Lévy flights describe aspecial class of random walks whose step sizes satisfy a power-lawtaileddistribution.

It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encoding of such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions using a spike based spatio-temporal code. Our model combines the computational advantages of the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, the model highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative population-level approaches for the experimental validation of distributed representations. Core brain computations, such as sensory perception, have been successfully characterized as probabilistic inference, whereby sensory stimuli are interpreted in terms of the objects or features that gave rise to them [1, 2].

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: The authors present a model of persistent activity in neural networks as typically observed in working memory tasks and modeled as attractor dynamics. The authors note the shortcomings of existing models, namely the reliance on implausible global excitatory or inhibitory signals to reset the network dynamics after settling into an attractor state and the superfluousness of such a stable attractor, since in working memory tasks, the dynamics need only persistent as long as the task requires, not indefinitely. In the proposed model, these issues are confronted by incorporating short term synaptic facilitation and depression into a network model. Using a mean-field approach, the authors identify stable fixed points of the rate dynamics and how these fixed-points change as a function of network connectivity and timescale parameters.

How are firing rates in a spiking network related to neural input, connectivity and network function? This is an important problem because firing rates are one of the most important measures of network activity, in both the study of neural computation and neural network dynamics. However, it is a difficult problem, because the spiking mechanism of individual neurons is highly non-linear, and these individual neurons interact strongly through connectivity. We develop a new technique for calculating firing rates in optimal balanced networks. These are particularly interesting networks because they provide an optimal spike-based signal representation while producing cortex-like spiking activity through a dynamic balance of excitation and inhibition.