It has been shown [Minsky and Papert, 1969] that, even though feed-forward
networks might contain a non-linearity, they must have at least two
layers of non-linear units if they are to be able to compute
non-linearly-separable functions, which can be as simple as the
function XOR (exclusive OR). Thus, for any reasonably powerful form
of quantum learning, it might be better to think of a quantum
beam/barrier/screen apparatus as implementing one unit in a layered
network of units. Any units in a layer beyond the input layer would
not have their input slits positions determined by the input sample
*x* directly, but rather by the outputs of the units in the previous
layer. In such a case, it would be typical to take the output of a
unit to be uni-dimensional, usually soft-thresholded.

This would differ substantially from standard feed-forward networks, in that each weight would modulate all inputs to a unit. In standard networks, each weight only modulates the input from one other unit. This has the result of making the derivative computation during learning a relatively local computation. Whether or not this difference can be avoided, or whether it would be disadvantageous if it could not, has yet to be worked out.

Wed Nov 20 01:10:59 GMT 1996