What can perceptrons do?
They can only solve tasks if the
hand-coded features convert the
original task into a linearly
separable one. How difficult is this?
The N-bit parity task :
Requires N features of the form:
Are at least m bits on?
Each feature must look at all the
components of the input.
The 2-D connectedness task
requires an exponential number
of features!
The 7-bit parity task
1011010 0
0111000 1
1010111 1