Leaky Integrate and fire neuron model

Question

Ive been diving into neural networks lately. They're awesome but a little obscure and very inaccessible to say the least. I am particularly interested in liquid state machines which heavily use the integrate and fire neuron model. This totally escapes me though. Here are some questions:

1. What is the perfect neuron configuration for a leaky integrate and fire neuron: https://en.wikipedia.org/wiki/Biological_neuron_model#Leaky_integrate-and-fire ? IE If the leaky integrate and fire neuron was an artificial one and not limited by biological constraints.

2. Would it then fit into a typical artificial neuron structure or would it retain its leakiness?

3. In plain english how does the leaky integrate and fire neuron work? How does it fit into a liquid state machine (if you happen to know kinda obscure i know).

If you know the answers to any of these questions feel free to respond!

Thanks!

Answer 1

Your question seems to be quite generalistic (hence the downvote I presume), but I will try to explain you what the "Leaky Integrate-and-Fire" (LIF) neuron is. You will have to relate the Liquid State Machine stuff on your own, since I'm no an expert on that.

The LIF model is devised like so, to explain how current changes in relation to voltage (or vice-versa). It is an oversimplification of what happens in the real neuron, meaning that we created a model, which is basically an RC-circuit , to describe the electrochemical interactions that happen through a neuron.

What the LIF neuron does, is that it tells you that if you input current (I) into a neuron, it becomes capacitative current ( Cm*dVm/dt ) and resistive current (Vm/Rm).

We say "integrate", because the neuron integrates all incoming inputs from the previous neurons together. We use the word "leak", since this model takes into account the fact that it leaks some of the integrating input over time (because in nature you usually get to a final state with gradual/exponential changes).

Here is another explanation by Gerstner , probably much better.