Greetings. I am currently working in modeling part of the visual system
with artificial neural networks. In the area with which I am working,
there are neurons that linearly encode eye position--that is, the firing
rate of the neuron increases linearly with position in degrees. These
are input neurons. When I examine the emergent behavior of the hidden
neurons in the networks that I train, I find a multiplicative effect of
this linear input on the hidden neuron activity; this phenomenon has been
referred to as a "gain field". The pattern of response of a hidden unit
might be one value at eye position (-10,-10) and another value at eye
position (10,10). The shape of this gain field is planar.
My research suggests that the appearance of this gain field is not due to
either the learning rule used (I have utilized both propagation and a
genetic selection algorithm) or the function of the network, but rather
due to the linearity of the input data. I would like to determine
whether this behavior is a trait of just ANN's or information in general
(and thus of the brain as well).
So, my question is, what other areas of the brain involve linearly
encoded inputs? I know that linear inputs in the brain are fairly rare,
but there must be others. Furthermore, has anyone familiar with these
other areas of the brain observed a similar "gain field" effect?
Any advice or pointers to the appropriate literature would be greatly
Indiana University CS Dept.