Exploring Neural Network Models of Mathematical Cognition

Silvester Sabathiel
Session kindly contributed by Silvester Sabathiel in SEMF’s 2021 Numerous Numerosity Workshop: https://semf.org.es/numerosity/

ABSTRACT
The rise of artificial intelligence has increased the opportunities to better understand the mechanisms that govern mathematical cognition. Machine learning systems have been studied extensively to learn how to solve differential equations, algebraic problems and integrals, or prove complex theorems. The input and output are preprocessed symbols. In order to find cognitive mechanisms that are comparable to humans in terms of generalizability, and the ability to apply mathematical concepts outside of mathematics, a grounded approach may be needed. It is important to start with the fundamental mathematical concepts acquired by humans at an early age and learn them in a multimodal and interactive environment. This talk will examine how artificial network systems in such a framework can provide a controlled environment to uncover possible cognitive mechanisms that are responsible for intuitive numerical perception or culturally acquired concepts such as counting. We will first review some of the most important research findings from the past before I discuss my own contributions. We can then discuss future challenges in the field of numerical cognition, and the direction this research could take.

SABATHIEL SILVESTER
NTNU Trondheim.
Personal website: http://silsab.com
NTNU profile: https://www.ntnu.edu/employees/silvester.sabathiel.
ResearchGate: https://www.researchgate.net/profile/Silvester-Sabathiel-3
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