  Spike timing dependent plasticity (STDP) is believed to play an important
role in shaping the structure of neural circuits. Here we show that STDP
generates effective interactions between synapses of different neurons, which
were neglected in previous theoretical treatments, and can be described as a
sum over contributions from structural motifs. These interactions can have a
pivotal influence on the connectivity patterns that emerge under the influence
of STDP. In particular, we consider two highly ordered forms of structure: wide
synfire chains, in which groups of neurons project to each other sequentially,
and self connected assemblies. We show that high order synaptic interactions
can enable the formation of both structures, depending on the form of the STDP
function and the time course of synaptic currents. Furthermore, within a
certain regime of biophysical parameters, emergence of the ordered connectivity
occurs robustly and autonomously in a stochastic network of spiking neurons,
without a need to expose the neural network to structured inputs during
learning.
