Artificial Numerosity: When Machines ‘Get’ Numbers

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Picture a machine observing a series of dot-covered images. At some point, the machine demonstrates that it gets the difference between two dots and ten dots—regardless of how those dots appear on the screen. This ability to abstract quantities and distinguish between the resulting numbers may not seem like a big deal because it’s so easy for humans. But new research shows that machines now have this ability to conceptualize numbers—something we might think of as “artificial numerosity.”

Artificial Numerosity

What Is Numerosity?

Numerosity is the ability to recognize specific quantities. It’s the ability to tune our perception of objects so that we sense how many of them there are. Numerosity is seeing seven red apples on the table and having the number “seven” pop into your head.

Animals show signs of numerosity, but it’s particularly strong in humans. Individuals with savant syndrome are even able to to look at a pile of pick-up sticks and instantly know how many there are. For most people, though, we’re much better at distinguishing between smaller numbers. That might be because smaller numbers are more common or because the difference between a “2” and a “3” is statistically much greater than between “82” and “83.”

Like a Brain

This research matters partially because it creates a link between the biological numerosity in humans and numerosity in machines. The researchers found that their artificial neurons system ‘tuned’ themselves to numbers much the way biological neurons do. The artificial neural networks, for example, were less able to distinguish large numbers than small numbers—just like us. In this sense, this research could help us better understand the way humans (and other animals) sense numbers.

Let’s Get (Meta) Physical

Artificial Numerosity
What did I tell you? Even a monkey gets abstract.

We’ve confirmed numerosity in humans, fish, birds, rats, dogs, monkeys, and chimpanzees. What we’re now seeing is that it’s not just living creatures that can sense the “two-ness” implicit in a couple of rocks. Machines can sense it too.

Seeing this capacity in the artificial neural networks, I can’t help thinking about Plato. He argued that abstract ideals undergird the diversity of forms on the physical plane of reality. This ability to abstract is a general property of neural networks—what enables them to categorize and predict. We know, for example, that there are neurons within our brains that map to specific concepts (and that we can detect their signals to effectively read what someone is thinking about).

Numerosity is the brain using its ability to abstract and categorize in order to recognize the specific numbers behind quantity. Artificial numerosity is simply extending that ability to artificial neural networks.

Artificial Numerosity

It’s too early to know exactly whether artificial numerosity will lead to valuable applications of machine learning. There are industrial processes—such as pill counting—that would benefit from faster, more accurate methods of recognizing quantity. There are probably important scientific and medical applications too, like counting cells and other biological phenomena.

To be useful, artificial numerosity needs to be able to handle large numbers, which may be an inherent limitation of neural networks—natural or artificial. But what if we could figure out a way to mimic the human savant’s ability to instantly recognize that that’s 167 pick-up sticks there on the table? If artificial numerosity could match that feat, it would mark another important augmentation to our ability to sense the world. For it would represent a new type of sensor—a sensor for numbers.

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