Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T21:48:23.092Z Has data issue: false hasContentIssue false
  • English
  • Français

Computational foundations of the visual number sense

Published online by Cambridge University Press:  27 July 2017

Ivilin Peev Stoianov  and
Marco Zorzi
Ivilin Peev Stoianov
Affiliation:
Institute of Cognitive Sciences and Technologies, CNR, 35137 Padova, [email protected] Centre National de la Recherche Scientifique, Aix-Marseille Université, Marseille, France
Marco Zorzi
Affiliation:
Department of General Psychology, University of Padova, 35131 Padova, [email protected]://ccnl.psy.unipd.it/ IRCCS San Camillo Hospital Foundation, 30126 Venice-Lido, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

We provide an emergentist perspective on the computational mechanism underlying numerosity perception, its development, and the role of inhibition, based on our deep neural network model. We argue that the influence of continuous visual properties does not challenge the notion of number sense, but reveals limit conditions for the computation that yields invariance in numerosity perception. Alternative accounts should be formalized in a computational model.

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 40 , 2017 , e191
Check for updates
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agrillo, C., Piffer, L., Bisazza, A. & Butterworth, B. (2012) Evidence for two numerical systems that are similar in humans and guppies. PLoS ONE 7(2):e31923. doi: 10.1371/journal.pone.0031923.CrossRefGoogle ScholarPubMed
Allik, J. & Tuulmets, T. (1991) Occupancy model of perceived numerosity. Perception & Psychophysics 49:303–14.CrossRefGoogle ScholarPubMed
Brannon, E. M. & Terrace, H. S. (1998) Ordering of the numerosities 1 to 9 by monkeys. Science 282(5389):746–49.CrossRefGoogle ScholarPubMed
Bugden, S. & Ansari, D. (2016) Probing the nature of deficits in the ‘approximate number system’ in children with persistent developmental dyscalculia. Developmental Science 19(5):817–33. doi: 10.1111/desc.12324.CrossRefGoogle ScholarPubMed
Burr, D. & Ross, J. (2008) A visual sense of number. Current Biology 18(6):425–28. doi: 10.1016/j.cub.2008.02.052.CrossRefGoogle ScholarPubMed
Cappelletti, M., Didino, D., Stoianov, I. & Zorzi, M. (2014) Number skills are maintained in healthy ageing. Cognitive Psychology 69:25–45. doi: 10.1016/j.cogpsych.2013.11.004.CrossRefGoogle ScholarPubMed
Dakin, S. C., Tibber, M. S., Greenwood, J. A., Kingdom, F. A. A. & Morgan, M. J. (2011) A common visual metric for approximate number and density. Proceedings of the National Academy of Sciences of the United States of America 108(49):19552–57. doi: 10.1073/Pnas.1113195108.CrossRefGoogle ScholarPubMed
Dehaene, S. & Changeux, J. P. (1993) Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience 5:390–407. doi: 10.1162/jocn.1993.5.4.390.CrossRefGoogle ScholarPubMed
Durgin, F. H. (1995) Texture density adaptation and the perceived numerosity and distribution of texture. Journal of Experimental Psychology: Human Perception and Performance 21(1):149–69. doi: 10.1037/0096-1523.21.1.149.Google Scholar
Frith, C. D. & Frith, U. (1972) The solitaire illusion: An illusion of numerosity. Perception & Psychophysics 11:409–10.CrossRefGoogle Scholar
Gebuis, T. & Reynvoet, B. (2012b) The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General 141(4):642–48. doi: 10.1037/a0026218.CrossRefGoogle ScholarPubMed
Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q. & Germine, L. (2012) Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences of the United States of America 109(28):11116–20. doi: 10.1073/pnas.1200196109.CrossRefGoogle ScholarPubMed
Nieder, A. & Dehaene, S. (2009) Representation of number in the brain. Annual Review of Neuroscience 32:185–208. doi: 10.1146/annurev.neuro.051508.135550.CrossRefGoogle ScholarPubMed
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S. & Zorzi, M. (2010) Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition 116(1):33–41. doi: 10.1016/j.cognition.2010.03.012.CrossRefGoogle ScholarPubMed
Roitman, J. D., Brannon, E. M., & Platt, M. L. (2007) Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biology 5(8):e208. doi: 10.1371/journal.pbio.0050208.CrossRefGoogle ScholarPubMed
Stoianov, I. & Zorzi, M. (2012) Emergence of a “visual number sense” in hierarchical generative models. Nature Neuroscience 15:194–96. doi: 10.1038/nn.2996.CrossRefGoogle Scholar
Stoianov, I. & Zorzi, M. (2013) Developmental trajectories of numerosity perception. Poster presented at the College de France workshop “Interactions between space, time and number: 20 years of research” (Paris).Google Scholar
Testolin, A. & Zorzi, M. (2016) Probabilistic models and generative neural networks: Towards an unified framework for modeling normal and impaired neurocognitive functions. Frontiers in Computational Neuroscience 10:73. doi: 10.3389/fncom.2016.000731.CrossRefGoogle ScholarPubMed
Zorzi, M., Testolin, A. & Stoianov, I. P. (2013) Modeling language and cognition with deep unsupervised learning: A tutorial overview. Frontiers in Psychology 4:515. doi: 10.3389/fpsyg.2013.00515.CrossRefGoogle ScholarPubMed