A previous study has suggested that complex cells perform a MAX-like operation on their inputs: when two bar stimuli are presented within the receptive field, regardless of their relative separation, the cell's response is similar in amplitude to the larger of the responses elicited by the individual stimuli. This description of complex cells seems at odds with the classical energy model in which complex cells receive input from multiple simple cells with overlapping receptive fields. The energy model predicts, and experiments have confirmed, that bar stimuli should facilitate or suppress one another depending on their relative separation. We have recorded intracellularly from a population of complex cells and studied their responses to paired bar stimuli in detail. A wide range of behavior was observed, from the more classical separation-dependent interactions to purely MAX-like responses. We also found that the more MAX-like a cell was, the broader its spatial-frequency tuning as measured with drifting gratings. These observations are consistent with energy models in which classical complex cells receive input from simple cells with similar preferred spatial frequencies, and MAX-like complex cells receive input from simple cells with disparate preferred spatial frequencies. Generalized energy models, then, can account for diverse modes of computation in cortical complex cells.

Despite popular belief that the primary function of the thalamus is to gate sensory inputs by state, few studies have attempted to directly characterize the efficacy of such gating in the awake, behaving animal. I measured efficacy of retinogeniculate transmission in the awake cat by taking advantage of the fact that many neurons in the lateral geniculate nucleus (LGN) are dominated by a single retinal input, and that this input produces a distinct event known as the S-potential. Retinal input failed to produce an LGN action potential half of the time. However, success or failure was powerfully tied to the recency of the S-potential. Short intervals tend to be successful, and long intervals unsuccessful. For 4 of 12 neurons, the probability that a given S-potential could cause a spike exceeded 90% if that S-potential was preceded by an S-potential within the previous 10 msec (100 Hz). Whereas this temporal influence on efficacy has been demonstrated extensively in anesthetized animals, wakefulness is different in several ways. In wakefulness, overall efficacy is better, the duration of facilitating effects are briefer, efficacy of long intervals is superior, and the temporal dependence can be briefly disrupted by altering background illumination. Finally, S-potential amplitude, duration, and even slope are dynamic and systematic within wakefulness; providing further support that the S-potential is the extracellular signature of the retinal EPSP.

Probability distributions of macaque complex cell responses to a large set of images were determined. Measures of selectivity were based on the overall shape of the response probability distribution, as quantified by either kurtosis or entropy. We call this non-parametric selectivity, in contrast to parametric selectivity, which measures tuning curve bandwidths. To examine how receptive field properties affected non-parametric selectivity, two models of complex cells were created. One was a standard Gabor energy model, and the other a slight variant constructed from a Gabor function and its Hilbert transform. Functionally, these models differed primarily in the size of their DC responses. The Hilbert model produced higher selectivities than the Gabor model, with the two models bracketing the data from above and below. Thus we see that tiny changes in the receptive field profiles can lead to major changes in selectivity. While selectivity looks at the response distribution of a single neuron across a set of stimuli, sparseness looks at the response distribution of a population of neurons to a single stimulus. In the model, we found that on average the sparseness of a population was equal to the selectivity of cells comprising that population, a property we call ergodicity. We raise the possibility that high sparseness is the result of distortions in the shape of response distributions caused by non-linear, information-losing transforms, unrelated to information theoretic issues of efficient coding.