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064631054&partnerID=8YFLogxK

U2 - 10.1147/JRD.2019.2893907

DO - 10.1147/JRD.2019.2893907

M3 - Article

VL - 63

JO - IBM Journal of Research and Development

JF - IBM Journal of Research and Development

SN - 0018-8646

IS - 1

M1 - 8618382

ER -