Self-Organization

The model consisted of an array of neurons, and a retina of receptors. The anatomical receptive field of each neuron covered receptors. The initial lateral excitation radius was 19 and was gradually decreased to 1. The lateral inhibitory radius of each neuron was 47, and weak inhibitory connections were pruned away at intervals of 10,000 iterations. The network had approximately 400 million connections in total, took 10 hours to simulate on 64 processors of the Cray T3D at the Pittsburgh Supercomputing Center.

The self-organization of afferents results in a variety of oriented RFs similar to those found in the visual cortex (figure 2). Some are highly selective to inputs of a particular orientation, others unselective. The global organization of such receptive fields can be visualized by labeling each neuron by the preferred angle and degree of selectivity to inputs at that angle. The resulting orientation map (figure 3; movie 1) is remarkably similar in structure to those observed in the primary visual cortex by recent imaging techniques [6,7] and contains structures such as pinwheels, fractures and linear zones. The results strongly suggest that Hebbian self-organization of afferent weights, based on recurrent lateral interactions, underlie the development of orientation maps in the cortex.

(a) RF shaprly tuned to	(b) RF shaprly tuned to	(c) Unselective RF

(a) Initial unordered map and connections	(b) Final oriented map and connections

(click on the image to view a larger version) Self-organization of the orientation map and lateral connections. Each neuron in this central region of the map is colored by the orientation preference of its afferent weights, as illustrated by the color bar. Colors varying between red magenta blue green orange represent continuously-changing eye preference from 0 to 180 degrees. The brightness of the color indicates how selective the receptive field is to its preferred orientation. (a) Initially, the afferent weights of each neuron are random, and the receptive fields are randomly oriented and are mostly unselective (indicated by the dim colors). (b) After several thousand input presentations, the receptive fields organize into continuous and highly selective (brightly colored) bands of orientation columns, and only lateral connections between similar orientation columns remain. The orientation sensitivity patterns have all the significant features of primary visuo-cortical maps, as observed by techniques such as voltage-sensitive dye imaging [6,7]: (1) pinwheel centers, around which orientation preference changes through , seen as a color wheel from red to blue to orange, (2) linear zones, where orientation preference changes almost linearly, seen as a rainbow-like patch with all colors, and (3) fractures, where there is a discontinuous change of orientation preference (e.g. locations where colors change rapidly from magenta to green or magenta to yellow). In addition to the orientation preference and selectivity, the figures also display the lateral connections of one particular neuron on the map. The small white dots indicate neurons from which the neuron marked with the big white dot receives lateral input. (a) Initially, the lateral connections are uniform and widespread. (b) After pruning, only connections between similar orientation columns remain. The marked neuron is colored magenta, and its connections come mostly from magenta and blue neurons. In the near vicinity, the lateral connections follow the twists and turns of the magenta-colored iso-orientation column. The magenta color represents an orientation of 60 degrees, and the lateral connections are elongated along this direction.

  
Movie 1 (small (348K) and large (958K)): Self-Organization of the Orientation Map. Starting from initially random orientation preferences and low selectivity (indicated by the dark colors), the map gradually develops more selectivity, and the preferences become globally ordered over the course of 35,000 presentations. The frames were taken in approximately exponentially increasing intervals, with 10 presentations between frames in the beginning, and increasing to 2500 presentations between frames in the end of the simulation.

The lateral connection weights self-organize at the same time as the orientation map forms. Initially, the connections are spread over long distances and cover a substantial part of the network (figure 3 a). As lateral weights self-organize, the connections between uncorrelated regions grow weaker, and after pruning, only the strongest connections remain (figure 3 b). The surviving connections of highly-tuned cells, such as the one illustrated in figure 3 b, link areas of similar orientation preference, and avoid neurons with the orthogonal orientation preference. Furthermore, the connection patterns are elongated along the direction that corresponds to the neuron's preferred stimulus orientation. This organization reflects the activity correlations caused by the elongated Gaussian input pattern: such a stimulus activates primarily those neurons that are tuned to the same orientation as the stimulus, and located along its length. At locations such as fractures, where a cell is sandwiched between two orientation columns of very different orientation preference, the lateral connections are elongated along the two directions preferred by the two adjacent columns (figure 4 a). Finally, the lateral connections of unselective cells, such as those at pinwheel centers, connect to all orientations around the cell (figure 4 b). Thus the pattern of lateral connections of each neuron closely follows the global organization of receptive fields, and represents the long-term activity correlations over large areas of the network.

(a) Connections at fractures	(b) Connections at pinwheels

Some of these results have already been confirmed in very recent neurobiological experiments [13]. In the iso-orientation columns of the tree-shrew cortex, horizontal connections were found to be distributed anisotropically, extending farther and giving rise to more terminals along the preferred orientation of the neuron. Most of these terminals also connected to cells with the same orientation preference. The connection patterns at pinwheel centers and fractures have not been studied experimentally so far; our model predicts that they will have unselective and biaxial distributions, respectively.

So far this article has focused on how the model can give a computational explanation for a number of observed structures in the visual cortex, and how it can predict others. In related work, we have also shown how patterns of ocular dominance and lateral connections can self-organize cooperatively, and how their periodicity varies with between-eye correlations [40,41,42]. The model can also be used to study dynamic phenomena in the adult cortex. One such study analyzed how the network reorganizes in response to cortical lesions and intracortical microstimulation [39]. The phenomenon of dynamic receptive fields, which has captured much scientific attention recently, can also be given a computational account, as will be described below.