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...

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Autores principales:	Romano, S., Salles, A., Amalric, M., Dehaene, S., Sigman, M., Figueira, S.
Formato:	JOUR
Materias:	article geometry grammar human human experiment language probability scientist sequence learning theoretical study thinking validation process Bayes theorem cognition linguistics probability learning theoretical model Bayes Theorem Cognition Humans Linguistics Models, Theoretical Probability Learning Thinking
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_19326203_v13_n7_p_Romano
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_19326203_v13_n7_p_Romano
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spelling	todo:paper_19326203_v13_n7_p_Romano2023-10-03T16:34:58Z Bayesian validation of grammar productions for the language of thought Romano, S. Salles, A. Amalric, M. Dehaene, S. Sigman, M. Figueira, S. article geometry grammar human human experiment language probability scientist sequence learning theoretical study thinking validation process Bayes theorem cognition linguistics probability learning theoretical model Bayes Theorem Cognition Humans Linguistics Models, Theoretical Probability Learning Thinking 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. © 2018 Romano et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_19326203_v13_n7_p_Romano
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	article geometry grammar human human experiment language probability scientist sequence learning theoretical study thinking validation process Bayes theorem cognition linguistics probability learning theoretical model Bayes Theorem Cognition Humans Linguistics Models, Theoretical Probability Learning Thinking
spellingShingle	article geometry grammar human human experiment language probability scientist sequence learning theoretical study thinking validation process Bayes theorem cognition linguistics probability learning theoretical model Bayes Theorem Cognition Humans Linguistics Models, Theoretical Probability Learning Thinking Romano, S. Salles, A. Amalric, M. Dehaene, S. Sigman, M. Figueira, S. Bayesian validation of grammar productions for the language of thought
topic_facet	article geometry grammar human human experiment language probability scientist sequence learning theoretical study thinking validation process Bayes theorem cognition linguistics probability learning theoretical model Bayes Theorem Cognition Humans Linguistics Models, Theoretical Probability Learning Thinking
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. © 2018 Romano et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
format	JOUR
author	Romano, S. Salles, A. Amalric, M. Dehaene, S. Sigman, M. Figueira, S.
author_facet	Romano, S. Salles, A. Amalric, M. Dehaene, S. Sigman, M. Figueira, S.
author_sort	Romano, S.
title	Bayesian validation of grammar productions for the language of thought
title_short	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_sort	bayesian validation of grammar productions for the language of thought
url	http://hdl.handle.net/20.500.12110/paper_19326203_v13_n7_p_Romano
work_keys_str_mv	AT romanos bayesianvalidationofgrammarproductionsforthelanguageofthought AT sallesa bayesianvalidationofgrammarproductionsforthelanguageofthought AT amalricm bayesianvalidationofgrammarproductionsforthelanguageofthought AT dehaenes bayesianvalidationofgrammarproductionsforthelanguageofthought AT sigmanm bayesianvalidationofgrammarproductionsforthelanguageofthought AT figueiras bayesianvalidationofgrammarproductionsforthelanguageofthought
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Bayesian validation of grammar productions for the language of thought

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