A neural model for learning of number representation in children and adults
Setic M., Domijan D.
First author's affiliation: University of Rijeka, Rijeka, Croatia
Investigations with children showed that they gradually develop an approximate representation of magnitude (numerosity). Lipton and Spelke (2004) investigated the children capacity to distinguish sequences of sounds. Six month babies were able to discriminate sequence with 16 sounds from the sequence of 8 sounds. However, they were not able to discriminate between sequences of 12 and 8 sounds. On the other hand, nine month babies were able to discriminate sequences of 12 and 8 sounds. Similar process could be observed in adults when they are faced with the problem of learning new system of relationships between numbers. For instance, Marques and Dehaene (2004; Dehaene & Marques, 2002) showed that participants in Portugal and Austria had problems in estimating values of various goods when they are shown in euro and not in national currency. These problems were seen immediately after the euro was introduced. Few years of experience with euro reduces the problem. Described results are explained (simulated) using neural network for number representation proposed by Domijan (2004). In the original version, the model simulated the neurophysiological findings about neurons in the prefrontal cortex, which are sensitive to numerosity. In the model, all connections were fixed. Here, we proposed a new version of the model which is able to learn using Hebb rule. This type of associative learning has a plausible neurophysiological interpretation (long-term potentiation). Computer simulations showed that the width of the tuning curves for the neurons sensitive to different numbers gradually decrease as a function of experience. In other words, tuning curves become sharper with learning, which enable better discrimination of numbers. The same result is obtained with different sensory modalities. We conclude that the proposed model explains neural mechanisms for the construction of number representation in the parietal and prefrontal cortex.