The Network Equations

The output of each unit at any time is represented by a non-negative real number. The connections between units have weights associated with them which modify the inputs from the previous layer.

The equations describing the operation of the units are complex, and the description which follows is condensed and simplified.

Each unit in each of the U_S layers takes the outputs from the excitatory units in the previous layer to which it is connected, multiplies them by the appropriate weights, and sums the products. We will denote this sum by e. It also has an input from an inhibitory unit, which is multiplied by its own weight. This product is denoted by h. The effects of the excitation and inhibition are combined by computing x=((1+e)/(1+h))-1. The output of the unit is 0 if x<0 and x otherwise. The output will be equal to e if h=0 and 0 if h>e.

Each unit in each of the U_C layers takes the outputs from the excitatory units in the previous layer to which it is connected, multiplies them by the appropriate weights, and sums the products. We will denote this sum by x. The output of the unit is $x/(\alpha_l + x)$ is $x \geq 0$ and 0 otherwise. $\alpha_l$ is a parameter associated with the lth layer which determines the degree of saturation of the output of all the units in that layer.

The inter-layer inhibitory units each send an output to a single unit in the following U_S unit and receive inputs from the same units in the preceeding U_C layer as the cell which receives its output. The output of each inhibitory unit is the weighted root mean square of its inputs.