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The network consists of three input layers and an intermediate layer. The three input layers – an eye-centered layer, an eye position layer and a head-centered layer – are also output layers; the final estimates of the network are read from these layers after relaxation. The three input layers consist of three topographic layers of N units indexed by their position, i(or j,k), where i(or j,k) = 1…N. Similarly, the intermediate layer is a topographic 2D map of N´N units indexed by their position l, m, where l = 1…N and m=1…N.

Connection weights

      The input layers are symmetrically interconnected with the intermediate layer (hidden layer), and the corresponding matrices of connection weights are denoted by W^r, W^e, W^a for, respectively, the eye-centered, eye position and head-centered layers. The connection strengths between unit i (j,k) in each  input layer and unit (l,m) in the intermediate layer are given by

      The variable s_w represents lateral spread: unit i is strongly connected if . Note that with these connection matrices, unit (l,m) in the intermediate layer is most strongly interconnected with unit i=l in the eye-centered layer, j=m in the eye position layer and k=l+m in the head-centered layer. Unit (l,m) is connected more weakly to neighboring units in each layers, with the spatial extent of these connections is controlled by s_w .

Network initialization

      R_ri(t), R_ej(t), and R_ak(t) are denoted as the activity of unit i (j,k) in the eye-centered, eye-position and head-centered layer at time t.

      For eye-centered position, the probability distribution for the initial activity, denoted R_ri(0), is given by

      The expressions for P(R_ej(0)|x_e) and P(R_ak(0)|x_a) are identical to P(R_ri(0)|x_r), except that r is replaced by e or a. The expressions for f (x_a) and f (x_e) are identical to fi(x_r) except that r is replaced by a or e.

      The activity in the intermediate layer, A_lm(0), is initialized to 0: A_lm(0) = 0 for all l,m.

Recurrent network evolution

      The evolution of the activities in the recurrent network is described by a set of coupled nonlinear equations. Denoting A_lm(t) as the activity of unit (l,m) in the intermediate layer at time t, the evolution equations are written