stdp_nn_symm

Synapse type for spike-timing dependent plasticity with symmetric nearest-neighbour spike pairing scheme

Description

stdp_nn_symm_synapse is a connector to create synapses with spike time dependent plasticity with the symmetric nearest-neighbour spike pairing scheme [1].

When a presynaptic spike occurs, it is taken into account in the depression part of the STDP weight change rule with the nearest preceding postsynaptic one, and when a postsynaptic spike occurs, it is accounted in the facilitation rule with the nearest preceding presynaptic one (instead of pairing with all spikes, like in stdp_synapse). For a clear illustration of this scheme see fig. 7A in [2].

The pairs exactly coinciding (so that presynaptic_spike == postsynaptic_spike + dendritic_delay), leading to zero delta_t, are discarded. In this case the concerned pre/postsynaptic spike is paired with the second latest preceding post/presynaptic one (for example, pre=={10 ms; 20 ms} and post=={20 ms} will result in a potentiation pair 20-to-10).

The implementation involves two additional variables - presynaptic and postsynaptic traces [2]. The presynaptic trace decays exponentially over time with the time constant tau_plus and increases to 1 on a pre-spike occurrence. The postsynaptic trace (implemented on the postsynaptic neuron side) decays with the time constant tau_minus and increases to 1 on a post-spike occurrence.

Figure 7 from Morrison, Diesmann and Gerstner

Original caption:

Phenomenological models of synaptic plasticity based on spike timing”, Biological Cybernetics 98 (2008). “Examples of nearest neighbor spike pairing schemes for a pre-synaptic neuron j and a postsynaptic neuron i. In each case, the dark gray indicate which pairings contribute toward depression of a synapse, and light gray indicate which pairings contribute toward potentiation. (a) Symmetric interpretation: each presynaptic spike is paired with the last postsynaptic spike, and each postsynaptic spike is paired with the last presynaptic spike (Morrison et al. 2007). (b) Presynaptic centered interpretation: each presynaptic spike is paired with the last postsynaptic spike and the next postsynaptic spike (Izhikevich and Desai 2003; Burkitt et al. 2004: Model II). (c) Reduced symmetric interpretation: as in (b) but only for immediate pairings (Burkitt et al. 2004: Model IV, also implemented in hardware by Schemmel et al. 2006)

References

[1]

Morrison A., Aertsen A., Diesmann M. (2007) Spike-timing dependent plasticity in balanced random networks, Neural Comput. 19:1437–1467

[2] (1,2)

Morrison A., Diesmann M., and Gerstner W. (2008) Phenomenological models of synaptic plasticity based on spike timing, Biol. Cybern. 98, 459–478

Parameters

Name	Physical unit	Default value	Description
d	ms	1ms	Synaptic transmission delay
lambda	real	0.01
tau_tr_pre	ms	20ms
tau_tr_post	ms	20ms
alpha	real	1.0
mu_plus	real	1.0
mu_minus	real	1.0
Wmax	real	100.0
Wmin	real	0.0

State variables

Name	Physical unit	Default value	Description
w	real	1.0	Synaptic weight
pre_trace	real	0.0
post_trace	real	0.0

Source code

The model source code can be found in the NESTML models repository here: stdp_nn_symm.

Characterisation