Purpose: The paper presents an exhaustive examination of the mathematical frameworks that support the creation and operation of large language models. The document commences with an introduction to the core mathematical concepts that are foundational to large language models. It delves into the mathematical algorithms employed in training these models and scrutinizes how various mathematical notions influence their efficacy. Methodology: Furthermore, it dissects the structure of large language models, analyzing the mathematical tenets that dictate their design and functionality. It also considers the mathematical logic underpinning these models' performance and the intricacies involved in their expansion. Additionally, it probes into the mathematical underpinnings of attention mechanisms within large language models, assessing how these mechanisms bolster the models' effectiveness and comprehensibility. Findings: Subsequently, it examines the mathematical bases of attention mechanisms in large language models, considering how these mechanisms augment the models' efficiency and clarity. It also debates the mathematical methods for refining large language models and the hurdles faced in enhancing their interpretability. By understanding the mathematical foundations of LLMs, we can leverage insights from the algorithms and principles driving these models, thus enhancing their inventive output and broadening the horizons of design and artistic expression. Unique contribution to theory, policy and practice: Lastly, it ventures into the ethical considerations surrounding large language models, scrutinizing the mathematical aspects related to these concerns.
{"title":"Mathematical Insights into Large Language Models","authors":"Ranjith Gopalan","doi":"10.47941/ijms.2006","DOIUrl":"https://doi.org/10.47941/ijms.2006","url":null,"abstract":"Purpose: The paper presents an exhaustive examination of the mathematical frameworks that support the creation and operation of large language models. The document commences with an introduction to the core mathematical concepts that are foundational to large language models. It delves into the mathematical algorithms employed in training these models and scrutinizes how various mathematical notions influence their efficacy. \u0000Methodology: Furthermore, it dissects the structure of large language models, analyzing the mathematical tenets that dictate their design and functionality. It also considers the mathematical logic underpinning these models' performance and the intricacies involved in their expansion. Additionally, it probes into the mathematical underpinnings of attention mechanisms within large language models, assessing how these mechanisms bolster the models' effectiveness and comprehensibility. \u0000Findings: Subsequently, it examines the mathematical bases of attention mechanisms in large language models, considering how these mechanisms augment the models' efficiency and clarity. It also debates the mathematical methods for refining large language models and the hurdles faced in enhancing their interpretability. By understanding the mathematical foundations of LLMs, we can leverage insights from the algorithms and principles driving these models, thus enhancing their inventive output and broadening the horizons of design and artistic expression. \u0000Unique contribution to theory, policy and practice: Lastly, it ventures into the ethical considerations surrounding large language models, scrutinizing the mathematical aspects related to these concerns.","PeriodicalId":476440,"journal":{"name":"International Journal of Modern Statistics","volume":"2 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141335610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Purpose: The aim of this paper was to investigate the effect of students ‘perception on teaching and learning Mathematics students in public Schools in El’arish in North Sinai Governorate in Egypt. The hypothesis of the study was formulated and tested to guide the study. Methodology: The survey research design type was adopted and the targeted population of one hundred and ninety-nine (119) respondents composed by 5 principals, 16 mathematic teachers and 98 students from senior secondary schools, were sampled by using stratified sampling and sample random sampling techniques. The collected data was analyzed using descriptive statistics, correlation, and regression analysis through the statistical package for social science (SPSS) version 21. The data collected were analysed using descriptive statistics and multiple regression. Findings: The results of the findings indicated that the students’ perception was more correlated with teaching and learning Mathematics (r = 0.822; p= 0.000). Multiple linear regression analysis showed that students ‘perception contributed to 70.2% of variation on the performance, hence plays a vital role in teaching and learning Mathematics students in secondary schools in El Arish in North Sinai Governorate in Egypt. Additionally, the relationship between perception and students Mathematics performance in the study was very strong. Unique Contribution to Theory, Practice and Policy: The study recommended that Mathematics teacher should be diverse in their use of methodology which can as well help their student in their own area of learning mathematics.
{"title":"Effect of Student Perception on Teaching and Learning Mathematics in Secondary Schools in El’arish in North Sinai Governorate in Egypt","authors":"E. Byiringiro","doi":"10.47941/ijms.1613","DOIUrl":"https://doi.org/10.47941/ijms.1613","url":null,"abstract":"Purpose: The aim of this paper was to investigate the effect of students ‘perception on teaching and learning Mathematics students in public Schools in El’arish in North Sinai Governorate in Egypt. The hypothesis of the study was formulated and tested to guide the study. \u0000Methodology: The survey research design type was adopted and the targeted population of one hundred and ninety-nine (119) respondents composed by 5 principals, 16 mathematic teachers and 98 students from senior secondary schools, were sampled by using stratified sampling and sample random sampling techniques. The collected data was analyzed using descriptive statistics, correlation, and regression analysis through the statistical package for social science (SPSS) version 21. The data collected were analysed using descriptive statistics and multiple regression. \u0000Findings: The results of the findings indicated that the students’ perception was more correlated with teaching and learning Mathematics (r = 0.822; p= 0.000). Multiple linear regression analysis showed that students ‘perception contributed to 70.2% of variation on the performance, hence plays a vital role in teaching and learning Mathematics students in secondary schools in El Arish in North Sinai Governorate in Egypt. Additionally, the relationship between perception and students Mathematics performance in the study was very strong. \u0000Unique Contribution to Theory, Practice and Policy: The study recommended that Mathematics teacher should be diverse in their use of methodology which can as well help their student in their own area of learning mathematics.","PeriodicalId":476440,"journal":{"name":"International Journal of Modern Statistics","volume":"37 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139532218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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