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Poster B104 in Poster Session B - Thursday, August 8, 2024, 1:30 – 3:30 pm, Johnson Ice Rink
Computational journey from numerical cognition to arithmetic ability
Denis Turcu1 (), Katharyn Fatehi2; 1Neuroscience Department, Columbia University, 2Engineering Undergraduate Program, Columbia University
Numerical cognition sets the foundation for developing arithmetic abilities, yet performing arithmetic operations is much more abstract, complex and subtle than identifying numbers. This poses the question whether animals that demonstrate numerical cognition are necessarily equipped to develop arithmetic abilities. Recent experimental studies explored this question in multiple species and found that these animals learn to add and subtract. Here, we used recurrent neural networks (RNNs) to investigate possible neural mechanisms underlying arithmetic abilities. We found that our models perform very well on in-distribution test data, but do not generalize well to out-of-distribution test data. The two main reasons for poor generalization are 1) models do not learn the basic underlying arithmetic operation, and 2) bounded activation function prohibits models to compute on arbitrarily large scales. Our work suggests that developing arithmetic abilities requires specific capacity for abstraction on top of learned or innate numerical cognition, consistent with previous cognitive studies. While most times lack of numerical cognition implies lack of arithmetic abilities, we point out that the inverse, i.e. having numerical cognition implies having arithmetic abilities, need not be true, and we demonstrate this result in an RNN model.
Keywords: decision making numerical cognition arithmetic ability recurrent neural network