Associative arithmetic with Boltzmann Machines: The role of number representations

Ivilin Stoianov, Marco Zorzi, Suzanna Becker, Carlo Umilta

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents a study on associative mental arithmetic with mean-field Boltzmann Machines. We examined the role of number representations, showing theoretically and experimentally that cardinal number representations (e.g., numerosity) are superior to symbolic and ordinal representations w.r.t. learnability and cognitive plausibility. Only the network trained on numerosities exhibited the problem-size effect, the core phenomenon in human behavioral studies. These results urge a reevaluation of current cognitive models of mental arithmetic.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages277-283
Number of pages7
Volume2415 LNCS
ISBN (Print)9783540440741
Publication statusPublished - 2002
Event2002 International Conference on Artificial Neural Networks, ICANN 2002 - Madrid, Spain
Duration: Aug 28 2002Aug 30 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2415 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other2002 International Conference on Artificial Neural Networks, ICANN 2002
CountrySpain
CityMadrid
Period8/28/028/30/02

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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  • Cite this

    Stoianov, I., Zorzi, M., Becker, S., & Umilta, C. (2002). Associative arithmetic with Boltzmann Machines: The role of number representations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2415 LNCS, pp. 277-283). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2415 LNCS). Springer Verlag.