From basic network principles to neural architecture (series)

Orientation-selective cells-cells that are selectively responsive to bars and edges at particular orientations-are a salient feature of the architecture of mammalian visual cortex. In the previous paper of this series, I showed that such cells emerge spontaneously during the development of a simple multilayered network having local but initially random feedforward connections that mature, one layer at a time, according to a simple development rule (of Hebb type). In this paper, I show that, in the presence of lateral connections between developing orientation cells, these cells self-organize into banded patterns of cells of similar orientation. These patterns are similar to the "orientation columns" found In mammalian visual cortex. No orientation preference is specified to the system at any stage, none of the basic developmental rules is specific to visual processing, and the results emerge even In the absence of visual input to the system (as has been observed in macaque monkey). This series of papers explores, with reference to the mammalian visual system, the structures that emerge in a network consisting of several layers of cells with connections of initially random strength, which develop according to a Hebb-type rule that "rewards" correlated activity of connected cells. In papers 1 and 2 (1, 2), I showed the emergence of spatial-opponent and orientation-selective cells in a layered system with parallel feedforward connections only and with random spontaneous uncorrelated activity (no environmental input) in the first layer. In primate visual cortex, orientation-selective cells are organized, prior to any visual experience, into banded regions ("columns"), such that the preferred cell orientation tends to vary monotonically, but with frequent breaks and reversals, as one traverses these regions (3, 4). In this paper, we will explore the self-organization of orientation-selective cells that occurs when lateral connections between cells of the orientation-selective cell-forming layer are added to the purely feedforward network of papers 1 and 2. I will demonstrate a resulting columnar organization that agrees with the qualitative observations, and I will show why this organization is irregular (exhibits breaks and reversals in orientation sequence). The approach, and some of the early results, were described in IBM Research Report RC11642, January 1986 (R.L., unpublished). The present series of three papers is, however, self-contained. The System Through Layer F. To summarize the state of the network through layer F, as derived in papers 1 and 2: There is random spontaneous activity in layer A. The A-to-B connections are all excitatory (1). The cells of layers C, D, E, and F are approximately circularly symmetric spatial-opponent cells (1, 2). The character of layers A-F affects layer-G development only through a function QF(s) which The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. ?1734 solely to indicate this fact. describes the correlation of signaling activities of a pair of F cells as a function of the distance s between them. For the present case, I have found that QF(s) is of "Mexican-hat" form: positive for small s, negative (implying anticorrelation of activities) for intermediate s, and near zero for large s (2). Layer G in Absence of Lateral Connections. For this case, it was shown (2) that there is a parameter regime for which the cells of layer G mature to become "bilobed" cells, each such cell having a bar-shaped excitatory central region that extends to the periphery and is flanked by two inhibitory lobes. These cells have approximate bilateral symmetry. Each cell develops an arbitrary orientation that is independent of its neighbors' orientations. Let us choose the same illustrative parameter values used in paper 2; namely, nEG = 0.5, rG/rF = 1.8, k, = 0.6, k2 = -3 (see paper 2 for definitions). In the limit of a large number NG of feedforward synaptic inputs to each G cell, random variations in synaptic density (due to random synaptic placement) become arbitrarily small. The mature cell morphology can then be obtained by solving for the development of the connection-strength values, on a polar grid having a Gaussian density of sites (see Fig. la and paper 2). The number of synapses lying within the grid box represented by each site is the same for all sites in the large-NG limit. In paper 2, I derived an essentially unique "energy" or "objective function" corresponding to the ensemble-averaged development equation and showed that the mature states obtained by explicitly solving the development equation are the states having globally near-minimal values of this energy function. I called such states "nearly Hebb-optimal" (2) and calculated them using the method of simulated annealing (5). Fig. la shows a symmetric bilobed cell that is nearly Hebb-optimal for the parameter values given above. I shall refer to this cell, when rotated counterclockwise through angle 6, as the "standard cell" of orientation 6 (for these parameter values). Introduction of Lateral Connections. I now treat the development of the same system, except that each G cell now receives lateral inputs from a surrounding neighborhood of other G cells, as well as the feedforward inputs from cells of the predecessor layer F. Each of the lateral and feedforward connections may in general be excitatory or inhibitory and have initially random strength. The distribution of these connections exhibits no directional preference. The cellresponse and development rules are the same as in papers 1 and 2 (1, 2). Because there is a new class of connections, however, the mathematical form of these rules is slightly different. (See Appendix for equations.) Assume that each set of input activities from layer F [called a "presentation" (1)] persists long enough so that a G cell is still receiving a presentation from layer F at the same time that it is receiving from other G cells their responses to the *This is paper no. 3 in a series. Paper no. 2 is ref. 2.