Learning sub-patterns in piecewise continuous functions

Kratsios, Anastasis; Zamanlooy, Behnoosh

doi:10.1016/j.neucom.2022.01.036

Cited by 2 publications

(3 citation statements)

References 38 publications

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“…During an interview, students mentioned that it was not a single function, and their responses showed that there is a gap in the knowledge of sketching piecewise functions and finding the domain. According to different studies, students who do not understand the concept of domain functions may have difficulties understanding piecewise functions (Kratsios & Zamanlooy, 2022;Triutami, Hanifah, Novitasari, Apsari, & Wulandari, 2021).…”

Section: Discussion On Limits and Continuity Of Piecewise Functions (...mentioning

confidence: 99%

Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan secondary schools

Munyaruhengeri,

Umugiraneza,

Ndagijimana

et al. 2024

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This study investigates students’ difficulties and misconceptions with learning limits and explores the factors contributing to these misconceptions. The study used a mixed method approach, and the participants comprised 252 students and 21 teachers. Data collection methods included the Limits and Continuity of Functions Achievement Test, classroom observations, and focus group interviews. The study's findings revealed significant differences in the mean scores of the Limits and Continuity of Functions Achievement Test among different representations. It also identified that students' misconceptions stemmed from their limited exposure to active learning approaches and their tendency to rely on rote memorization. The study pointed out that teaching strategies, along with students' haste in providing responses, contributed to these misconceptions and learning difficulties. The fast-paced nature of teaching aimed at covering the syllabus requirements also played a role in creating knowledge gaps and reinforcing misconceptions. Through continuous professional development, this study recommends improving mathematics teachers’ content, pedagogical knowledge of teaching and learning limits, and continuity of functions.

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Section: Discussion On Limits and Continuity Of Piecewise Functions (...mentioning

confidence: 99%

Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan secondary schools

Munyaruhengeri,

Umugiraneza,

Ndagijimana

et al. 2024

View full text Add to dashboard Cite

show abstract

“…(2018); Gonon et al. (2020); Kratsios and Zamanlooy (2022). Not only is this column most pertinent to transformer networks trained with randomized methods, but it also highlights the potential of transformer approaches to geometric deep learning, applications to stochastic analysis, and mathematical finance.…”

Section: Static Case: Universal Approximation Into Qas Spacesmentioning

confidence: 99%

“…(2021); Shen et al. (2021b); Kratsios and Zamanlooy (2022). Briefly, such activation functions allow us to build neural networks achieving exponential approximation rates.…”

Section: Introductionmentioning

confidence: 99%

Designing universal causal deep learning models: The geometric (Hyper)transformer

Acciaio

Kratsios

Pammer

2023

Mathematical Finance

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Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable of encoding these geometric structures remains largely unknown. We address this open problem by introducing a universal causal geometric DL framework in which the user specifies a suitable pair of metric spaces and and our framework returns a DL model capable of causally approximating any “regular” map sending time series in to time series in while respecting their forward flow of information throughout time. Suitable geometries on include various (adapted) Wasserstein spaces arising in optimal stopping problems, a variety of statistical manifolds describing the conditional distribution of continuous‐time finite state Markov chains, and all Fréchet spaces admitting a Schauder basis, for example, as in classical finance. Suitable spaces are compact subsets of any Euclidean space. Our results all quantitatively express the number of parameters needed for our DL model to achieve a given approximation error as a function of the target map's regularity and the geometric structure both of and of . Even when omitting any temporal structure, our universal approximation theorems are the first guarantees that Hölder functions, defined between such and can be approximated by DL models.

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Learning sub-patterns in piecewise continuous functions

Cited by 2 publications

References 38 publications

Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan secondary schools

Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan secondary schools

Designing universal causal deep learning models: The geometric (Hyper)transformer

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