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They are referring to Minsky and Papert's 1967 book "Perceptrons". Which said that a single layer NN can't be turing complete because it can't do XOR. The big 1990s breakthrough was having multilayer networks...which actually were also described in the Perceptrons book, though at the time computers weren't powerful enough to implement them.

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I don't understand how it took an entire book to show that a linear classifier can't learn the xor function.

There’s more to the book than my one-sentence summary. Believe Minsky and Papert have something extensive to say on a subject it’s probably not shallow. There’s an ok, if brief discussion about the book’s influence on NN research in its Wikipedia entry.

It’s not a super long book and an excellent, eye opening read even 50 years later.

You should check out the book. It is really fun (especially the illustrations).

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