Perceptrons

Marvin Minsky and Seymour Papert's Perceptrons is a careful piece of mathematics with a devastating reputation. The book proves what a single layer of Rosenblatt's units can and cannot represent. It cannot compute exclusive-or, the function that is true when exactly one of two inputs is on, because no straight line separates the cases. It cannot tell whether a figure is connected without looking at the whole image at once. These limits are real, and Rosenblatt knew them.

The damage came from the framing. The authors suggested that multi-layer networks, which can represent XOR, would probably be no better, because nobody knew how to train them. That guess was wrong, and the answer, backpropagation, was already in Seppo Linnainmaa's 1970 thesis and Paul Werbos's 1974 one. But funding agencies read the book as a proof that the whole approach was a dead end, and for fifteen years it largely was, in the sense that almost nobody was paid to work on it.

Rosenblatt died in a boating accident in 1971. Minsky and Papert dedicated the 1988 edition to him. The XOR problem became the standard first exercise for every student of neural networks, because a two-layer net solves it in seconds, and the lesson it teaches is about what a proof of limits does and does not show.