Simulating Problem Difficulty in Arithmetic Cognition Through Dynamic Connectionist Models

TL;DR

This study compares human and connectionist model experiences of arithmetic difficulty, showing both are similarly affected by the number of carries, with model hyperparameters influencing computational steps.

Contribution

It demonstrates that connectionist models can simulate human-like difficulty patterns in arithmetic, highlighting the role of specific hyperparameters.

Findings

Both humans and models find difficulty increases with the number of carries.

Difficulty increases more steeply in subtraction than in addition.

Higher confidence thresholds and larger hidden dimensions lead to more computational steps.

Abstract

The present study aims to investigate similarities between how humans and connectionist models experience difficulty in arithmetic problems. Problem difficulty was operationalized by the number of carries involved in solving a given problem. Problem difficulty was measured in humans by response time, and in models by computational steps. The present study found that both humans and connectionist models experience difficulty similarly when solving binary addition and subtraction. Specifically, both agents found difficulty to be strictly increasing with respect to the number of carries. Another notable similarity is that problem difficulty increases more steeply in subtraction than in addition, for both humans and connectionist models. Further investigation on two model hyperparameters --- confidence threshold and hidden dimension --- shows higher confidence thresholds cause the model to take more computational steps to arrive at the correct answer. Likewise, larger hidden dimensions cause the model to take more computational steps to correctly answer arithmetic problems; however, this effect by hidden dimensions is negligible.