Exploring a Cognitive Architecture for Learning Arithmetic Equations

TL;DR

The paper investigates how arithmetic skills can be learned within a neurobiologically plausible cognitive architecture using a numerical embedding SDR-based network and a connectionist associative memory model. It evaluates learning, generalization, dyscalculia simulations via lesioning, and catastrophic interference through sequential task training, highlighting both capabilities and limitations of the proposed architecture. Key findings show successful training on seen data but limited generalization and pronounced vulnerability to interference, with lesioning revealing critical thresholds for maintaining accurate number encoding. These results advance our understanding of mathematical cognition in AI systems and underscore the importance of abstract representations and integrated learning mechanisms for robust arithmetic learning.

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.

Figures (6)

• Figure 1: Numerical embedding network simulation.
• Figure 2: Associative memory network simulation.
• Figure 3: Train Epoch Plot for numerical embedding network.
• Figure 4: Train Epoch Plot for associative memory network.
• Figure 5: Testing results on addition table for 1 following training on 2.