Zhang, Kechen, Iris Ginzburg, Bruce L. McNaughton, and Ter-decoding problems have been studied previously (Abbott rence J. Sejnowski. Interpreting neuronal population activity by re-1994; Bialek et al. 1991;Optican and Richmond 1987; Saliconstruction: unified framework with application to hippocampal nas and Abbott 1994; Seung and Sompolinsky 1993; Snippe place cells. J. Neurophysiol. 79: 1017-1044, 1998. Physical variables 1996Zemel et al. 1997;Zohary et al. 1994).such as the orientation of a line in the visual field or the location of Two main goals for reconstruction are approached in this the body in space are coded as activity levels in populations of paper. The first goal is technical and is exemplified by the neurons. Reconstruction or decoding is an inverse problem in which population vector method applied to motor cortical activities the physical variables are estimated from observed neural activity.during various reaching tasks (Georgopoulos et al. 1986(Georgopoulos et al. , 1989 Reconstruction is useful first in quantifying how much information Schwartz 1994) and the template matching method applied to about the physical variables is present in the population and, second, in providing insight into how the brain might use distributed represen-disparity selective cells in the visual cortex (Lehky and Sejnowtations in solving related computational problems such as visual ob-ski 1990) and hippocampal place cells during rapid learning of ject recognition and spatial navigation. Two classes of reconstruction place fields in a novel environment (Wilson and McNaughton methods, namely, probabilistic or Bayesian methods and basis func-1993). In these examples, reconstruction extracts information tion methods, are discussed. They include important existing methods from noisy neuronal population activity and transforms it to a as special cases, such as population vector coding, optimal linear more explicit and convenient representation of movement and estimation, and template matching. As a representative example for position. In this paper, various reconstruction methods that are the reconstruction problem, different methods were applied to multitheoretically optimal under different frameworks are considelectrode spike train data from hippocampal place cells in freely ered; the ultimate theoretical limits on the best achievable accumoving rats. The reconstruction accuracy of the trajectories of the racy for all possible methods also are derived. rats was compared for the different methods. Bayesian methods were especially accurate when a continuity constraint was enforced, and Our second goal for reconstruction is biological. Because the best errors were within a factor of two of the information-theoretic the brain extracts information distributed among the activity limit on how accurate any reconstruction can be and were comparable of populations of neurons to solve various computational with the intrinsic experimental errors in position tracking. In addition, problems, the question arises as to which algor...

One of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity. In general, however the interpretation of the observed correlations is di cult, since the correlation between a pair of neurons is in uenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong. Thus, a comparison between the observed correlations and the predictions from speci c model networks is needed. In this paper we develop the theory of neuronal correlation functions in large networks comprising of several highly connected subpopulations, and obeying stochastic dynamic rules. When the networks are in asynchronous states, the cross-correlations are relatively weak, i.e., their amplitude relative to that of the auto-correlations is of order of 1=N, N being the size of the interacting populations. Using the weakness of the cross-correlations, general equations which express the matrix of cross-correlations in terms of the mean neuronal activities, and the e ective interaction matrix are presented. The e ective interactions are the synaptic e cacies multiplied by the the gain of the postsynaptic neurons. The time-delayed crosscorrelation matrix can be expressed as a sum of exponentially decaying modes that correspond to the (non-orthogonal) eigenvectors of the e ective interaction matrix. The theory is extended to networks with random connectivity, such as randomly dilute networks. This allows for the comparison between the contribution from the internal common input and that from the direct interactions to the correlations of monosynaptically coupled pairs. A closely related quantity is the linear response of the neurons to external time-dependent perturbations. We derive the form of the dynamic linear response function of neurons in the above architecture, in terms of the eigenmodes of the e ective interaction matrix. The behavior of the correlations and the linear response when the system is near a bifurcation point is analyzed. Near a saddle-node bifurcation the correlation matrix is dominated by a single slowly decaying critical mode. Near a Hopf-bifurcation the correlations exhibit weakly damped sinusoidal oscillations. The general theory is applied to the case of randomly dilute network consisting of excitatory and inhibitory subpopulations, using parameters that mimic the local circuit of 1mm 3 of rat neocortex. Both the e ect of dilution as well as the in uence of a nearby bifurcation to an oscillatory states are demonstrated. networks. Hence, the interpretation of the observed features of the CCs remains an open challenge, and is the topic of this paper. Another potentially important probe of the interactions in a neuronal network is the linear response function, namely the change in the average ring rates due to a su ciently weak externally applied perturbation. Here again, the magnitude as well as the temporal evolution of the response depend on the state of the network. Hence, it is importa...

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