Leaky Integrate-And-Fire

tags: Spiking Neural Networks

A Leaky Integrate-and-Fire neuron at layer $l$ and index $i$ can be described in differential form as:

$τ_{mem} \frac{d U_{i}^{(l)}}{d t} = - (U_{i}^{(l)} - U_{rest}) + R I_{i}^{(l)}$

where the terms denote:

$U_{i} (t)$: membrane potential
$U_{rest}$: resting potential
$τ_{mem}$: membrane time constant
$R$: input resistance
$i_{i} (t)$: input current

$U_{i}$ acts as a leaky integrator of the input current $I_{i}$ . Neurons emit spikes when the membrane voltage reaches firing threshold $θ$ , and resets to resting potential $U_{\rest}$ .

Equation eq:lif only describes the dynamics of a LIF neuron sub-threshold.

Jethro's Braindump

Leaky Integrate-And-Fire

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