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Bayesian validation of grammar productions for the language of thought
Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are bui...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6039029/ https://www.ncbi.nlm.nih.gov/pubmed/29990351 http://dx.doi.org/10.1371/journal.pone.0200420 |
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author | Romano, Sergio Salles, Alejo Amalric, Marie Dehaene, Stanislas Sigman, Mariano Figueira, Santiago |
author_facet | Romano, Sergio Salles, Alejo Amalric, Marie Dehaene, Stanislas Sigman, Mariano Figueira, Santiago |
author_sort | Romano, Sergio |
collection | PubMed |
description | Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem. |
format | Online Article Text |
id | pubmed-6039029 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-60390292018-07-19 Bayesian validation of grammar productions for the language of thought Romano, Sergio Salles, Alejo Amalric, Marie Dehaene, Stanislas Sigman, Mariano Figueira, Santiago PLoS One Research Article Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem. Public Library of Science 2018-07-10 /pmc/articles/PMC6039029/ /pubmed/29990351 http://dx.doi.org/10.1371/journal.pone.0200420 Text en © 2018 Romano et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Romano, Sergio Salles, Alejo Amalric, Marie Dehaene, Stanislas Sigman, Mariano Figueira, Santiago Bayesian validation of grammar productions for the language of thought |
title | Bayesian validation of grammar productions for the language of thought |
title_full | Bayesian validation of grammar productions for the language of thought |
title_fullStr | Bayesian validation of grammar productions for the language of thought |
title_full_unstemmed | Bayesian validation of grammar productions for the language of thought |
title_short | Bayesian validation of grammar productions for the language of thought |
title_sort | bayesian validation of grammar productions for the language of thought |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6039029/ https://www.ncbi.nlm.nih.gov/pubmed/29990351 http://dx.doi.org/10.1371/journal.pone.0200420 |
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