stdp_nn_pre_centered

stdp_nn_pre_centered - Synapse type for spike-timing dependent plasticity, with nearest-neighbour spike pairing

Description

stdp_nn_pre_centered_synapse is a connector to create synapses with spike time dependent plasticity with the presynaptic-centered nearest-neighbour spike pairing scheme, as described in 1.

Each presynaptic spike is taken into account in the STDP weight change rule with the nearest preceding postsynaptic one and the nearest succeeding postsynaptic one (instead of pairing with all spikes, like in stdp_synapse). So, when a presynaptic spike occurs, it is accounted in the depression rule with the nearest preceding postsynaptic one; and when a postsynaptic spike occurs, it is accounted in the facilitation rule with all preceding presynaptic spikes that were not earlier than the previous postsynaptic spike. For a clear illustration of this scheme see fig. 7B 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, increases by 1 on a pre-spike occurrence, and is reset to 0 on a post-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

Izhikevich E. M., Desai N. S. (2003) Relating STDP to BCM, Neural Comput. 15, 1511–1523

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
the_delay	ms	1ms	!!! cannot have a variable called “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
pre_trace	real	0.0
post_trace	real	0.0

Source code

synapse stdp_nn_pre_centered:
  state:
    w real = 1
    pre_trace real = 0.0
    post_trace real = 0.0
  end
  parameters:
    the_delay ms = 1ms # !!! cannot have a variable called "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
  end
  equations:
    # nearest-neighbour trace of presynaptic neuron
    pre_trace'=-pre_trace / tau_tr_pre
    # nearest-neighbour trace of postsynaptic neuron
    post_trace'=-post_trace / tau_tr_post
  end

  input:
    pre_spikes nS <-spike
    post_spikes nS <-spike
  end

  output: spike

  onReceive(post_spikes):
    post_trace = 1
    # potentiate synapse
    w_ real = Wmax * (w / Wmax + (lambda * (1.0 - (w / Wmax)) ** mu_plus * pre_trace))
    w = min(Wmax,w_)
    pre_trace = 0
  end

  onReceive(pre_spikes):
    pre_trace += 1
    # depress synapse
    w_ real = Wmax * (w / Wmax - (alpha * lambda * (w / Wmax) ** mu_minus * post_trace))
    w = max(Wmin,w_)
    # deliver spike to postsynaptic partner
    deliver_spike(w,the_delay)
  end

end

Characterisation