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Multiplying with neurons: Compensation for irregular input spike trains by using time-dependent synaptic efficiencies

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Abstract

A leaky integrate-and-fire (LIF) neurons can act as multipliers by detecting coincidences of input spikes. However, in case of input spike trains with irregular interspike delays, false coincidences are also detected and the operation as a multiplier is degraded. This problem can be solved by using time dependent synaptic weights which are set to zero after each input spike and recover with the same time constant as the decay time of the corresponding excitatory postsynaptic potentials (EPSP). Such a mechanism results in EPSP's with amplitudes independent on the input interspike delays. Neuronal computation is then performed without frequency decoding.

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Abbreviations

C :

Capacitance of the cellular membrane (F)

Ds :

Duration of the spikes and inward current pulse. (s)

ΔV :

Contribution to the capacitor (membrane) potential reached at the end of an input spike at synapse j (V)

V + :

Membrane potential increase due to one input spike at synapse j (V)

f in :

Maximum input frequency (Hz)

f n :

Output frequency of a LIF neuron when n connected inputs fire at their maximum frequency f in . (Hz)

n :

Number of inputs connected to a neuron.

R :

Leak resistance of the membrane (Ohm)

RC :

Discharge time constant of the membrane (= R · C) (s)

RSD:

Relative standard deviation of the interspike intervals (=σ Ti / Ti)

σ Ti :

Standard deviation of the interspike intervals (s)

S :

Selectivity of the LIF neuron as a multiplier.

τ :

Time window for input spikes (s)

T i :

Average interspike interval of the spikes produced by neuron i (s).

T :

Delay between the preceding spike and the spike under consideration (s).

T in :

Average interspike interval corresponding to the maximum input frequency f in (s)

T r :

Duration of the refractory time (starting at same time as an output spike) (s)

V :

Potential of the cellular membrane or the capacitor (V)

V 0 :

Potential remaining from preceding spikes on synapse j (V)

V th :

Threshold potential for spike initiation (V)

W ij :

Time dependent synaptic weight for inputs from neuron j to neuron i. In this model, the synaptic weight is the amplitude of the input current pulse induced by the spike (A).

W ijo :

Time independent synaptic weight according to the theory of the multiplication mode for regular input spike trains with interspike delays Tin (Bugmann 1991c) (A)

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Author notes

  1. Guido Bugmann

    Present address: Centre for Neural Networks, Kings College London, Strand, 2R 2LS, London, WC, UK

Authors and Affiliations

  1. NEC Fundamental Research Laboratories, 4 Miyukigaoka, 305, Tsukuba — Ibaraki, Japan

    Guido Bugmann

Authors
  1. Guido Bugmann
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Bugmann, G. Multiplying with neurons: Compensation for irregular input spike trains by using time-dependent synaptic efficiencies. Biol. Cybern. 68, 87–92 (1992). https://doi.org/10.1007/BF00203140

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  • DOI: https://doi.org/10.1007/BF00203140

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