Fig. 1. (a) The architecture used by Grossberg and Somers (1991). Fast excitatory cells are connected to slow inhibitory cells. This fast versus slow time constant can generate oscillations in suitable situations. (b) If the cells are not connected, then their initial out-of-phase activities remain out-of-phase through time with an approximately constrain oscillation jitter. (c) The out-of-phase activities rapidly synchronize, within a single oscillation cycle.

Fig. 2. Key circuit features of the LAMINART model: (a) LGN excites both layers 6 and 4. Layer 6 indirectly inhibits layer 4 through the inhibitory interneurons. Therefore, the excitation from layer 6 to layer 4 is modulatory (direct excitation approximately balanced by indirect inhibition). (b) Layer 4 directly excites layer 6. This combined with the 6→4 inhibition can generate oscillations in a suitable parameter range. Layer 4 also excites layer 2/3 cells, which have long horizontal axonal connections that also input to short-range inhibitory interneurons. The convergent excitation and inhibition results in the bipole property at target layer 2/3 cells. The cells in layer 2/3 send feedback to layer 6, which in turn subliminally excites layer 4 in the on-center and can strongly inhibit layer 4 cells through the off-surround. (c) Attention can also activate layer 6, and thereby have a modulatory effect on layer 4 that can help to select which grouping will win.

Fig. 3. Activity of the different layers of the LAMINART circuit with no horizontal bipole connections within layer 2/3. Each panel is composed of superimposed oscillatory activity of all 40 cells. Layer 4 excitatory, inhibitory, and layer 6 cell activities are shown. The initial activity of the all layer units are randomly set (uniform random distribution between 0.2 and 0.8) to bring them into different phase relations. This random initiation can be seen easily by looking at the ordinate of layer 6 and 4 activity panels. Fast resynchronization funnels all of the activities together within a small fraction of one oscillation period and afterward they oscillate together. The jitter curve shows that the jitter after this funneling-in of curves is on the order of 1–2 ms. There is also a slight increase of oscillation standard deviation in time (from 1 to 2 ms).

Fig. 4. This simulation shows that inputs within the on-center of the network from layer 6 to layer 4 can only provide excitatory modulation of layer 4 cells, but cannot fire these cells strongly. Strong inhibition within the off-surround can also occur.

Fig. 5. Here the bipole grouping cells are included, and are connected to layer 6, as shown in Fig. 2b. The inputs from the LGN are zero, and the cells again start out with randomly set initial values. Fast synchronization again occurs, this time via the recurrent layer 2/3 long-range connections.

Fig. 6. Here, the bipole grouping cells are again included in (a) and (b), and constant inputs from the LGN are on. Again the network rapidly synchronizes, even though there are no LGN inputs to cells 18–23 of layers 6 and 4 in (b). Comparing the oscillation pattern with that in Fig. 3 shows that, first, the absolute value of the oscillation jitter is less and, second, that the slight increase of the oscillation jitter is less too. (c) When there is no bottom-up LGN input to cells 18–23, and no bipole grouping cells, then the initial randomized activities of these cells fade away. The lateral cells (1–17 and 24–40), however, follow the same pattern of fast synchronized oscillation as in (a) and (b). Thus, the bipole grouping cells are needed to complete groupings across occluded image regions to form illusory contours.

Fig. 7. The activities of layer 2/3 cells retain their analog sensitivity to LGN input amplitude for both real and illusory contours. In (a), oscillations for different LGN inputs are shown. In (b), the solid curve shows the oscillation amplitude versus LGN input in the real contour case. The dotted curve shows the same in the illusory contour case.