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Emergence of a 'visual number sense' in hierarchical generative models


Numerosity estimation is phylogenetically ancient and foundational to human mathematical learning, but its computational bases remain controversial. Here we show that visual numerosity emerges as a statistical property of images in 'deep networks' that learn a hierarchical generative model of the sensory input. Emergent numerosity detectors had response profiles resembling those of monkey parietal neurons and supported numerosity estimation with the same behavioral signature shown by humans and animals.

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Figure 1: Deep network model and number-sensitive neurons.
Figure 2: Numerosity comparison task.


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This study was supported by the European Research Council (grant no. 210922 to M.Z.)

Author information




M.Z. and I.S. conceived the experiments, discussed the results and wrote the paper. I.S. wrote the code, ran the model and analyzed data.

Corresponding author

Correspondence to Marco Zorzi.

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Competing interests

The authors declare no competing financial interests.

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Supplementary Text and Figures

Supplementary Figures 1–4, Supplementary Methods (PDF 242 kb)

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Stoianov, I., Zorzi, M. Emergence of a 'visual number sense' in hierarchical generative models. Nat Neurosci 15, 194–196 (2012).

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