ALIF¶

class ALIF(shape: tuple[int, ...] | int, step_time: float, *, rest_v: float, reset_v: float, thresh_eq_v: float, refrac_t: float, tc_membrane: float, tc_adaptation: float | tuple[float, ...], spike_increment: float | tuple[float, ...], resistance: float = 1.0, batch_size: int = 1, batch_reduction: Callable[[Tensor, tuple[int, ...]], Tensor] | None = None)[source]¶

Bases: AdaptiveThresholdMixin, VoltageMixin, SpikeRefractoryMixin, InfernoNeuron

Simulation of adaptive leaky integrate-and-fire (ALIF) neuron dynamics.

ALIF is implemented as a step of leaky integrate-and-fire applying existing adaptations, using linear spike-dependent adaptive thresholds, then updating those adaptations for the next time step.

\[\begin{split}\begin{align*} V_m(t + \Delta t) &= \left[ V_m(t) - V_\text{rest} - R_mI(t) \right] \exp\left(-\frac{t}{\tau_m}\right) + V_\text{rest} + R_mI(t) \\ \Theta(t) &= \Theta_\infty + \sum_k \theta_k(t) \\ \theta_k(t + \Delta t) &= \theta_k(t) \exp\left(-\frac{\Delta t}{\tau_k}\right) \end{align*}\end{split}\]

If a spike was generated at time $t$, then.

\[\begin{split}\begin{align*} V_m(t) &\leftarrow V_\text{reset} \\ \theta_k(t) &\leftarrow \theta_k(t) + d_k \end{align*}\end{split}\]

Parameters:

shape (tuple[int, ...] | int) – shape of the group of neurons being simulated.
step_time (float) – length of a simulation time step, $\Delta t$, in $\text{ms}$.
rest_v (float) – membrane potential difference at equilibrium, $V_\text{rest}$, in $\text{mV}$.
reset_v (float) – membrane voltage after an action potential is generated, $V_\text{reset}$, in $\text{mV}$.
thresh_eq_v (float) – equilibrium of the firing threshold, $\Theta_\infty$$, in $\text{mV}$.
refrac_t (float) – length the absolute refractory period, in $\text{ms}$.
tc_membrane (float) – time constant of exponential decay for membrane voltage, $\tau_m$, in $\text{ms}$.
tc_adaptation (float | tuple[float, ...]) – time constant of exponential decay for threshold adaptations, $\tau_k$, in $\text{ms}$.
spike_increment (float | tuple[float, ...]) – amount by which the adaptive threshold is increased after a spike, $d_k$, in $\text{mV}$.
resistance (float, optional) – resistance across the cell membrane, $R_m$, in $\text{M}\Omega$. Defaults to 1.0.
batch_size (int, optional) – size of input batches for simulation. Defaults to 1.
batch_reduction (Callable[[torch.Tensor, tuple[int, ...]], torch.Tensor] | None) – function to reduce adaptation updates over the batch dimension, torch.mean() when None. Defaults to None.

Note

batch_reduction can be one of the functions in PyTorch including but not limited to torch.sum(), torch.mean(), and torch.amax(). A custom function with similar behavior can also be passed in. Like with the included function, it should not keep the original dimensions by default.