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Probability Without Counting and Dividing:A Fresh Computational Perspective

Creative Commons 'BY' version 4.0 license
Abstract

Recent experiments show that preverbal infants can reasonprobabilistically. This raises a deep puzzle because infants lackthe counting and dividing abilities presumably required tocompute probabilities. In the standard way of computingprobabilities, they would have to count or accurately estimatelarge frequencies and divide those values by their total. Here, wepresent a novel neural-network model that learns and usesprobability distributions without explicit counting or dividing.Probability distributions emerge naturally from neural-networklearning of event sequences, providing a computationallysufficient explanation of how infants could succeed atprobabilistic reasoning. Several alternative explanations arediscussed and ruled out. Our work bears on several other activeliteratures, and it suggests an effective way to integrate Bayesianand neural-network approaches to cognition.

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