Neural networks help us understand how the brain recognizes numbers

Over the past half-century, neuroscientists have made extraordinary strides in understanding the human brain by inserting wires into the brains of animals like cats, rats and monkeys and characterizing how their neurons fire. . Although such experiments cannot be performed so easily in humans, examining neurons in animals has nevertheless helped scientists understand the underpinnings of phenomena such as optical illusionsmemory and drug addiction.

But animal brains have their limits. Some sophisticated human behaviors, like mathematical reasoning, are beyond the reach of animals – and while animals can be trained to use numbers, it’s unclear whether they learn them the same way humans do, being given that they do not have the same capacity for language. So when Vinod Menonprofessor of psychiatry and behavioral sciences at Stanford, and Percy Mistry, a researcher in Menon’s lab, wanted to try to understand how children learn numbers, they didn’t turn to biology. Instead, they decided to try to approach the process of learning human numbers using a deep neural network.

Deep neural networks were originally modeled on the brain, and they have been widely used to probe the inner workings of the visual system. So, by training a brain-like network to recognize numbers, Menon and Mistry were able to gather evidence about number learning in humans that would have been impossible to obtain otherwise. Their results, Posted in Nature Communicationsuggest that an innate sense of number may not be as important as other researchers have proposed.

Because there are limits to the neurophysiological experiments that can be conducted ethically in humans, this type of research could prove critical to understanding the complex capabilities of the human brain, Menon says. “It is difficult to make breakthroughs in understanding the neural mechanisms of complex human cognitive processes without building models like this.”

Testing “spontaneous number neurons”

In a previous study, the researchers trained a deep neural network to recognize images and found, to their surprise, that some neurons in the network were number-sensitive – they responded particularly strongly to images of a particular number of objects, although have never been trained to identify the number of objects in an image. These results seemed to lend credence to the idea that numerosity is, in some sense, innate: that children can have number sense without being explicitly taught about it, and that future learning may depend on this sense. .

But no one had actually tested whether these “spontaneous number neurons” helped with number learning. To do this, one would first need to take a neural network trained to recognize objects, identify its number-sensitive neurons, retrain that network to report the number of objects in an image, and then see if those neurons help the network to learn this task. – this is precisely what Mistry, Menon and their colleagues have done.

They discovered that the spontaneous number neurons did not help learning at all. Most of the neurons that started to be sensitive to numbers either lost that number sensitivity during training or became sensitive to a different number. And the neurons that remained sensitive to the same numbers didn’t seem to be doing anything particularly critical: removing them from the network during the training process had no effect on the network’s final performance.

Bridging AI and Human Intelligence

Although this study was done entirely on computers, there’s reason to think it might have something to say about how the human brain works. The team intentionally started with an object recognition network that had has already been demonstrated look like parts of the monkey’s visual system – and after training, number-sensitive neurons in the neural network behaved like number-sensitive neurons in the monkey brain.

Without invasive human experiments, it is impossible to make the same comparisons between the network and the human brain. But the team found other ways to tackle the problem. Looking at the pool of number-aware neurons as a whole, they found that the network used two different strategies to differentiate between different numbers. One strategy used a linear number line, where the end points – 1 and 9 – were easy to distinguish, but the numbers in the middle – 4, 5 and 6 – were harder to distinguish. The second strategy, however, was based around the middle of the number line – so 4, 5 and 6 were seen as very different from each other. This same model is seen in humans as they learn: As they develop their number sense, children begin to be sensitive to low and high numbers, but over time they also begin to to use the midpoint of the number line as a reference point. “It was exciting to watch the emergence of number line representations similar to those seen in children, even though we didn’t explicitly train the neural network to do so,” Menon said.

However, it would be premature to conclude that human children learn in exactly the same way as this neural network. The model is ultimately “a very, very simple approximation of what the brain does, even with all of its complexity,” says Mistry. This simplicity makes it easier to study and train the network, but it also limits what it can tell us about human biology.

Nonetheless, the model does a pretty impressive job of approximating the number learning process in children that Mistry and Menon have high hopes for its future. Menon spent years studying dyscalculia, a disability that affects number and math skills. The team’s goal now is to use the network to study potential neural mechanisms of dyscalculia, implementing these mechanisms in the network and seeing how they interfere with number learning.

“We can make assumptions about different mechanisms that might be possible causes and assess which ones might be relevant. We can even consider possible interventions,” explains Mistry. “We can use this model as a sandbox.”

The study, “Learning-Induced Reorganization of Number Neurons and Emergence of Numerical Representations in a Biologically Inspired Neural Network”, published in Nature Communications in June. Other Stanford contributors include postdoctoral fellows Anthony Strock and Ruizhe Liu, and co-term student Griffin Young.

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