| Abstract: | The study of numerical abilities, and how they are acquired, is being used to explore the continuity between ontogenesis and environmental learning. One technique that proves useful in this exploration is the artificial simulation of numerical abilities with neural networks, using different learning paradigms to explore development. A neural network simulation of subitization, sometimes referred to as visual enumeration, and of counting, a recurrent operation, has been developed using the so-called multi-net architecture. Our numerical ability simulations use two or more neural networks combining supervised and unsupervised learning techniques to model subitization and counting. Subitization has been simulated using networks employing unsupervised self-organizing learning, the results of which agree with infant subitization experiments and are comparable with supervised neural network simulations of subitization reported in the literature. Counting has been simulated using a multi-net system of supervised static and recurrent backpropagation networks that learn their individual tasks within an unsupervised, competitive framework. The developmental profile of the counting simulation shows similarities to that of children learning to count and demonstrates how neural networks can learn how to be combined together in a process modelling development. |
