A Microscopic Theory of Intrinsic Timescales in Spiking Neural Networks
Abstract
A complex interplay of singleneuron properties and the recurrent network structure shapes the activity of individual cortical neurons, which differs in general from the respective population activity. We develop a theory that makes it possible to investigate the influence of both network structure and singleneuron properties on the singleneuron statistics in blockstructured sparse random networks of spiking neurons. In particular, the theory predicts the neuronlevel autocorrelation times, also known as intrinsic timescales, of the neuronal activity. The theory is based on a postulated extension of dynamic meanfield theory from rate networks to spiking networks, which is validated via simulations. It accounts for both static variability, e.g. due to a distributed number of incoming synapses per neuron, and dynamical fluctuations of the input. To illustrate the theory, we apply it to a balanced random network of leaky integrateandfire neurons, a balanced random network of generalized linear model neurons, and a biologically constrained network of leaky integrateandfire neurons. For the generalized linear model network, an analytical solution to the colored noise problem allows us to obtain selfconsistent firing rate distributions, singleneuron power spectra, and intrinsic timescales. For the leaky integrateandfire networks, we obtain the same quantities by means of a novel analytical approximation of the colored noise problem that is valid in the fluctuationdriven regime. Our results provide a further step towards an understanding of the dynamics in recurrent spiking cortical networks.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.01908
 Bibcode:
 2019arXiv190901908V
 Keywords:

 Quantitative Biology  Neurons and Cognition;
 Condensed Matter  Disordered Systems and Neural Networks