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some planning capacities. AlphaZero has another interesting feature: It works by playing hundreds of millions of games against itself. As it does so, it prunes mistakes that led to losses, and it repeats and elaborates on strategies that led to wins. Such systems, and others involving techniques called generative adversarial networks, generate data as well as observing data.

When you have the computational power to apply those techniques to very large data sets or millions of email messages, Instagram images, or voice recordings, you can solve problems that seemed very difficult before. That’s the source of much of the excitement in computer science. But it’s worth remembering that those problems—like recognizing that an image is a cat or a spoken word is “Siri”—are trivial for a human toddler. One of the most interesting discoveries of computer science is that problems that are easy for us (like identifying cats) are hard for computers—much harder than playing chess or Go. Computers need millions of examples to categorize objects that we can categorize with just a few. These bottom-up systems can generalize to new examples; they can label a new image as a “cat” fairly accurately, over all. But they do so in ways quite different from how humans generalize. Some images almost identical to a cat image won’t be identified by us as cats at all. Others that look like a random blur will be.

Top-down Bayesian Models
The top-down approach played a big role in early AI, and in the 2000s it, too, experienced a revival, in the form of probabilistic, or Bayesian, generative models.

The early attempts to use this approach faced two kinds of problems. First, most patterns of evidence might in principle be explained by many different hypotheses: It’s possible that my journal email message is genuine, it just doesn’t seem likely. Second, where do the concepts that the generative models use come from in the first place? Plato and Chomsky said you were born with them. But how can we explain how we learn the latest concepts of science? Or how even young children understand about dinosaurs and rocket ships?

Bayesian models combine generative models and hypothesis testing with probability theory, and they address these two problems. A Bayesian model lets you calculate just how likely it is that a particular hypothesis is true, given the data. And by making small but systematic tweaks to the models we already have, and testing them against the data, we can sometimes make new concepts and models from old ones. But these advantages are offset by other problems. The Bayesian techniques can help you choose which of two hypotheses is more likely, but there are almost always an enormous number of possible hypotheses, and no system can efficiently consider them all. How do you decide which hypotheses are worth testing in the first place?

Brenden Lake at NYU and colleagues have used these kinds of top-down methods to solve another problem that’s easy for people but extremely difficult for computers: recognizing unfamiliar handwritten characters. Look at a character on a Japanese scroll. Even if you’ve never seen it before, you can probably tell if it’s similar to or different from a character on another Japanese scroll. You can probably draw it and even design a fake Japanese character based on the one you see—one that will look quite different from a Korean or Russian character. 37

37 Brenden M. Lake, Ruslan Salakhutdinov & Joshua B. Tenenbaum, “Human-level concept learning through probabilistic program induction,” Science, 350:6266, pp. 1332-38 (2015).

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