4
on
the current. The switch points representing your ten cities would
flicker on and off for a few fractions of a second as the network sought
an equilibrium. Then, it would disgorge the answer to your problem.1
In essence, the neural network works by using a model of the
terrain the salesman is planning to travel. What's the advantage of this
electronic model-making? California Institute of Technology's John
Hopfield showed that neural networks can solve the traveling
salesman problem ten thousand times faster than a normal computer.
Neural nets, like the human brain, can infer an invisible world
from scraps of visible information. Give the word "bat" to a neural
network built by neuroscientist James Anderson at Brown University,
and it'll respond with a list of the qualities of animals. Give the
machine the word diamond, and it will spit out geometric shapes.
Give the two words together, and the machine will come up with
baseball.2 In its limited way, the neural net has inferred a broad picture
of a complex and, at the moment, invisible mini-world--the baseball
stadium--from two tiny fragments of information.
Humans do the same. At this moment, thanks to the words bat
and diamond, you can picture a runner stealing bases. Look around
you. How many runners in baseball uniform do you see before your
eyes? Like the neural net, humans infer a picture of the world from
two little words.
The neural network technique does have its drawbacks. In the
case of the traveling salesman problem, for example, Cal Tech's
Hopfield points out that there is a bit of fuzziness about the net's
answers. They are only the one very best solution 50% of the time. But
they are close enough for all practical purposes. Ninety percent of the
time, the neural nets pick one of the two best answers. That's one of
the two best out of 181,440. Normal computers, on the other hand,
solve the traveling salesman problem with 100% accuracy. But they do
it too slowly to be of any earthly value.
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