Feedforward and feedback models of cortical function

Of all the receptive field properties in the visual cortex, orientation selectivity has received the most attention. In the cat, the vast majority of neurons are orientation selective, whereas the neurons of the lateral geniculate nucleus (LGN) show only rudimentary orientation selectivity. Orientation selectivity is also a very striking property and one that is easy to quantify. The first model of orientation selectivity was proposed by Hubel and Wiesel, who first described the receptive fields of cortical neurons (Hubel and Wiesel, 1962). Reasoning from the similarity between the responses of ON centers in ON geniculate neurons and the ON regions of simple cells (and the corresponding similarity between OFF centers and OFF regions), Hubel and Wiesel proposed that simple cell ON regions were constructed from the input of ON center cells whose centers overlapped the ON region. Since the simple cell ON regions are elongated relative to geniculate cell ON centers, they further reasoned that the ON region was constructed from inputs from multiple ON center cells whose receptive fields were distributed in a line down the center of the ON region (Fig. 43.1). A similar arrangement could occur for the OFF region and presynaptic OFF-center geniculate neurons. Some measure of orientation selectivity immediately falls out of the model: when a stimulus such as a bright bar is oriented correctly, it can simultaneously fall onto the centers of all of the presynaptic ON-center geniculate neurons. In the model, the resulting barrage of excitatory synaptic input brings the simple cell to threshold and causes it to fire in response to this optimal stimulus. When the bar is oriented away from the orientation of the subfields, it can only activate a fraction of the presynaptic ON center cells at any one time, so that the simple cell never reaches threshold. Note that a bar passing over the simple cell receptive field evokes the same number of spikes from each presynaptic geniculate neuron, so that at every orientation the simple cell receives the same total amount of synaptic excitation. But the excitation from the many inputs is spread out in time for nonpreferred orientations as the bar passes the long way down the receptive field, whereas the excitation is nearly simultaneous for the preferred orientation when the bar hits the receptive field broadside. It is the nonlinearity of the spike threshold that converts the long-lasting, low-amplitude input evoked by the nonpreferred orientation into a lack of spike response and the short, high-amplitude input evoked by the preferred orientation into a significant spike response.

Figure 43.1..  

To the right is the receptive field of a simple cell. Crosses represent ON subfields; triangles represent OFF regions. To the left is Hubel and Weisel's proposal for how the ON subfield arises from excitatory input from ON-center geniculate relay cells whose receptive fields are aligned in a row. (Adapted from Hubel and Wiesel, 1962.)

This model and its successors have been referred to as feedforward models, since the information flows only in the forward direction, from the LGN to simple cells (and later to complex cells). One could also characterize the cortex in these models as a passive filter: the magnitude of a neuron's response is directly and monotonically related to the strength of the stimulus and to how well the stimulus matches the cell's preferred stimulus.

Hubel and Wiesel's model has an almost irresistible elegance and simplicity that has kept it at the center of the debate for 40 years. But the physiology of simple cells is surprisingly complex, and it has not been easy to account for all the properties of simple cells in detail with quantitative elaborations of Hubel and Wiesel's ideas. The difficulties will be discussed in detail below. But to deal with them, a separate class of models of cortical function has been developed (Ben-Yishai et al., 1995; Douglas et al., 1995; Somers et al., 1995; Sompolinsky and Shapley, 1997). These models are completely different in character from the original. First, they are feedback models as opposed to feedforward models: information reverberates within an excitatory feedback loop formed by the cells in a cortical column, and the responses of the cells are refined on each pass through the loop. Second, these models depend less on the spatially specific organization of the excitatory input from geniculate cells to simple cells and more on the orientation-specific organization of the lateral inhibitory connections within the cortex. Finally, the feedback models do not act merely as passive filters; as will be discussed below, they impose their internal structure, that is, their internal model of the world, on the representation of the retinal image in a way that the feedforward models do not. Thus, the debate over feedforward and feedback models is a debate over the essence of cortical function. In classical fashion, however, the dialectic between the two models and the interplay between experiments and models has increased our understanding of the cortex dramatically.

The structure of the feedback models is illustrated in Figure 43.2. Though details vary from one implementation to another, the models rely on three key features of cortical organization. First, neurons within a column excite one another and, by doing so, amplify any signals coming from the LGN (hence the feedback). Second, the amplification from within any one column is prevented from spreading to adjacent columns by lateral inhibitory projections that originate from within the column. (The inhibitory interneurons are coactivated with the excitatory feedback neurons.) Third, the neurons in each column all prefer the same orientation. The circuits operate by implementing a form of winner-take-all behavior. Imagine, for example, that two nearby columns (representing nearby orientations within a small region of the image) are receiving significant input from the LGN, but one is receiving somewhat stronger input. The column with the stronger input will initially be activated more strongly, and its lateral inhibitory projections will partly suppress the feedback amplification in the column with weaker input. As the feedback develops within each column, the activity and therefore the inhibition originating from the more strongly activated column will grow. At the same time, the more strongly active column will inhibit activity in the more weakly activated column, which will in turn disinhibit the more strongly activated column. Eventually, the column with stronger initial input will become fully active and the column with weaker input will become almost completely silent. The result is a single bubble of activity centered on the location of the strongest input from the LGN, that is, in the column in which the visual stimulus most closely matches the preferred orientation.

Figure 43.2..  

A diagram of a feedback model of orientation selectivity in visual cortex. Excitatory neurons within a column (open circles) excite one another and amplify the input coming from the LGN. Inhibitory neurons are coactivated with the excitatory neurons within their column and inhibit neurons in adjacent columns. As a result, the most stable activity pattern within the cortex is a single bubble of activity (solid curves below), but the location of the bubble will depend on which orientation is most prevalent in the image (dashed curves).

The feedback models have a number of important properties. (1) The orientation selectivity of cortical neurons does not depend on strongly orientation-sensitive input from the LGN, as would be generated by the Hubel and Wiesel model. (2) The overwhelming majority of the excitatory input to simple cells comes from other cortical cells and not from the LGN. (3) Only a weak orientation bias in the geniculate input is necessary. (4) Because of the lateral inhibition and local excitatory feedback, the cortex responds to many stimuli that contain more than one orientation with a single bubble of cortical activity centered on one orientation column (Carandini and Ringach, 1997). This relative lack of dependence of the shape of the cortical response on the exact details of the stimulus or of the organization of the geniculate input gives the feedback models their power to account for some properties of cortical neurons. But it also is the way in which the models impose their internal model of the world on the retinal image.