AbstractNon-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP) which depends on the interactions of three precisely-timed spikes and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We describe synaptic changes arising from emergent higher-order correlations, and investigate their influence on different connectivity motifs in the network. Our motif expansion framework reveals novel motif structures under the triplet STDP rule, which support the formation of bidirectional connections and loops in contrast to the classical pair-based STDP rule. Therefore, triplet STDP drives the spontaneous emergence of self-connected groups of neurons, or assemblies, proposed to represent functional units in neural circuits. Assembly formation has often been associated with plasticity driven by firing rates or external stimuli. We propose that assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule commonly assumed in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of triplet STDP or the synaptic transmission function differentially promote connectivity motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.
R-spaces associated with a Hermitian symmetric pair
