Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV

Abstract

In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence

“…This agrees with previous results where only the recurrent connections were plastic (with additive STDP) and the fixed input connections were already organized in a similar manner to the configuration obtained in Fig. 12a (Gilson et al 2009d). At the end of the learning epoch, we obtain two groups of 54 and 46 neurons each, respectively, which are selective to a different input pool, as illustrated in Fig.…”

“…When w out = 0, inhomogeneous input firing rates can thus lead to input selectivity. However, this does not generate structure among the recurrent weights since neurons will all specialize in the same manner (Gilson et al 2009d): after all weights have equilibrated, all neurons still receive the same overall homogeneous influx, in contrast to the specialization to one of the two input pools obtained with spike-time correlations.…”

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: Partially connected neurons driven by spontaneous activity

“…This also implies the stabilization of the mean incoming weight, but their actual equilibrium value depends on the neuronal activation mechanism. The present analysis of the weight drift (rate-based learning) is a first step toward the study of network structure induced by STDP in recurrently connected neuronal networks (Gilson et al 2009c). …”

“…We keep in mind that such effects may have an impact on the dynamics, which will actually be discussed in Sect. 4; the general case will be the focus of a subsequent companion article (Gilson et al 2009c). In this way, the spike trains are probabilistically quasi-independent for all pairs of neurons, i and j; the correlation coefficients, Q W i j , defined in (4) satisfy…”

“…In this article, we focus on the case of plastic recurrent synapses with no external inputs; in other words, each neuron receives excitation from the same external background activity. This analysis is a first step toward investigating a network with plastic recurrent synapses and external inputs with a firing-rate and spike-time correlation structure (Gilson et al 2009c), similar to that described by Gilson et al (2009a). We constrain our study to additive STDP (Sect.…”