Spike-timing-dependent plasticity for neurons with recurrent connections

Abstract

The dynamics of the learning equation, which describes the evolution of the synaptic weights, is derived in the situation where the network contains recurrent connections. The derivation is carried out for the Poisson neuron model. The spiking-rates of the recurrently connected neurons and their cross-correlations are determined self- consistently as a function of the external synaptic inputs. The solution of the learning equation is illustrated by the analysis of the particular case in which there is no external synaptic input. The general learning equation and the fixed-point structure of its solutions is discussed.

Symmetry breaking induced by Spike-Timing-Dependent Plasticity in the presence of recurrent connections

“…We investigate the dynamics of recurrently connected linear Poisson neurons excited by steady external pulse trains with a correlation structure [1,2]. The input synaptic weights are modified in accordance to "additive" STDP that relies upon both rate-based and pairwise-correlationbased changes [1,2]; the recurrent weights are kept fixed.…”

“…The input synaptic weights are modified in accordance to "additive" STDP that relies upon both rate-based and pairwise-correlationbased changes [1,2]; the recurrent weights are kept fixed. The network dynamics (evolution of the firing rates, of the correlations, and of the weights) is described by a dynamical system [2].…”

“…The input synaptic weights are modified in accordance to "additive" STDP that relies upon both rate-based and pairwise-correlationbased changes [1,2]; the recurrent weights are kept fixed. The network dynamics (evolution of the firing rates, of the correlations, and of the weights) is described by a dynamical system [2]. We focus in this paper on symmetry breaking among the input connections in the case of two input pools with the same characteristics (correlation within each pool but not between each other), particularly the influence of the recurrent connections.…”

“…Spike-Timing-Dependent Plasticity (STDP) is a candidate for such plasticity that has received considerable experimental support and has been studied in feed-forward network architectures [1] and more recently in recurrently connected networks [2], which corresponds to more biologically realistic situations.…”

A forecast-based biologically-plausible STDP learning rule

“…: [8]) which have proven to replicate the biology. Burkitt et al [6] found a mathematical and statistical description of the standard STDP rule.…”