Jens Burmeister wrote:
How can you do without a bias? I.e. with a (tilted) plane passing through
the origin?
I understood your example well. But when I have a hidden layer with a number
of neurons (let's say 10), I thought, that it is possible to solve that
separation problem, because with the hidden layer, I have a number of
degrees of freedom with which I can separate.
Perhaps, but I can think about only one neuron at a time and I would
like to give all neurons' hyperplanes as much freedom as possible.
Moreover, I would really hate to use a hidden layer when one was not
necessary --- all for the want of a bias input.
If you look at section 4.2 of:
http://www.jgcampbell.com/ip/pr.pdf
you will see an arm-wavy construction that shows that a p-h-1 network
can implement an arbitrarily complex decision region (not my idea,
originally in a Lippman paper, I think).
