A Fokker-Planck approach to graded information propagation in pulse-gated feedforward neuronal networks

TL;DR

This paper uses a Fokker-Planck approach to analyze graded information transfer in pulse-gated feedforward neuronal networks, revealing an underlying line attractor that explains the invariance in spike timing and amplitude.

Contribution

It introduces a Fokker-Planck framework to understand the invariance in information transfer and identifies a line attractor as the core structure in such networks.

Findings

Good correspondence between Fokker-Planck and mean-field solutions.

Identification of a line attractor in state space.

Insights into the roles of synaptic coupling and gating pulses.

Abstract

Information transmission is a key element for information processing in the brain. A number of mechanisms have been proposed for transferring volleys of spikes between layers of a feedforward neural circuit. Many of these mechanisms use synchronous activity to provide windows in time when spikes may be transferred more easily from layer to layer. Recently, we have demonstrated that a pulse-gating mechanism can transfer graded information between layers in a feedforward neuronal network. Our transfer mechanism resulted in a time-translationally invariant firing rate and synaptic current waveforms of arbitrary amplitude, thus providing exact, graded information transfer between layers. In this paper, we apply a Fokker-Planck approach to understand how this translational invariance manifests itself in a high-dimensional, non-linear feedforward integrate-and-fire network. We show that there is good correspondence in spiking probabilities between the Fokker-Planck solutions and our previous mean-field solutions. We identify an approximate line attractor in state space as the essential structure underlying the time-translational invariance of our solutions. This approach has enabled us to better understand the role played by the synaptic coupling, gating pulse and the membrane potential probability density function in information transfer.