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Number sense: emergence from the recognition of visible objects

Number sense: emergence from the recognition of visible objects

Humans and animals have a “number sense,” or the capacity to intuitively estimate the numerosity of visual elements in a collection. This capacity suggests that processes for extracting numerosity are inside the brain’s visual system, which is largely concerned with visual object recognition. Researchers have long questioned if these number neurons are created in the brain simply by the capacity to see – and, if so, how.

Using an artificial neural network, a team of researchers led by Professor Andreas Nieder from the University of Tübingen’s Institute of Neurobiology studied the origins of number perception. The results show that it is generated spontaneously by the visual system, with no prior experience with counting.

The intrinsic existence of the number sense suggests that mechanisms for extracting numerosity are in the brain’s visual system, despite the fact that it is primarily concerned with visual objects by nature. Deep neural networks inspired by biology have offered significant insights into the workings of the visual system in recent years.

“The network model is based on an architecture structured like the early developmental stage of the human visual cortex,” Andreas Nieder explains. “It has been discovered there that nerve cells work together in different hierarchical levels to enable vision.”

On the basis of 1.2 million pictures categorized into 1,000 categories, the artificial network learned to detect things. Following this training, the network was able to categorize hundreds of fresh pictures with a high success rate.

Numerosity-tuned units emerging in the HCNN.(A) Examples of the stimuli used to assess numerosity encoding. Standard stimuli contain dots of the same average radius. Dots in Area & Density stimuli have a constant total area and density across all numerosities. Dots in Shape & Convex hull stimuli have random shapes and a uniform pentagon convex hull (for numerosities >4). (B) Tuning curves for individual numerosity-selective network units. Colored curves show the average responses for each stimulus set. Black curves show the average responses overall stimulus set. Error bars indicate SE measure. PN preferred numerosity. (C) Same as (B), but for neurons in the monkey prefrontal cortex. Only the average responses overall stimulus sets are shown. (D) Distribution of preferred numerosities of the numerosity-selective network units. (E) Same as (D), but for real neurons recorded in monkey prefrontal cortex. © Khaled Nasr et. al

The network is divided into two sections. The first extracts the features of the item from the pictures and converts them into an abstract representation; the second classifies the object into a category based on likelihood.

“We separated the two network parts and to the first part we presented not photos but simple dot patterns of one to 30 dots,” Nieder says. In the following cycles of the experiment, the patterns were repeated with varying dot patterns and densities. 

The researchers next investigated whether the network’s artificial neurons replied to the same amount of points regardless of other factors. Almost 10% of the artificial neurons were individually specialized in a certain number, despite the fact that the network was never trained to discriminate between numbers. The network has formed a sense of numbers on its own, the artificial neurons’ responses resembling that of real number neurons in animals and humans.

See Also

Number sense does not seem to depend on a specific, specialized area of the brain, but rather on neural networks formed by vision. This now makes it possible to explain why even newborns or untrained, wild animals have a number sense.

Number detectors spontaneously emerge in a deep neural network designed for visual object recognition, Khaled Nasr, Pooja Viswanathan, and Andreas Nieder

Published: May 2019
DOI: 10.1126/sciadv.aav7903

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