Learning the structure of correlated synaptic subgroups using stable and competitive spike-timing-dependent plasticity

Abstract

Synaptic plasticity must be both competitive and stable if ongoing learning of the structure of neural inputs is to occur. In this paper, a wide class of spike-timing-dependent plasticity (STDP) models is identified that have both of these desirable properties in the case in which the input consists of subgroups of synapses that are correlated within the subgroup through the occurrence of simultaneous input spikes. The process of synaptic structure formation is studied, illustrating one particular class of these models. When the learning rate is small, multiple alternative synaptic structures are possible given the same inputs, with the outcome depending on the initial weight configuration. For large learning rates, the synaptic structure does not stabilize, resulting in neurons without consistent response properties. For learning rates in between, a unique and stable synaptic structure typically forms. When this synaptic structure exhibits a bimodal distribution, the neuron will respond selectively to one or more of the subgroups. The robustness with which this selectivity develops during learning is largely determined by the ratio of the subgroup correlation strength to the number of subgroups. The fraction of potentiated subgroups is primarily determined by the balance between potentiation and depression.

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways

“…The firing rates of inputs within a pool are all equal to, say, ν 0 . The positive within-pool correlation is generated so that, for any input, a given portion of its spikes occur at the same time as some other spikes within its pool, while the remainder occur at independent times (Gütig et al 2003;Meffin et al 2006).…”

“…The spikes from input k are selected from two homogeneous Poisson spike trains each of rateν 0 such that the withingroup correlation strength is 0 ≤ĉ ≤ 1 (Meffin et al 2006). The first spike train is common to all inputs in the pool and generates the correlated events; distinct pools have different common reference spike trains.…”

“…Such spike-timing-dependent plasticity (STDP) has been the subject of both theoretical (Gerstner et al 1996;Kempter et al 1999;Gütig et al 2003;Burkitt et al 2004;Meffin et al 2006) and experimental (Markram et al 1997;Bi and Poo 2001) research; for a review, see Morrison et al (2008). Although experiments have shown that the effect of STDP can depend upon triplets of spikes or the post-synaptic membrane potential (Sjöström et al 2001(Sjöström et al , 2004, we will constrain our study to pairwise STDP in order to study its functional properties, knowing the limitations of the model.…”

“…Previous studies of STDP have primarily investigated single neurons and the resulting implications for the development of network structure in feed-forward architectures (Kempter et al 1999;Song et al 2000;Gütig et al 2003;Burkitt et al 2004;Meffin et al 2006). STDP has been observed in various areas of the central neuronal system (e.g., hippocampus and cortex), which show recurrent connections between local neurons.…”

Spike-Timing–Dependent Synaptic Plasticity and Synaptic Democracy in Dendrites

“…Among the possible functional roles attributed to STDP are the emergence of functional maps during development (Song and Abbott 2001), enhancement of correlated inputs (Gütig et al 2003;Meffin et al 2006;van Rossum et al 2000), enhancement of input temporal precision (Kistler and van Hemmen 2000), and the generation of a negative sensory image (Roberts and Bell 2000).…”