Cortical neurons selective for numerosity may underlie an innate number sense in both animals and humans. We hypothesize that the number- selective responses of cortical neurons may in part be extracted from coherent, object-specific oscillations . Here, indirect evidence for this hypothesis is obtained by analyzing the numerosity information encoded by coherent oscillations in artificially generated spikes trains. Several experiments report that gamma-band oscillations evoked by the same object remain coherent, whereas oscillations evoked by separate objects are uncorrelated. Because the oscillations arising from separate objects would add in random phase to the total power summed across all stimulated neurons, we postulated that the total gamma activity, normalized by the number of spikes, should fall roughly as the square root of the number of objects in the scene, thereby implicitly encoding numerosity. To test the hypothesis, we examined the normalized gamma activity in multiunit spike trains, 50 to 1000 msec in duration, produced by a model feedback circuit previously shown to generate realistic coherent oscillations. In response to images containing different numbers of objects, regardless of their shape, size, or shading, the normalized gamma activity followed a square-root-of- n rule as long as the separation between objects was sufficiently large and their relative size and contrast differences were not too great. Arrays of winner-take-all numerosity detectors, each responding to normalized gamma activity within a particular band, exhibited tuning curves consistent with behavioral data. We conclude that coherent oscillations in principle could contribute to the number-selective responses of cortical neurons, although many critical issues await experimental resolution.

Synchronous firing limits the amount of information that can be extracted by averaging the firing rates of similarly tuned neurons. Here, we show that the loss of such rate-coded information due to synchronous oscillations between retinal ganglion cells can be overcome by exploiting the information encoded by the correlations themselves. Two very different models, one based on axon-mediated inhibitory feedback and the other on oscillatory common input, were used to generate artificial spike trains whose synchronous oscillations were similar to those measured experimentally. Pooled spike trains were summed into a threshold detector whose output was classified using Bayesian discrimination. For a threshold detector with short summation times, realistic oscillatory input yielded superior discrimination of stimulus intensity compared to rate-matched Poisson controls. Even for summation times too long to resolve synchronous inputs, gamma band oscillations still contributed to improved discrimination by reducing the total spike count variability, or Fano factor. In separate experiments in which neurons were synchronized in a stimulus-dependent manner without attendant oscillations, the Fano factor increased markedly with stimulus intensity, implying that stimulus-dependent oscillations can offset the increased variability due to synchrony alone.