The ability to figure out any quantity is called number sense. Number sense is key to mathematical cognition. Our nervous system easily performs various activities, such as organizing large quantities into small groups and categorizing numerical quantities as numbers, but the emergence of these number senses is unknown. It is necessary to better understand how numerical representations arise in the human brain.
Stanford Human-Centered Artificial Intelligence (HAI) researchers say that biologically inspired neural architecture can be used to understand the emergence of number sense. Using the neural architecture of the V1, V2, and V3 cortical layers combined with the intraparietal sulcus (IPS), changes in neural representations can be understood. Analogous to the visual cortex of the human brain; V1, V2, V3 and IPS are visual processing streams in the deep neural network. With deep neural networks at both the single unit and distributed population level, the neural coding of the occurrence of quantities with learning can be investigated.
The HAI researchers found that due to the statistical property of images in deep neural networks, visual numerosity arises and quantity-sensitive neurons emerge spontaneously in convolutional neural networks, which were trained to categorize objects in standardized ImageNet data sets. Instead of using convolutional neural networks, they used a numerical DNN (nDNN) model with a more biologically plausible architecture.
Most real life images consist of non-symbolic stimuli. They are assigned to quantity representations through numerosity training and interpreted. The researchers found that tuned neurons spontaneously change with numerosity training and lead to hierarchy. Similar to the procedures used in the brain for the study of images, the researchers implemented representation similarity analysis to assess how distributed representations of numerical quantities arise through information processing.
The HAI researchers experimented with children’s numeracy skills, as they are often described as mapping non-symbolic representations onto abstract symbolic representations. These are critical for the development of numerical problem solving skills. These symbolic number processing and number sense capabilities are based on separate neural systems. Apart from the differences, they found that children often tend to learn small numbers by assigning them to non-symbolic representations and large numbers through counting principles and arithmetic. Studies also show that neural representation similarity between symbolic and non-symbolic quantities predicted arithmetic skills in children, as the parietal, frontal, and hippocampal cortices positively correlated with arithmetic skills.
Most neuropsychology studies are conducted on animals to obtain data in understanding the emergence of cognitive reasoning. But animal brains have their limitations. It is not clear if the way of comprehension is actually the same as that of humans. The solution lies in research similar to HAI, as it has important implications for understanding the development of cognitively meaningful number sense and learning representations of numerosity in children by training deep neural networks to perform activities such as cognitive and mathematical reasoning.
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Arshad is an intern at MarktechPost. He is currently pursuing his Int. Physics Master’s degree from the Indian Institute of Technology, Kharagpur. Understanding things down to the fundamental level leads to new discoveries that lead to the advancement of technology. He is passionate about understanding nature fundamentally with the help of tools like mathematical models, ML models, and AI.
