Exploring a Cognitive Architecture for Learning Arithmetic Equations

TL;DR

This paper presents a neurobiologically plausible cognitive architecture that models how systems learn and recall arithmetic equations, offering insights into neural mechanisms and generalization in mathematical cognition.

Contribution

It introduces a novel cognitive architecture with a number embedding network and associative memory, advancing understanding of arithmetic learning in AI systems.

Findings

Insights into generalization capabilities of connectionist models

Potential neurological causes of dyscalculia

Impact of network architecture on cognitive performance

Abstract

The acquisition and performance of arithmetic skills and basic operations such as addition, subtraction, multiplication, and division are essential for daily functioning, and reflect complex cognitive processes. This paper explores the cognitive mechanisms powering arithmetic learning, presenting a neurobiologically plausible cognitive architecture that simulates the acquisition of these skills. I implement a number vectorization embedding network and an associative memory model to investigate how an intelligent system can learn and recall arithmetic equations in a manner analogous to the human brain. I perform experiments that provide insights into the generalization capabilities of connectionist models, neurological causes of dyscalculia, and the influence of network architecture on cognitive performance. Through this interdisciplinary investigation, I aim to contribute to ongoing research into the neural correlates of mathematical cognition in intelligent systems.