Necessary Conditions for Reliable Representation of Asynchronous Spikes Through a Single-layered Feedforward Network

Abstract

Reliable propagation of firing rate - specifically slow modulation of asynchronous spikes in fairly short time windows [20-500]ms across multiple layers of a feedforward network (FFN) receiving background synaptic noise has proven difficult to capture in spiking models. We, in this paper, explore how information of asynchronous spikes disrupted in the first layer of a typical FFN, and which factors can enable reliable information representation. Our rationale is that the reliable propagation of information across layers of a FFN is likely if that information can be preserved in the first layer of the FFN. In a typical FFN, each layer comprises a certain number (network size) of excitatory neurons - leaky integrate and fire (LIF) model neuron in this paper - receiving correlated input (common stimulus from the upstream layer) plus independent background synaptic noise. We develop a reduced network model of FFN which captures main features of a conventional all-to-all connected FFN. Exploiting the reduced network model, synaptic weights are calculated using a closed-form optimization framework that minimizes the mean squared error between reconstructed stimulus (by spikes of the first layer of FFN) and the original common stimulus. We further explore how representation of asynchronous spikes in a FFN changes with respect to other factors like the network size and the level of background synaptic noise while synaptic weights are optimized for each scenario. We show that not only synaptic weights but also the network size and the level of background synaptic noise are crucial to preserve a reliable representation of asynchronous spikes in the first layer of a FFN. This work sheds light in better understanding of how information of slowly time-varying fluctuations of the firing rate can be transmitted in multi-layered FFNs.