Emergence of Scale-free Spike Flow Graphs in Recurrent Neural Networks

Abstract

D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t [7], [8] we believe that the edge of these two dynamically growing disciplines might be an interesting field for research. In this paper we introduce a simplified model of spike flow network which in some details resembles a recurrent neural network with stochastic dynamics. We argue that within this setup a scale-free network structure emerges as a natural consequence of model structuring principles and we provide numerical evidence supporting this claim. Further in the paper we investigate a number of interesting properties of this network and discuss some consequences of this result.

Emergence of Scale-free Graphs in Dynamical Spiking Neural Networks

“…This interpretation sets the following constraints to dynamic behavior: the more activity a unit receives, the more active it becomes and retains this activity for some period of time, depending on the initial excitation. We claim that this property, first analyzed in discrete setup in [3], cannot be successfully reproduced with single neurons (even fairly complex dynamical spiking neurons e.g. those introduced in [4]).…”

“…This research is based on previous results presented in [3], which dealt with a discreete model, that resembled to some extent Hopfield model. In this previous work we examined a model of a spike flow graph, with simple units whose states were in N. A system consisting of number of such units was randomly wired (normally distributed weights), and equipped with an energy function as follows:…”

“…The more potential a unit gains the more likely it will become more active. By labeling each edge that was used to exchange a unit of potential one receives a weighted graph, which displays a scale free property as well as some other interesting properties (see [3] for details as well as [16]). …”