How the brain encodes information in population activity, and how it combines and manipulates that activity as it carries out computations, are questions that lie at the heart of systems neuroscience. During the past decade, with the advent of multi-electrode recording and improved theoretical models, these questions have begun to yield answers. However, a complete understanding of neuronal variability, and, in particular, how it affects population codes, is missing. This is because variability in the brain is typically correlated, and although the exact effects of these correlations are not known, it is known that they can be large. Here, we review studies that address the interaction between neuronal noise and population codes, and discuss their implications for population coding in general.

/pdf/neural-correlations-population-coding-and-computation-2gxvggmch9.pdf

Neural correlations, population coding and computation

The computational brain: Patricia S. Churchland and Terrence J. Sejnowski (MIT Press, Cambridge, MA, 1992); xi, 544 pages, $39.95

Correlated spiking is often observed in cortical circuits, but its functional role is controversial. It is believed that correlations are a consequence of shared inputs between nearby neurons and could severely constrain information decoding. Here we show theoretically that recurrent neural networks can generate an asynchronous state characterized by arbitrarily low mean spiking correlations despite substantial amounts of shared input. In this state, spontaneous fluctuations in the activity of excitatory and inhibitory populations accurately track each other, generating negative correlations in synaptic currents which cancel the effect of shared input. Near-zero mean correlations were seen experimentally in recordings from rodent neocortex in vivo. Our results suggest a reexamination of the sources underlying observed correlations and their functional consequences for information processing.

/pdf/the-asynchronous-state-in-cortical-circuits-7v5d570jer.pdf

The Asynchronous State in Cortical Circuits

心臓病診療プラクティス 16. 心不全を癒す

This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundacion BBVA.

/pdf/dynamical-principles-in-neuroscience-3b8nfk3ipm.pdf

Dynamical principles in neuroscience

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).

/pdf/population-coding-in-neuronal-systems-with-correlated-noise-54ejw4og08.pdf

Population coding in neuronal systems with correlated noise.

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.

/pdf/mexican-hats-and-pinwheels-in-visual-cortex-1un3pyx8hh.pdf

Mexican hats and pinwheels in visual cortex

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 ?-band (25---90 Hz) of the LFP power spectrum in macaque V1. The height and location of the ?-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 ?-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 ?-band peaks in the LFP power spectrum of the primary visual cortex.

/pdf/lfp-spectral-peaks-in-v1-cortex-network-resonance-and-gc1beqjetk.pdf

LFP spectral peaks in V1 cortex: network resonance and cortico-cortical feedback

Neurons in macaque primary visual cortex (V1) show a diversity of orientation tuning properties, exhibiting a broad distribution of tuning width, baseline activity, peak response, and circular variance (CV). Here, we studied how the different tuning features affect the performance of these cells in discriminating between stimuli with different orientations. Previous studies of the orientation discrimination power of neurons in V1 focused on resolving two nearby orientations close to the psychophysical threshold of orientation discrimination. Here, we developed a theoretical framework, the information tuning curve, that measures the discrimination power of cells as a function of the orientation difference, δθ, of the two stimuli. This tuning curve also represents the mutual information between the neuronal responses and the stimulus orientation. We studied theoretically the dependence of the information tuning curve on the orientation tuning width, baseline, and peak responses. Of main interest is the finding that narrow orientation tuning is not necessarily optimal for all angular discrimination tasks. Instead, the optimal tuning width depends linearly onδθ. We applied our theory to study the discrimination performance of a population of 490 neurons in macaque V1. We found that a significant fraction of the neuronal population exhibits favorable tuning properties for large δθ. We also studied how the discrimination capability of neurons is distributed and compared several other measures of the orientation tuning such as CV with Chernoff distances for normalized tuning curves.

https://www.jneurosci.org/content/jneuro/24/15/3726.full.pdf

Information tuning of populations of neurons in primary visual cortex.

We studied the mutual information between a stimulus and a system consisting of stochastic, statistically independent elements that respond to a stimulus. Using statistical mechanical methods the properties of the mutual information (MI) in the limit of a large system size N are calculated. For continuous valued stimuli, the MI increases logarithmically with N and is related to the log of the Fisher information of the system. For discrete stimuli the MI saturates exponentially with N. We find that the exponent of saturation of the MI is the Chernoff distance between response probabilities that are induced by different stimuli.

Kukjin Kang

Papers

Population coding in neuronal systems with correlated noise.

Mexican hats and pinwheels in visual cortex

LFP spectral peaks in V1 cortex: network resonance and cortico-cortical feedback

Information tuning of populations of neurons in primary visual cortex.

Mutual information of population codes and distance measures in probability space.