Throwing Away Where, to Keep What
Last timeHow Far a Unit Can See
Reducing the resolution is the cheapest way to widen a view and the only way to make a network tolerate small shifts, and it is paid for in location.
Every layer so far has had weights. Pooling has none. Divide a map into blocks of
two by two, and replace each block with a single number: the largest of the four,
or their average. That is the whole operation. The map comes out half the size on
each side, a quarter of the area, and nothing was learned to achieve it.
- take the largest of the four, which keeps the strongest response and discards the rest
- take the average instead, which keeps a blurred version of all four
Because there is nothing to learn, there is nothing to tune and nothing to go
wrong. The gradient is simple too: for the maximum, the whole gradient goes to
whichever of the four inputs was largest and the other three get nothing, which
is a routing decision rather than a computation.
What the reduction buys
Two things, and they are different. The first is cost, and it is the reason
pooling appeared at all. A quarter as many positions means a quarter of the
arithmetic in every layer that follows, and it means the reach of those layers
grows twice as fast in input pixels, by the argument of the previous lesson.
The second is subtler and was the original justification. Consider a pattern
sitting at an even position, and pool over blocks of two. Move the pattern one
pixel to the right and it is still in the same block, so the maximum is the same
and the output is unchanged. The layer has become insensitive to a movement
that the convolution beneath it faithfully tracked.
The lesson stops here
4 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents