Abstract
Spike-Timing Dependent Plasticity (STDP) is characterized by a wide range of temporal kernels. However, much of the theoretical work has focused on a specific kernel – the “temporally asymmetric Hebbian” learning rules. Previous studies linked excitatory STDP to positive feedback that can account for the emergence of response selectivity. Inhibitory plasticity was associated with negative feedback that can balance the excitatory and inhibitory inputs. Here we study the possible computational role of the temporal structure of the STDP. We represent the STDP as a superposition of two processes: potentiation and depression. This allows us to model a wide range of experimentally observed STDP kernels, from Hebbian to anti-Hebbian, by varying a single parameter. We investigate STDP dynamics of a single excitatory or inhibitory synapse in purely feed-forward architecture. We derive a mean-field-Fokker-Planck dynamics for the synaptic weight and analyze the effect of STDP structure on the fixed points of the mean field dynamics. We find a phase transition along the Hebbian to anti-Hebbian parameter from a phase that is characterized by a unimodal distribution of the synaptic weight, in which the STDP dynamics is governed by negative feedback, to a phase with positive feedback characterized by a bimodal distribution. The critical point of this transition depends on general properties of the STDP dynamics and not on the fine details. Namely, the dynamics is affected by the pre-post correlations only via a single number that quantifies its overlap with the STDP kernel. We find that by manipulating the STDP temporal kernel, negative feedback can be induced in excitatory synapses and positive feedback in inhibitory. Moreover, there is an exact symmetry between inhibitory and excitatory plasticity, i.e., for every STDP rule of inhibitory synapse there exists an STDP rule for excitatory synapse, such that their dynamics is identical.
Highlights
Spike timing dependent plasticity (STDP) is a generalization of the celebrated Hebb postulate that ‘‘neurons that fire together wire together’’ to the temporal domain, according to the temporal order of the presynaptic and postsynaptic spike times
We describe a workable parameterization for the STDP temporal kernel
The computational role of the temporal kernel of STDP has been studied in the past
Summary
Spike timing dependent plasticity (STDP) is a generalization of the celebrated Hebb postulate that ‘‘neurons that fire together wire together’’ to the temporal domain, according to the temporal order of the presynaptic and postsynaptic spike times. In the interesting regime, aw, a ‘‘weak’’ synapse will tend to become weaker; producing the positive feedback mechanism that can generate bi-stability It was further shown [7] that this positive feedback can be weakened by introducing the weight dependent STDP component via the non-linearity parameter m in equations (3) and (4). Vogels and colleagues [14] studied a temporally symmetric STDP rule for inhibitory synapses, and reported that this type of plasticity rule results in negative feedback that can balance the feed-forward excitation. We study the effect of the temporal structure of the STDP kernel on the resultant synaptic weight for both excitatory and inhibitory synapses We discuss the symmetry between inhibitory and excitatory STDP dynamics
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