Neuronal representations of external events are often distributed across large populations of cells. We study the effect of correlated noise on the accuracy of these neuronal population codes. Our main question is whether the inherent error in the population code can be suppressed by increasing the size of the population N in the presence of correlated noise. We address this issue using a model of a population of neurons that are broadly tuned to an angular variable in two dimensions. The fluctuations in the neuronal activities are modeled as Gaussian noises with pairwise correlations that decay exponentially with the difference between the preferred angles of the correlated cells. We assume that the system is broadly tuned, which means that both the correlation length and the width of the tuning curves of the mean responses span a substantial fraction of the entire system length. The performance of the system is measured by the Fisher information (FI), which bounds its estimation error. By calculating the FI in the limit of a large N, we show that positive correlations decrease the estimation capability of the network, relative to the uncorrelated population. The information capacity saturates to a finite value as the number of cells in the population grows. In contrast, negative correlations substantially increase the information capacity of the neuronal population. These results are supplemented by the effect of correlations on the mutual information of the system. Our analysis provides an estimate of the effective number of statistically independent degrees of freedom, denoted N(eff), that a large correlated system can have. According to our theory N(eff) remains finite in the limit of a large N. Estimating the parameters of the correlations and tuning curves from experimental data in some cortical areas that code for angles, we predict that the number of effective degrees of freedom embedded in localized populations in these areas is less than or of the order of approximately 10(2).

Many models of cortical function assume that local lateral connections are specific with respect to the preferred features of the interacting cells and that they are organized in a Mexican-hat pattern with strong ''center'' excitation flanked by strong ''surround'' inhibition. However, anatomical data on primary visual cortex indicate that the local connections are isotropic and that inhibition has a shorter range than excitation. We address this issue in an analytical study of a neuronal network model of the local cortical circuit in primary visual cortex. In the model, the orientation columns specified by the convergent lateral geniculate nucleus inputs are arranged in a pinwheel architecture, whereas cortical connections are isotropic. We obtain a trade-off between the spatial range of inhibition and its time constant. If inhibition is fast, the network can operate in a Mexican-hat pattern with isotropic connections even with a spatially narrow inhibition. If inhibition is not fast, Mexican-hat operation requires a spatially broad inhibition. The Mexican-hat operation can generate a sharp orientation tuning, which is largely independent of the distance of the cell from the pinwheel center.M odels of cortical function often assume that cortical circuitry acts in a center-surround fashion, namely that nearby cells excite each other, whereas separated pairs of cells have a mutually suppressive influence (1-9). Because of their selective enhancement of local groups of cells, center-surround interactions are attractive dynamic mechanisms for sharpening, or even spontaneously generating, spatial patterns of activity in the neuronal assembly. Further, to make the enhanced cortical patterns congruent with the sensory representation of the system, the cortical interactions must depend on the functional distance between the cells, determined by the features coded by them. This functional circuitry, known as ''Mexican hat'' organization, has been adopted in network models of orientation selectivity (OS) (1-5), working memory in frontal cortex (7), multiplicative neural responses in parietal cortex (8), and in general winner-take-all circuits (9). However, the underlying anatomical and physiological basis of this architecture is not well understood. For instance, experiments in primary visual cortex (V1) suggest that inhibitory connections in cortex tend to be more spatially restricted than the excitatory ones (10, 11). Furthermore, although there is anatomical evidence that longrange connections are feature-specific (11, 12), several experimental studies find that the local connectivity in cortex has roughly a symmetric organization (12, 13), depending primarily on cortical distances. The functional implications of this isotropic organization of connectivity depend on the columnar organization of the coded features. In cat, monkey, and several other primates, orientation columns are organized in pinwheel architectures with singularities at their centers. Given that near the pinwheel centers, cells with orthogonal prefer...

This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the γ-band (25–90 Hz) of the LFP power spectrum in macaque V1. The height and location of the γ-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model’s resonance frequency (ResF) was in the γ-band and varied up or down in frequency depending on cortical feedback. The model’s ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for γ-band peaks in the LFP power spectrum of the primary visual cortex.