An emergentist perspective on the origin of number sense

“…These findings are consistent with both our retrieval of an early and late number effect (Fig. 4) and the biphasic dynamic of the neural networks mentioned above 49,50 . Lastly, the numerical representations of the rhesus macaque have been proven to be partially cross-modal 55,56 .…”

“…Untrained networks showed correlated numerosity responses across conditions, suggesting that a degree of numerical sensitivity can arise from the inherent aggregation of local feature statistics within the feedforward visual hierarchy (Landerl et al, 2004). This is consistent with previous reports that numerosity-selective units can emerge spontaneously in untrained networks (Kim et al, 2021;Stoianov & Zorzi, 2012;Zorzi & Testolin, 2018), and with evidence that basic numerical abilities are present early in development (Rugani et al, 2015) and untrained animals (Viswanathan & Nieder, 2013;Wagener et al, 2018). Yet untrained networks did not show a reliable connectedness effect.…”

“…Our computational simulations provide further support for an impairment in numerosity representation. As in previous reports (Testolin, Dolfi, et al, 2020;Zorzi & Testolin, 2018), deep neural networks trained with generative learning on dot arrays showed a developmental improvement in number acuity and a reduction in the influence of non-numerical magnitudes. This is consistent with the notion that numerosity (as a latent factor of images of object sets; Stoianov & Zorzi, 2012) is progressively disentangled (i.e., better factorized) from other continuous magnitudes during unsupervised learning (Testolin, Dolfi, et al, 2020).…”

“…These findings are consistent with both our retrieval of an early and late number effect (Fig. 4) and the biphasic dynamic of the neural networks mentioned above 49,50 . Lastly, the numerical representations of the rhesus macaque have been proven to be partially cross-modal 55,56 .…”

“…Untrained networks showed correlated numerosity responses across conditions, suggesting that a degree of numerical sensitivity can arise from the inherent aggregation of local feature statistics within the feedforward visual hierarchy (Landerl et al, 2004). This is consistent with previous reports that numerosity-selective units can emerge spontaneously in untrained networks (Kim et al, 2021;Stoianov & Zorzi, 2012;Zorzi & Testolin, 2018), and with evidence that basic numerical abilities are present early in development (Rugani et al, 2015) and untrained animals (Viswanathan & Nieder, 2013;Wagener et al, 2018). Yet untrained networks did not show a reliable connectedness effect.…”

“…Our computational simulations provide further support for an impairment in numerosity representation. As in previous reports (Testolin, Dolfi, et al, 2020;Zorzi & Testolin, 2018), deep neural networks trained with generative learning on dot arrays showed a developmental improvement in number acuity and a reduction in the influence of non-numerical magnitudes. This is consistent with the notion that numerosity (as a latent factor of images of object sets; Stoianov & Zorzi, 2012) is progressively disentangled (i.e., better factorized) from other continuous magnitudes during unsupervised learning (Testolin, Dolfi, et al, 2020).…”

“…These findings are consistent with both our retrieval of an early and late number effect (Fig. 4) and the biphasic dynamic of the neural networks mentioned above 49,50 . Lastly, the numerical representations of the rhesus macaque have been proven to be partially cross-modal 55,56 .…”

“…Untrained networks showed correlated numerosity responses across conditions, suggesting that a degree of numerical sensitivity can arise from the inherent aggregation of local feature statistics within the feedforward visual hierarchy (Landerl et al, 2004). This is consistent with previous reports that numerosity-selective units can emerge spontaneously in untrained networks (Kim et al, 2021;Stoianov & Zorzi, 2012;Zorzi & Testolin, 2018), and with evidence that basic numerical abilities are present early in development (Rugani et al, 2015) and untrained animals (Viswanathan & Nieder, 2013;Wagener et al, 2018). Yet untrained networks did not show a reliable connectedness effect.…”

“…Our computational simulations provide further support for an impairment in numerosity representation. As in previous reports (Testolin, Dolfi, et al, 2020;Zorzi & Testolin, 2018), deep neural networks trained with generative learning on dot arrays showed a developmental improvement in number acuity and a reduction in the influence of non-numerical magnitudes. This is consistent with the notion that numerosity (as a latent factor of images of object sets; Stoianov & Zorzi, 2012) is progressively disentangled (i.e., better factorized) from other continuous magnitudes during unsupervised learning (Testolin, Dolfi, et al, 2020).…”