Desarrollo de un modelo para la medición de la implicación lógica en problemas de matemática elemental

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dc.contributor.advisorGonzález Galeano, Andrei Alain
dc.contributor.authorSánchez Tovar, Edwin Alejandro
dc.date.accessioned2024-12-05T14:25:31Z
dc.date.available2024-12-05T14:25:31Z
dc.date.issued2024-11
dc.description.abstractActualmente, existen modelos de lenguaje integrados en sistemas que pueden superar las capacidades humanas en una variedad de pruebas. Sin embargo, ¿cómo podemos medir la coherencia de estos modelos? En este trabajo, proponemos un enfoque que utiliza la arquitectura de transformers para abordar el problema de la implicación lógica (IL), es decir, determinar qué oraciones se derivan de otras dentro de un texto. Esto se logra mediante el uso de su mecanismo de atención y predicción del siguiente token. Se encontró que, con un modelo muy simple basado en la arquitectura del transformer, es posible la identificación de la IL en problemas de conteo y probabilidad con una precisión del 60 % en una muestra de 95 ejercicios matemáticos de diversos temas. Este método podría contribuir a mejorar la precisión con la que se evalúa la coherencia de los modelos de lenguaje, proporcionando los datos necesarios para realizar un análisis detallado de sus errores y examinar la validez lógica de sus respuestas correctas.
dc.description.abstractenglishToday, there are language models built into systems that can outperform human capabilities in a variety of tests. However, how can we measure the coherence of these models? In this work, we propose an approach that uses the transformer architecture to address the problem of logical implication (LI), that is, determining which sentences are derived from others within a text. This is achieved by using its attention mechanism and predicting the next token. It was found that, with a very simple model based on the transformer architecture, the identification of IL in counting and probability problems is possible with an accuracy of 60% in a sample of 95 mathematical exercises on various topics. This method could help improve the precision with which the consistency of language models is evaluated, providing the data necessary to perform a detailed analysis of their errors and examine the logical validity of their correct answers.
dc.description.degreelevelPregradospa
dc.description.degreenameMatemáticospa
dc.format.mimetypeapplication/pdf
dc.identifier.instnameinstname:Universidad El Bosquespa
dc.identifier.reponamereponame:Repositorio Institucional Universidad El Bosquespa
dc.identifier.repourlrepourl:https://repositorio.unbosque.edu.co
dc.identifier.urihttps://hdl.handle.net/20.500.12495/13595
dc.language.isoes
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.grantorUniversidad El Bosquespa
dc.publisher.programMatemáticasspa
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dc.rightsAttribution 4.0 Internationalen
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.rights.accessrightshttp://purl.org/coar/access_right/c_abf2
dc.rights.localAcceso abiertospa
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectAxiomas e IA
dc.subjectImplicación lógica
dc.subjectIA en matemáticas
dc.subjectAprendizaje automático
dc.subjectAprendizaje profundo
dc.subjectInteligencia artificial
dc.subjectModelos de lenguaje
dc.subject.ddc510
dc.subject.keywordsAxioms and AI
dc.subject.keywordsLogical implication
dc.subject.keywordsAI in mathematics
dc.subject.keywordsMachine learning
dc.subject.keywordsDeep learning
dc.subject.keywordsArtificial intelligence
dc.subject.keywordsLanguage model
dc.titleDesarrollo de un modelo para la medición de la implicación lógica en problemas de matemática elemental
dc.title.translatedDevelopment of a model for measuring logical implication in elementary mathematics problems
dc.type.coarhttps://purl.org/coar/resource_type/c_7a1f
dc.type.coarversionhttps://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.driverinfo:eu-repo/semantics/bachelorThesis
dc.type.hasversioninfo:eu-repo/semantics/acceptedVersion
dc.type.localTesis/Trabajo de grado - Monografía - Pregradospa

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