DeepAI AI Chat
Log In Sign Up

Simulating Problem Difficulty in Arithmetic Cognition Through Dynamic Connectionist Models

by   Sungjae Cho, et al.

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.


page 1

page 2

page 3

page 4


Agents facilitate one category of human empathy through task difficulty

One way to improve the relationship between humans and anthropomorphic a...

Rigid models of Presburger arithmetic

We present a description of rigid models of Presburger arithmetic (i.e.,...

Difficulty Rating of Sudoku Puzzles: An Overview and Evaluation

How can we predict the difficulty of a Sudoku puzzle? We give an overvie...

Guiding the Growth: Difficulty-Controllable Question Generation through Step-by-Step Rewriting

This paper explores the task of Difficulty-Controllable Question Generat...

A Rule-Based Computational Model of Cognitive Arithmetic

Cognitive arithmetic studies the mental processes used in solving math p...

Controlling Transaction Rate in Tangle Ledger: A Principal Agent Problem Approach

Tangle is a distributed ledger technology that stores data as a directed...