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A Number Sense as an Emergent Property of the Manipulating Brain

Kondapaneni, N. and Perona, P. (2020) A Number Sense as an Emergent Property of the Manipulating Brain. . (Unpublished)

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The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which this ability is developed is still poorly understood. In particular, it is not known whether acquiring such a number sense is possible without supervision from a teacher. To explore this question, we propose a model in which spontaneous and undirected manipulation of small objects trains perception to predict the resulting scene changes. We find that, from this task, an image representation emerges that exhibits regularities that foreshadow numbers and quantity. These include distinct categories for zero and the first few natural numbers, a notion of order, and a signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. We conclude that important aspects of a facility with numbers and quantities may be learned without explicit teacher supervision.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Perona, P.0000-0002-7583-5809
Additional Information:Attribution 4.0 International (CC BY 4.0). We are very grateful to the Simons Foundation for generously supporting this work. We are in debt to a number of colleagues who provided references to the literature and insightful suggestions: Alessandro Achille, Katie Bouman, David Burr, Eli Cole, Mario Perona, Giovanni Paolini, Markus Meister, Stefano Soatto, Kate Stevenson, Doris Tsao.
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Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20210119-161642919
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107572
Deposited By: George Porter
Deposited On:20 Jan 2021 15:21
Last Modified:20 Jan 2021 15:21

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