A competitive neural model of small number detection

The ability to represent numbers is a key attribute for both humans and animals. Recent developments in the understanding of numerical processing has led to the proposal that humans utilise two independent representations of number, one for real numbers and another for integers. We describe a computational model of small number detection to explore the relationship between these core systems of number. We use a combination of unsupervised and supervised neural networks to simulate the interaction between the real and integer representations. For real values we use a self-organised spatial representation of number. For integer values we use a supervised network motivated by linguistic processing. During training and testing, the networks exhibit behavioural characteristics such as the number size and numerical distance effects. Each representation is combined using the mixture-of-experts architecture that allows us to model the subitization limit (the maximum number of visual stimuli that can be accurately quantified almost immediately) as the competitive allocation of representations for number detection, where the crossover point between deploying the real and integer representations of number is obtained through a process of learning. Our results suggest that the existence of two core systems of number is at least computationally plausible and further suggests that the subitization limit emerges through the interaction of spatial and linguistic numerical processing. This provides computational evidence for one way in which small and large numbers are related in humans.