Sparse and Dense Encoding in Layered Associative Network of Spiking Neurons

TL;DR

This paper investigates how the sparsity or density of connections in layered associative networks of spiking neurons affects synchronous activity, memory capacity, and stability, using the Fokker-Planck method.

Contribution

It reveals the contrasting effects of sparse and dense connectivity on synchronization, basin of attraction, and storage capacity in neural networks.

Findings

Sparse networks promote synchronous firing.

Dense networks inhibit synchronous firing.

Sparsity increases storage capacity.

Abstract

A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the activity of a layered associative network of Leaky Integrate-and-Fire neurons in which connection we embed memory patterns by the Hebbian Learning. We analyzed their activity by the Fokker-Planck method. In our previous report, when a half of neurons belongs to each memory pattern (memory pattern rate $F=0.5$), the temporal profiles of the network activity is split into temporally clustered groups called sublattices under certain input conditions. In this study, we show that when the network is sparsely connected ($F<0.5$), synchronous firings of the memory pattern are promoted. On the contrary, the densely connected network ($F>0.5$) inhibit synchronous firings. The sparseness and denseness also effect the basin of attraction and the storage capacity of the embedded memory patterns. We show that the sparsely(densely) connected networks enlarge(shrink) the basion of attraction and increase(decrease) the storage capacity.