Simulating Problem Difficulty in Arithmetic Cognition Through Dynamic Connectionist Models
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...
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Main Authors | , , , , |
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Format | Journal Article |
Language | English |
Published |
09.05.2019
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.1905.03617 |