{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T21:39:05Z","timestamp":1790113145281,"version":"4.0.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T00:00:00Z","timestamp":1699574400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T00:00:00Z","timestamp":1699574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Humans possess an innate ability to visually perceive numerosities, which refers to the cardinality of a set. Numerous studies indicate that the lateral intraparietal cortex (LIP) and other intraparietal sulcus (IPS) regions (region) of the brain contain the neurological substrates responsible for number processing. Existing computational models of number perception often focus on a limited range of numbers and fail to account for important behavioral characteristics like adaptation effects, despite simulating fundamental aspects such as size and distance effects. To address these limitations, our study develops (introduces) a novel computational model of number perception utilizing a network of neurons with self-excitatory and mutual inhibitory properties. Our approach assumes that the mean activation of the network at steady state can encode numerosity by exhibiting a monotonically increasing relationship with the input variable set size. By optimizing the total number of inhibition strengths required, we achieve coverage of the full range of numbers through three distinct intervals: 1 to 4, 5 to 17, and 21 to 50. Remarkably, this division aligns closely with the breakpoints in numerosity perception identified in behavioral studies. Furthermore, our study develops a method for decoding the mean activation into a continuous scale of numbers spanning from 1 to 50. Additionally, we propose a mechanism for dynamically selecting the inhibition strength based on current inputs, enabling the network to operate effectively across an extended (entire) range of numerosities. Our model not only sheds new light on the generation of diverse behavioral phenomena in the brain but also elucidates how continuous visual attributes and adaptation effects influence perceived numerosity.<\/jats:p>","DOI":"10.1038\/s41598-023-44535-3","type":"journal-article","created":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T06:02:17Z","timestamp":1699596137000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Emergence of behavioral phenomena and adaptation effects in human numerosity decoder using recurrent neural networks"],"prefix":"10.1038","volume":"13","author":[{"given":"Bhavesh K","family":"Verma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rakesh","family":"Sengupta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,11,10]]},"reference":[{"key":"44535_CR1","doi-asserted-by":"publisher","DOI":"10.4159\/9780674037533","volume-title":"The Child\u2019s Understanding of Number","author":"R Gelman","year":"1986","unstructured":"Gelman, R. & Gallistel, C. R. The Child\u2019s Understanding of Number Vol. 1 (Harvard University Press, 1986)."},{"issue":"1","key":"44535_CR2","doi-asserted-by":"publisher","first-page":"B1","DOI":"10.1016\/S0010-0277(99)00066-9","volume":"74","author":"X Fei","year":"2000","unstructured":"Fei, X. & Spelke, E. S. Large number discrimination in 6-month-old infants. Cognition 74(1), B1\u2013B11 (2000).","journal-title":"Cognition"},{"issue":"1523","key":"44535_CR3","doi-asserted-by":"publisher","first-page":"1441","DOI":"10.1098\/rspb.2003.2414","volume":"270","author":"MD Hauser","year":"2003","unstructured":"Hauser, M. D., Tsao, F., Garcia, P. & Spelke, E. S. Evolutionary foundations of number: Spontaneous representation of numerical magnitudes by cotton-top tamarins. Proc. R. Soc. Lond. B 270(1523), 1441\u20131446 (2003).","journal-title":"Proc. R. Soc. Lond. B"},{"issue":"8","key":"44535_CR4","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/S0166-2236(98)01263-6","volume":"21","author":"S Dehaene","year":"1998","unstructured":"Dehaene, S., Dehaene-Lambertz, G. & Cohen, L. Abstract representations of numbers in the animal and human brain. Trends Neurosci. 21(8), 355\u2013361 (1998).","journal-title":"Trends Neurosci."},{"issue":"4","key":"44535_CR5","doi-asserted-by":"publisher","first-page":"498","DOI":"10.2307\/1418556","volume":"62","author":"EL Kaufman","year":"1949","unstructured":"Kaufman, E. L., Lord, M. W., Reese, T. W. & Volkmann, J. The discrimination of visual number. Am. J. Psychol. 62(4), 498\u2013525 (1949).","journal-title":"Am. J. Psychol."},{"issue":"2","key":"44535_CR6","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1111\/1467-9280.00120","volume":"10","author":"J Whalen","year":"1999","unstructured":"Whalen, J., Gallistel, C. R. & Gelman, R. Nonverbal counting in humans: The psychophysics of number representation. Psychol. Sci. 10(2), 130\u2013137 (1999).","journal-title":"Psychol. Sci."},{"issue":"7213","key":"44535_CR7","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1038\/nature07246","volume":"455","author":"J Halberda","year":"2008","unstructured":"Halberda, J., Mazzocco, M. M. M. & Feigenson, L. Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455(7213), 665\u2013668 (2008).","journal-title":"Nature"},{"issue":"1","key":"44535_CR8","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1177\/0956797613501520","volume":"25","author":"G Anobile","year":"2014","unstructured":"Anobile, G., Cicchini, G. M. & Burr, D. C. Separate mechanisms for perception of numerosity and density. Psychol. Sci. 25(1), 265\u2013270 (2014).","journal-title":"Psychol. Sci."},{"issue":"1","key":"44535_CR9","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1037\/0033-295X.101.1.80","volume":"101","author":"LM Trick","year":"1994","unstructured":"Trick, L. M. & Pylyshyn, Z. W. Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychol. Rev. 101(1), 80 (1994).","journal-title":"Psychol. Rev."},{"issue":"4","key":"44535_CR10","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1080\/13506280801937939","volume":"16","author":"HE Egeth","year":"2008","unstructured":"Egeth, H. E., Leonard, C. J. & Palomares, M. The role of attention in subitizing: Is the magical number 1?. Vis. Cogn. 16(4), 463\u2013473 (2008).","journal-title":"Vis. Cogn."},{"issue":"6","key":"44535_CR11","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1167\/10.6.20","volume":"10","author":"DC Burr","year":"2010","unstructured":"Burr, D. C., Turi, M. & Anobile, G. Subitizing but not estimation of numerosity requires attentional resources. J. Vis. 10(6), 20\u201320 (2010).","journal-title":"J. Vis."},{"issue":"2","key":"44535_CR12","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.neulet.2008.05.063","volume":"440","author":"X Xiaodong","year":"2008","unstructured":"Xiaodong, X. & Liu, C. Can subitizing survive the attentional blink? An erp study. Neurosci. Lett. 440(2), 140\u2013144 (2008).","journal-title":"Neurosci. Lett."},{"key":"44535_CR13","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/B978-0-12-385948-8.00017-7","volume":"55","author":"M Piazza","year":"2011","unstructured":"Piazza, M. Neurocognitive start-up tools for symbolic number representations. Space Time Number Brain 55, 267\u2013285 (2011).","journal-title":"Space Time Number Brain"},{"issue":"1","key":"44535_CR14","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.cognition.2011.05.007","volume":"121","author":"M Piazza","year":"2011","unstructured":"Piazza, M., Fumarola, A., Chinello, A. & Melcher, D. Subitizing reflects visuo-spatial object individuation capacity. Cognition 121(1), 147\u2013153 (2011).","journal-title":"Cognition"},{"issue":"1","key":"44535_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1037\/0096-3445.111.1.1","volume":"111","author":"G Mandler","year":"1982","unstructured":"Mandler, G. & Shebo, B. J. Subitizing: An analysis of its component processes. J. Exp. Psychol. Gen. 111(1), 1 (1982).","journal-title":"J. Exp. Psychol. Gen."},{"key":"44535_CR16","doi-asserted-by":"crossref","unstructured":"Krajcsi, A., Szab\u00f3, E. & M\u00f3rocz, I.\u00c1. Subitizing is sensitive to the arrangement of objects (Experimental psychology, 2013).","DOI":"10.1027\/1618-3169\/a000191"},{"issue":"7","key":"44535_CR17","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1068\/p5029","volume":"32","author":"J Ross","year":"2003","unstructured":"Ross, J. Visual discrimination of number without counting. Perception 32(7), 867\u2013870 (2003).","journal-title":"Perception"},{"issue":"4","key":"44535_CR18","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1162\/jocn.1993.5.4.390","volume":"5","author":"S Dehaene","year":"1993","unstructured":"Dehaene, S. & Changeux, J.-P. Development of elementary numerical abilities: A neuronal model. J. Cogn. Neurosci. 5(4), 390\u2013407 (1993).","journal-title":"J. Cogn. Neurosci."},{"issue":"1\u20132","key":"44535_CR19","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0010-0277(92)90050-R","volume":"44","author":"CR Gallistel","year":"1992","unstructured":"Gallistel, C. R. & Gelman, R. Preverbal and verbal counting and computation. Cognition 44(1\u20132), 43\u201374 (1992).","journal-title":"Cognition"},{"issue":"6","key":"44535_CR20","doi-asserted-by":"publisher","first-page":"555","DOI":"10.3758\/BF03207540","volume":"50","author":"JD Balakrishnan","year":"1991","unstructured":"Balakrishnan, J. D. & Ashby, F. G. Is subitizing a unique numerical ability?. Percept. Psychophys. 50(6), 555\u2013564 (1991).","journal-title":"Percept. Psychophys."},{"issue":"5","key":"44535_CR21","doi-asserted-by":"publisher","first-page":"1512","DOI":"10.3758\/s13414-019-01804-6","volume":"81","author":"M Portley","year":"2019","unstructured":"Portley, M. & Durgin, F. H. The second number-estimation elbow: Are visual numbers greater than 20 evaluated differently?. Attent. Percept. Psychophys. 81(5), 1512\u20131521 (2019).","journal-title":"Attent. Percept. Psychophys."},{"issue":"5587","key":"44535_CR22","doi-asserted-by":"publisher","first-page":"1708","DOI":"10.1126\/science.1072493","volume":"297","author":"A Nieder","year":"2002","unstructured":"Nieder, A., Freedman, D. J. & Miller, E. K. Representation of the quantity of visual items in the primate prefrontal cortex. Science 297(5587), 1708\u20131711 (2002).","journal-title":"Science"},{"issue":"5792","key":"44535_CR23","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1126\/science.1130308","volume":"313","author":"A Nieder","year":"2006","unstructured":"Nieder, A., Diester, I. & Tudusciuc, O. Temporal and spatial enumeration processes in the primate parietal cortex. Science 313(5792), 1431\u20131435 (2006).","journal-title":"Science"},{"issue":"8","key":"44535_CR24","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.0050208","volume":"5","author":"JD Roitman","year":"2007","unstructured":"Roitman, J. D., Brannon, E. M. & Platt, M. L. Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biol. 5(8), e208 (2007).","journal-title":"PLoS Biol."},{"key":"44535_CR25","first-page":"17","volume":"171","author":"T Gebuis","year":"2016","unstructured":"Gebuis, T., Kadosh, R. C. & Gevers, W. Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Physiol. (Oxf.) 171, 17\u201335 (2016).","journal-title":"Acta Physiol. (Oxf.)"},{"issue":"49","key":"44535_CR26","doi-asserted-by":"publisher","first-page":"19552","DOI":"10.1073\/pnas.1113195108","volume":"108","author":"SC Dakin","year":"2011","unstructured":"Dakin, S. C., Tibber, M. S., Greenwood, J. A., Kingdom, F. A. A. & Morgan, M. J. A common visual metric for approximate number and density. Proc. Natl. Acad. Sci. 108(49), 19552\u201319557 (2011).","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"5","key":"44535_CR27","doi-asserted-by":"publisher","first-page":"eaav7903","DOI":"10.1126\/sciadv.aav7903","volume":"5","author":"K Nasr","year":"2019","unstructured":"Nasr, K., Viswanathan, P. & Nieder, A. Number detectors spontaneously emerge in a deep neural network designed for visual object recognition. Sci. Adv. 5(5), eaav7903 (2019).","journal-title":"Sci. Adv."},{"key":"44535_CR28","first-page":"49","volume-title":"International Work-Conference on Artificial Neural Networks","author":"A Zanetti","year":"2019","unstructured":"Zanetti, A., Testolin, A., Zorzi, M. & Wawrzynski, P. Numerosity representation in infogan: An empirical study. In International Work-Conference on Artificial Neural Networks (eds Zanetti, A. et al.) 49\u201360 (Springer, 2019)."},{"issue":"1","key":"44535_CR29","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.tics.2012.10.011","volume":"17","author":"DJ Kravitz","year":"2013","unstructured":"Kravitz, D. J., Saleem, K. S., Baker, C. I., Ungerleider, L. G. & Mishkin, M. The ventral visual pathway: An expanded neural framework for the processing of object quality. Trends Cogn. Sci. 17(1), 26\u201349 (2013).","journal-title":"Trends Cogn. Sci."},{"key":"44535_CR30","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.brainres.2014.03.014","volume":"1582","author":"R Sengupta","year":"2014","unstructured":"Sengupta, R., Surampudi, B. R. & Melcher, D. A visual sense of number emerges from the dynamics of a recurrent on-center off-surround neural network. Brain Res. 1582, 114\u2013124 (2014).","journal-title":"Brain Res."},{"key":"44535_CR31","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1109\/ICIP.2012.6466941","volume-title":"2012 19th IEEE International Conference on Image Processing","author":"N Riche","year":"2012","unstructured":"Riche, N., Mancas, M., Gosselin, B. & Dutoit, T. Rare: A new bottom-up saliency model. In 2012 19th IEEE International Conference on Image Processing (eds Riche, N. et al.) 641\u2013644 (IEEE, 2012)."},{"issue":"4","key":"44535_CR32","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1037\/a0026218","volume":"141","author":"T Gebuis","year":"2012","unstructured":"Gebuis, T. & Reynvoet, B. The interplay between nonsymbolic number and its continuous visual properties. J. Exp. Psychol. Gen. 141(4), 642 (2012).","journal-title":"J. Exp. Psychol. Gen."},{"issue":"12","key":"44535_CR33","doi-asserted-by":"publisher","first-page":"178812","DOI":"10.1162\/jocn_a_01320","volume":"30","author":"M Fornaciai","year":"2018","unstructured":"Fornaciai, M. & Park, J. Early numerosity encoding in visual cortex is not sufficient for the representation of numerical magnitude. J. Cogn. Neurosci. 30(12), 178812\u20131802 (2018).","journal-title":"J. Cogn. Neurosci."},{"key":"44535_CR34","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.cognition.2016.03.006","volume":"151","author":"M Fornaciai","year":"2016","unstructured":"Fornaciai, M., Cicchini, G. M. & Burr, D. C. Adaptation to number operates on perceived rather than physical numerosity. Cognition 151, 63\u201367 (2016).","journal-title":"Cognition"},{"issue":"2","key":"44535_CR35","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1163\/187847511X570097","volume":"24","author":"D Burr","year":"2011","unstructured":"Burr, D., Anobile, G. & Turi, M. Adaptation affects both high and low (subitized) numbers under conditions of high attentional load. Seeing and Perceiving 24(2), 141\u2013150 (2011).","journal-title":"Seeing and Perceiving"},{"issue":"6","key":"44535_CR36","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1016\/j.cub.2008.02.052","volume":"18","author":"D Burr","year":"2008","unstructured":"Burr, D. & Ross, J. A visual sense of number. Curr. Biol. 18(6), 425\u2013428 (2008).","journal-title":"Curr. Biol."},{"key":"44535_CR37","doi-asserted-by":"publisher","first-page":"253","DOI":"10.3758\/s13414-016-1221-5","volume":"79","author":"R Sengupta","year":"2017","unstructured":"Sengupta, R., Bapiraju, S. & Melcher, D. Empirical support for a single, flexible mechanism for numerosity perception. Attent. Percept. Psychophys. 79, 253\u2013266 (2017).","journal-title":"Attent. Percept. Psychophys."},{"key":"44535_CR38","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1016\/j.neuroimage.2016.09.020","volume":"143","author":"E Castaldi","year":"2016","unstructured":"Castaldi, E., Aagten-Murphy, D., Michela Burr D, T. & Morrone, M. C. Effects of adaptation on numerosity decoding in the human brain. Neuroimage 143, 364\u2013377 (2016).","journal-title":"Neuroimage"},{"issue":"1","key":"44535_CR39","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1037\/0096-1523.21.1.149","volume":"21","author":"FH Durgin","year":"1995","unstructured":"Durgin, F. H. Texture density adaptation and the perceived numerosity and distribution of texture. J. Exp. Psychol. Hum. Percept. Perform. 21(1), 149 (1995).","journal-title":"J. Exp. Psychol. Hum. Percept. Perform."},{"issue":"1","key":"44535_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep32810","volume":"6","author":"E Zimmermann","year":"2016","unstructured":"Zimmermann, E. & Fink, G. R. Numerosity perception after size adaptation. Sci. Rep. 6(1), 1\u20137 (2016).","journal-title":"Sci. Rep."},{"issue":"3","key":"44535_CR41","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1177\/0956797617737385","volume":"29","author":"M Fornaciai","year":"2018","unstructured":"Fornaciai, M. & Park, J. Attractive serial dependence in the absence of an explicit task. Psychol. Sci. 29(3), 437\u2013446 (2018).","journal-title":"Psychol. Sci."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-023-44535-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-023-44535-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-023-44535-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T06:09:38Z","timestamp":1699596578000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-023-44535-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,10]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["44535"],"URL":"https:\/\/doi.org\/10.1038\/s41598-023-44535-3","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2645627\/v1","asserted-by":"object"}]},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,10]]},"assertion":[{"value":"2 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"19571"}}