Population coding in neuronal systems with correlated noise.

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).

[1]  A P Georgopoulos,et al.  On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[2]  D. Mastronarde.  Correlated firing of cat retinal ganglion cells. I. Spontaneously active inputs to X- and Y-cells. , 1983, Journal of neurophysiology.

[3]  A. P. Georgopoulos,et al.  Neuronal population coding of movement direction. , 1986, Science.

[4]  P. C. Murphy,et al.  Cerebral Cortex , 2017, Cerebral Cortex.

[5]  D. Sparks,et al.  Population coding of saccadic eye movements by neurons in the superior colliculus , 1988, Nature.

[6]  M. Young,et al.  Sparse population coding of faces in the inferotemporal cortex. , 1992, Science.

[7]  Néstor Parga,et al.  Information processing by a perceptron in an unsupervised learning task , 1993 .

[8]  B L McNaughton,et al.  Dynamics of the hippocampal ensemble code for space. , 1993, Science.

[9]  H Sompolinsky,et al.  Simple models for reading neuronal population codes. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Ehud Zohary,et al.  Correlated neuronal discharge rate and its implications for psychophysical performance , 1994, Nature.

[11]  J. Movshon,et al.  A computational analysis of the relationship between neuronal and behavioral responses to visual motion , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  Terrence J. Sejnowski,et al.  The Computational Brain , 1996, Artif. Intell..

[13]  Jorma Rissanen,et al.  Fisher information and stochastic complexity , 1996, IEEE Trans. Inf. Theory.

[14]  Terrence R. Stanford,et al.  A neuronal population code for sound localization , 1997, Nature.

[15]  Nicolas Brunel,et al.  Mutual Information, Fisher Information, and Population Coding , 1998, Neural Computation.

[16]  A. P. Georgopoulos,et al.  Variability and Correlated Noise in the Discharge of Neurons in Motor and Parietal Areas of the Primate Cortex , 1998, The Journal of Neuroscience.

[17]  著者なし.  16 , 1871, Animals at the End of the World.

[18]  Peter Dayan,et al.  The Effect of Correlated Variability on the Accuracy of a Population Code , 1999, Neural Computation.

[19]  E T Rolls,et al.  Correlations and the encoding of information in the nervous system , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  J. Donoghue,et al.  Neuronal Interactions Improve Cortical Population Coding of Movement Direction , 1999, The Journal of Neuroscience.

[21]  H. Sompolinsky,et al.  Mutual information of population codes and distance measures in probability space. , 2001, Physical review letters.

[22]  A Treves,et al.  Representational capacity of a set of independent neurons. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.