Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Brief Communication
  • Published:

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

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

Similar content being viewed by others


  1. Nieder, A. Nat. Rev. Neurosci. 6, 177–190 (2005).

    Article  CAS  Google Scholar 

  2. Halberda, J., Mazzocco, M.M.M. & Feigenson, L. Nature 455, 665–668 (2008).

    Article  CAS  Google Scholar 

  3. Piazza, M. et al. Cognition 116, 33–41 (2010).

    Article  Google Scholar 

  4. Burr, D. & Ross, J. Curr. Biol. 18, 425–428 (2008).

    Article  CAS  Google Scholar 

  5. Durgin, F.H. Curr. Biol. 18, R855–R856 (2008).

    Article  CAS  Google Scholar 

  6. Dehaene, S. & Changeux, J. J. Cogn. Neurosci. 5, 390–407 (1993).

    Article  CAS  Google Scholar 

  7. Allik, J. & Tuulmets, T. Percept. Psychophys. 49, 303–314 (1991).

    Article  CAS  Google Scholar 

  8. Hinton, G.E. & Salakhutdinov, R.R. Science 313, 504–507 (2006).

    Article  CAS  Google Scholar 

  9. Hinton, G.E. Trends Cogn. Sci. 11, 428–434 (2007).

    Article  Google Scholar 

  10. Roitman, J.D., Brannon, E. & Platt, M. PLoS Biol. 5, e208 (2007).

    Article  Google Scholar 

  11. Piazza, M. et al. Neuron 44, 547–555 (2004).

    Article  CAS  Google Scholar 

  12. Brannon, E.M. & Terrace, H.S. Science 282, 746–749 (1998).

    Article  CAS  Google Scholar 

  13. Nieder, A., Freedman, D. & Miller, E.K. Science 297, 1708–1711 (2002).

    Article  CAS  Google Scholar 

  14. Santens, S. et al. Cereb. Cortex 20, 77–88 (2010).

    Article  Google Scholar 

  15. Verguts, T. & Fias, W. J. Cogn. Neurosci. 16, 1493–1504 (2004).

    Article  Google Scholar 

Download references


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

Author information

Authors and Affiliations



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.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing