Does the Izhikevich neuron model use weights?

Question

I've been working a bit with neural networks and I'm interested on implementing a spiking neuron model.

I've read a fair amount of tutorials but most of them seem to be about generating pulses and I haven't found any application of it on a given input train.

Say for example I got input train:

Input[0] = [0,0,0,1,0,0,1,1]

It enters the Izhikevich neuron, does the input multiply a weight or only makes use of the parameters a, b, c and d?

Izhikevich equations are:

v[n+1] = 0.04*v[n]^2 + 5*v[n] + 140 - u[n] + I
u[n+1] = a*(b*v[n] - u[n])

where v[n] is input voltage and u[n] is a general recovery variable.

Are there any texts on implementations of Izhikevich or similar spiking neuron models on a practical problem? I'm trying to understand how information is encoded on this models but it looks different from what's done with standard second generation neurons. The only tutorial I've found where it deals with a spiking train and a set of weights is [1] but I haven't seen the same with Izhikevich.

[1] https://msdn.microsoft.com/en-us/magazine/mt422587.aspx

Answer 1

The plain Izhikevich model by itself, does not include weights.

The two equations you mentioned, model the membrane potential ( v[] ) over time of a point neuron. To use weights, you could connect two or more of such cells with synapses .

Each synapse could include some sort spike detection mechanism on the source cell (pre-synaptic), and a synaptic current mechanism in the target (post-synaptic) cell side. That synaptic current could then be multiplied by a weight term, and then become part of the I term (in the 1st equation above) for the target cell.

As a very simple example of a two cell network, at every time step, you could check if pre- cell v is above (say) 0 mV. If so, inject (say) 0.01 pA * weightPrePost into the post- cell. weightPrePost would range from 0 to 1, and could be modified in response to things like firing rate, or Hebbian-like spike synchrony like in STDP .

With multiple synaptic currents going into a cell, you could devise various schemes how to sum them. The simplest one would be just a simple sum, more complicated ones could include things like distance and dendrite diameters (eg simulated neural morphology).

This chapter is a nice introduction to other ways to model synapses: Modelling Synaptic Transmission