Communications of the ACM

I M A G E F R O M S H U T T E R S T O C K . C O M

Q: In 1969, Marvin Minsky and Seymour Papert published a book showing that Perceptrons could not recognize important patterns. 5 What effect did that have on the field?

The entire field faltered following publication of the Minsky-Papert book. They proved that single-layered perceptrons would only work as classifiers when the data was “linearly separable”—meaning that the multidimensional data space could be separated into regions bounded by hyperplanes. Data not clustered in this way could not be recognized. This finding caused interest in perceptrons to die off, until researchers discovered that adding layers and feedback to the neural network overcame the problem. 1–3 The multilayered perceptron (MLP) can reliably classify patterns of data in nonlinear spaces. More layers mean more accuracy and, of course, more computation. The modern term “deep learning” acknowledges the many-layers depth of a neural network.

An open problem for research today is finding the smallest number of neurons and layers to implement a given function.

for example, take the bitmap from a camera shown the digit “ 9” and output the ASCII code for “ 9”. A recommender network maps a pattern into a string representing an action the human might decide to take next. Netflix has developed a neural network that takes your entire film viewing history along with all the ratings you and others gave those items and returns a recommendation of a new film that you would probably rate highly.

Q: How do you program a neural
network?

You don’t. You teach it to learn how to do the function you want. Suppose you want to teach a network a function F that maps X patterns into Y patterns. You gather a large number of samples (X, Y), called the training set.

For each sample you use a training
algorithm to adjust the connection
weights inside the network so that the
network outputs Y when given X at its
input. There are so many neurons,
connections, and possible weights
that the training algorithm can suc-
cessfully embed a large number of
pairs (X,Y) into the network. It takes
an enormous amount of computa-
tion to train a large network on a large
training set. We now have the hard-
ware power and training algorithms
to do this. The trained network will
implement all the trained (X,Y) com-
binations very reliably.

Once the network is trained, it can compute its outputs very rapidly. It has a fixed function until its training is updated.

We want to use our networks to compute not only trained maps, but untrained ones as well. That means to compute Y=F(X) for a new pattern X not in the training set. An important question is how much trust can be put in the responses to untrained input patterns.

If we keep track of the new ( untrained) inputs and their correct outputs, we can run the training algorithm again with the additional training pairs. The process of training is called learning, and of retraining reinforcement learning.