So far we have focused on feedforward models in which orientation selectivity is generated by the spatial organization of the receptive fields of presynaptic geniculate relay cells. In these models, intracortical connections serve to sharpen and render contrast-invariant the orientation selectivity specified by the feedforward connections, and to amplify responses. In an alternative series of models, the cortical circuitry plays a much more central role in establishing orientation selectivity. These are the feedback models (Hansel and Sompolinsky, 1996, Ben-Yishai et al., 1995, Somers et al., 1995, Adorján et al., 1999, Ben-Yishai et al., 1997), the first set of models developed to address the problem of contrast-invariance of orientation selectivity (Figure 4). (See also related models of other visual cortical phenomena: Douglas et al., 1995, Douglas and Martin, 1991, Suarez et al., 1995).
In the feedback models, the geniculate input to simple cells is assumed to be relatively weak, compared to what is assumed by the feedforward model, and more importantly compared to the input from other cortical cells. The geniculate input is typically also assumed to be very poorly tuned for orientation, based on those experiments that find very small aspect ratios for the subfields of the simple cells (Pei et al., 1994). Sharp orientation tuning arises instead from excitatory interconnections among cortical cells with similar orientation preference and inhibitory interconnections among cells with more wide ranging orientation preferences. In this scheme, a plot of the strength and sign of connections between neurons against the difference in their preferred orientations forms a Mexican hat function (Somers et al., 1995, Sompolinsky and Shapley, 1997): Cells with nearby preferred orientations have net excitatory connections, while cells with more disparate preferred orientations have net inhibitory connections.
A key feature of the feedback models is that the mutually excitatory, or feedback connections among cells with similar preferred orientations dramatically amplify any suprathreshold input that they receive from the LGN. A suprathreshold geniculate input triggers a small amount of activity within the feedback loop, which is enhanced by reverberations within the loop. Key to the model is that with sufficiently strong feedback, the cortex acquires its own intrinsic spatial pattern of response that isindependent of the input . The only stable response is to have a ``bubble'' of cortical cells exciting one another while inhibiting those cortical cells immediately outside the bubble. The geometry of the lateral excitatory and inhibitory connections controls the size of the ``bubble'' or region that is activated by a geniculate input. The larger the spread of excitatory connections and the stronger they are, the larger the lateral spread of activity; conversely, the stronger the lateral inhibitory connections, the smaller the lateral spread of activity. The pattern of activity that develops in the cortex is therefore a uniquely cortical property, depending little on the pattern (orientation tuning width) of the initial, triggering input. A stimulus of higher strength (contrast) will evoke stronger activity without changing the shape of the activity bubble.
This last point means that any suprathreshold stimulus will evoke the appearance of a stereotypical pattern of activity in the cortex. The only aspects of the pattern that can change are its height (the strength of the activity), and its location on the surface of the cortex, which, by virtue of the columnar organization of the cortex, corresponds to its characteristic orientation. Both of these parameters are selected by the stimulus. The cortical circuit, in formal terms, forms a multistable attractor, in that there are many equally-favored possible states of activity, in this case all of which are identical in shape. It is this property -- and this is the point of the model -- that leads to the contrast invariance of the tuning width of individual cells. Tuning width is merely a function of the width of the activity pattern in the orientation domain: The wider the pattern, the farther away a stimulus can be from the preferred orientation of a cell, and still cause some activation in that cell. Since the width of the pattern of activity is a function of cortical connectivity alone and is therefore independent of the contrast (or any other attribute) of the stimulus, the orientation tuning width of the individual cells is independent of contrast and of other stimulus attributes.
It now becomes clear why the feedback models can tolerate very broad orientation tuning of the geniculate input and still maintain very sharp tuning in the cortical cells. Imagine that each simple cell receives geniculate input arranged in subfields, as originally suggested by Hubel and Wiesel (1962), but that these subfields have very small aspect ratios. As a result, the orientation tuning of the thalamic input to each simple cell will be extremely broad. A large number of simple cells will receive significant excitation when an oriented stimulus is presented. But one set of cells, whose preferred orientations are the same as the orientation of the stimulus, will receive slightly more excitation than all the rest. They will generate the strongest mutual excitation and the strongest inhibition of their neighbors. And when the cortical circuitry takes over, the stereotyped cortical activity pattern will form with fixed width, centered on the orientation of those cells that received the strongest excitation. The winner takes all. In this way, the final pattern of cortical activity can be much sharper in orientation than the geniculate input that triggered it.