norse.torch.functional.lif_adex.lif_adex_feed_forward_step#

norse.torch.functional.lif_adex.lif_adex_feed_forward_step(input_spikes: Tensor, state: LIFAdExFeedForwardState = (0, 0, 0), p: LIFAdExParameters = (tensor(4), tensor(0.0200), tensor(0.5000), tensor(2.), tensor(200.), tensor(100.), tensor(0.), tensor(1.), tensor(0.), 'super', 100.0), dt: float = 0.001) → Tuple[Tensor, LIFAdExFeedForwardState][source]#

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

$$\begin{array}{r}\begin{array}{rl}\dot{v}& =1/{\tau }_{\text{mem}}(v_{\text{leak}}-v+i+{\mathrm{\Delta }}_{T}exp\left(\frac{v-v_{\text{th}}}{{\mathrm{\Delta }}_T}\right)-a)\\ \dot{i}& =-1/{\tau }_{\text{syn}}i\\ \dot{a}& =1/{\tau }_{\text{ada}}(a_{current}(V-v_{\text{leak}})-a)\end{array}\end{array}$$

together with the jump condition

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

and transition equations

$$\begin{array}{r}\begin{array}{rl}v& =(1-z)v+z{v}_{\text{reset}}\\ i& =i+i_{\text{in}}\\ a& =a+a_{\text{spike}}{z}_{\text{rec}}\end{array}\end{array}$$

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