Jethro's Braindump

Leaky Integrate-And-Fire

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

\begin{equation} \label{eq:lif} \tau_{\mathrm{mem}} \frac{\mathrm{d} U_{i}^{(l)}}{\mathrm{d} t}=-\left(U_{i}^{(l)}-U_{\mathrm{rest}}\right)+R I_{i}^{(l)} \end{equation}

where the terms denote:

\(U_{i}(t)\)
membrane potential
\(U_{\text{rest}}\)
resting potential
\(\tau_{\text{mem}}\)
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 \(\theta\), and resets to resting potential \(U_{\text{\rest}}\).

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

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