Computes a single euler-integration step of an adaptive exponential LIF neuron-model adapted from http://www.scholarpedia.org/article/Adaptive_exponential_integrate-and-fire_model. It takes as input the input current as generated by an arbitrary torch module or function. More specifically it implements one integration step of the following ODE

\begin{split}\begin{align*} \dot{v} &= 1/\tau_{\text{mem}} \left(v_{\text{leak}} - v + i + \Delta_T exp\left({{v - v_{\text{th}}} \over {\Delta_T}}\right ) - a\right) \\ \dot{i} &= -1/\tau_{\text{syn}} i \\ \dot{a} &= 1/\tau_{\text{ada}} \left( a_{current} (V - v_{\text{leak}}) - a \right) \end{align*}\end{split}

together with the jump condition

$z = \Theta(v - v_{\text{th}})$

and transition equations

\begin{split}\begin{align*} v &= (1-z) v + z v_{\text{reset}} \\ i &= i + i_{\text{in}} \\ a &= a + a_{\text{spike}} z_{\text{rec}} \end{align*}\end{split}

where $$i_{\text{in}}$$ is meant to be the result of applying an arbitrary pytorch module (such as a convolution) to input spikes.

Parameters:

input_spikes (torch.Tensor): the input spikes at the current time step state (LIFAdExFeedForwardState): current state of the LIF neuron p (LIFAdExParameters): parameters of a leaky integrate and fire neuron dt (float): Integration timestep to use