McCulloch and Pitts realized that a simplified model of a real neuron could be represented using simple addition and thresholding, as shown in <>. Pitts was self-taught, and by age 12, had received an offer to study at Cambridge University with the great Bertrand Russell. He did not take up this invitation, and indeed throughout his life did not accept any offers of advanced degrees or positions of authority. Most of his famous work was done while he was homeless. Despite his lack of an officially recognized position and increasing social isolation, his work with McCulloch was influential, and was taken up by a psychologist named Frank Rosenblatt.

An MIT professor named Marvin Minsky (who was a grade behind Rosenblatt at the same high school!), along with Seymour Papert, wrote a book called Perceptrons (MIT Press), about Rosenblatt’s invention. They showed that a single layer of these devices was unable to learn some simple but critical mathematical functions (such as XOR). In the same book, they also showed that using multiple layers of the devices would allow these limitations to be addressed. Unfortunately, only the first of these insights was widely recognized. As a result, the global academic community nearly entirely gave up on neural networks for the next two decades.

Perhaps the most pivotal work in neural networks in the last 50 years was the multi-volume Parallel Distributed Processing (PDP) by David Rumelhart, James McClellan, and the PDP Research Group, released in 1986 by MIT Press. Chapter 1 lays out a similar hope to that shown by Rosenblatt:

: People are smarter than today’s computers because the brain employs a basic computational architecture that is more suited to deal with a central aspect of the natural information processing tasks that people are so good at. …We will introduce a computational framework for modeling cognitive processes that seems… closer than other frameworks to the style of computation as it might be done by the brain.

In fact, the approach laid out in PDP is very similar to the approach used in today’s neural networks. The book defined parallel distributed processing as requiring:

1. A set of processing units
2. A state of activation
3. A pattern of connectivity among units
4. A propagation rule for propagating patterns of activities through the network of connectivities
5. A learning rule whereby patterns of connectivity are modified by experience
6. An environment within which the system must operate

We will see in this book that modern neural networks handle each of these requirements.

In the 1980’s most models were built with a second layer of neurons, thus avoiding the problem that had been identified by Minsky and Papert (this was their “pattern of connectivity among units,” to use the framework above). And indeed, neural networks were widely used during the ‘80s and ‘90s for real, practical projects. However, again a misunderstanding of the theoretical issues held back the field. In theory, adding just one extra layer of neurons was enough to allow any mathematical function to be approximated with these neural networks, but in practice such networks were often too big and too slow to be useful.

This is what you will learn how to build in this book. But first, since we are going to be spending a lot of time together, let’s get to know each other a bit…