Disappearance of Spurious States in Analog Associative Memories

We show that symmetric n-mixture states, when they exist, are almost never stable in autoassociative networks with threshold-linear units. Only with a binary coding scheme we could find a limited region of the parameter space in which either 2-mixtures or 3-mixtures are stable attractors of the dynamics.Comment: 5 pages, 3 figures, accepted for publication in Phys Rev

Mean Field Theory For Non-Equilibrium Network Reconstruction

There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically-coupled, synchronously-updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one time step-delayed correlation functions.Comment: new version, accepted in PRL. For the Supp. Mat. (ref. 11), please contact the author

Localized activity profiles and storage capacity of rate-based autoassociative networks

We study analytically the effect of metrically structured connectivity on the behavior of autoassociative networks. We focus on three simple rate-based model neurons: threshold-linear, binary or smoothly saturating units. For a connectivity which is short range enough the threshold-linear network shows localized retrieval states. The saturating and binary models also exhibit spatially modulated retrieval states if the highest activity level that they can achieve is above the maximum activity of the units in the stored patterns. In the zero quenched noise limit, we derive an analytical formula for the critical value of the connectivity width below which one observes spatially non-uniform retrieval states. Localization reduces storage capacity, but only by a factor of 2~3. The approach that we present here is generic in the sense that there are no specific assumptions on the single unit input-output function nor on the exact connectivity structure.Comment: 4 pages, 4 figure

Dynamics and Performance of Susceptibility Propagation on Synthetic Data

We study the performance and convergence properties of the Susceptibility Propagation (SusP) algorithm for solving the Inverse Ising problem. We first study how the temperature parameter (T) in a Sherrington-Kirkpatrick model generating the data influences the performance and convergence of the algorithm. We find that at the high temperature regime (T>4), the algorithm performs well and its quality is only limited by the quality of the supplied data. In the low temperature regime (T<4), we find that the algorithm typically does not converge, yielding diverging values for the couplings. However, we show that by stopping the algorithm at the right time before divergence becomes serious, good reconstruction can be achieved down to T~2. We then show that dense connectivity, loopiness of the connectivity, and high absolute magnetization all have deteriorating effects on the performance of the algorithm. When absolute magnetization is high, we show that other methods can be work better than SusP. Finally, we show that for neural data with high absolute magnetization, SusP performs less well than TAP inversion.Comment: 9 pages, 7 figure

Multiscale relevance and informative encoding in neuronal spike trains

Neuronal responses to complex stimuli and tasks can encompass a wide range of time scales. Understanding these responses requires measures that characterize how the information on these response patterns are represented across multiple temporal resolutions. In this paper we propose a metric -- which we call multiscale relevance (MSR) -- to capture the dynamical variability of the activity of single neurons across different time scales. The MSR is a non-parametric, fully featureless indicator in that it uses only the time stamps of the firing activity without resorting to any a priori covariate or invoking any specific structure in the tuning curve for neural activity. When applied to neural data from the mEC and from the ADn and PoS regions of freely-behaving rodents, we found that neurons having low MSR tend to have low mutual information and low firing sparsity across the correlates that are believed to be encoded by the region of the brain where the recordings were made. In addition, neurons with high MSR contain significant information on spatial navigation and allow to decode spatial position or head direction as efficiently as those neurons whose firing activity has high mutual information with the covariate to be decoded and significantly better than the set of neurons with high local variations in their interspike intervals. Given these results, we propose that the MSR can be used as a measure to rank and select neurons for their information content without the need to appeal to any a priori covariate.Comment: 38 pages, 16 figure