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COMPUTING SCIENCE

Delving into Deep Learning

The latest neural networks learn to see and hear, and maybe even dream.

Brian Hayes

A Network for Stripes

Before diving into deep neural networks, let’s play in the shallow end of the pool, with a network that recognizes simple geometric patterns. The patterns come from an image sensor like the one in a digital camera, only simpler: It ignores color and shades of gray, merely reporting whether a pixel is light or dark. Signals from the pixels go to the input layer of the neural network. Each neuron in this layer receives signals from four pixels arranged in a 2×2 square; every such square patch in the sensor array reports to its own neuron. (The patches overlap.)

A 2×2 window of black or white pixels can display 16 different motifs:

The neurons of the input layer are programmed to recognize a specific subset of these patterns. If a neuron sees one of the designated motifs in its square patch, the neuron “fires,” producing a positive output; otherwise it stays silent. Signals from the input layer are passed on to a single output neuron, which fires only if all the input neurons fire. Thus the output neuron reports a unanimous yea-or-nay judgment.

This 2×2, black-or-white, all-or-nothing device is just about the simplest conceivable neural network, and yet it can do some interesting things. Let the input neurons respond positively to these four motifs (and no others):

Such a network recognizes any pattern of vertical stripes, regardless of the stripes’ width. It’s a wallpaper sensor. Other subsets of the 16 motifs yield networks triggered by horizontal stripes or by diagonals. The ability to detect stripes in various orientations is intriguing in that the primary visual cortex of the mammalian brain is full of stripe-sensitive neurons.

This rudimentary neural network can also be programmed to detect patterns other than stripes. You might try to find a set of motifs that picks out rectangles. But there are also tasks the system cannot perform. For example, no network of this kind can distinguish squares from other rectangles.




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