adaptive_thresholds_linear_spike¶

adaptive_thresholds_linear_spike(adaptations: Tensor, spikes: Tensor, *, step_time: float | Tensor, time_constant: float | Tensor, spike_increment: float | Tensor, refracs: Tensor | None = None) → Tensor[source]¶

Update adaptive thresholds based on postsynaptic spikes.

\[\theta_k(t + \Delta t) = \theta_k(t) \exp\left(-\frac{\Delta t}{\tau_k}\right)\]

If a spike was generated at time \(t\), then.

\[\theta_k(t) \leftarrow \theta_k(t) + a_k\]

Parameters:

adaptations (torch.Tensor) – last adaptations applied to membrane voltage threshold, \(\theta_k\), in \(\text{mV}\).
spikes (torch.Tensor) – if the corresponding neuron generated an action potential.
step_time (float | torch.Tensor) – length of a simulation time step, \(\Delta t\), in \(\text{ms}\).
time_constant (float | torch.Tensor) – time constant of exponential decay for the adaptations, \(\tau_k\), in \(\text{ms}\).
spike_increment (torch.Tensor) – amount by which the adaptive threshold is increased after a spike, \(a_k\), in \(\text{mV}\).
refracs (torch.Tensor | None) – remaining absolute refractory periods, in \(\text{ms}\), when not None, adaptations of neurons in their absolute refractory periods are maintained. Defaults to None.

Returns:

updated adaptations for membrane voltage threshold, in \(\text{mV}\).

Return type:

torch.Tensor

Shape

adaptations:

\(N_0 \times \cdots \times K\)

spikes, refracs:

\([B] \times N_0 \times \cdots\)

step_time, time_constant, spike_increment:

Broadcastable with adaptations.

return:

\([B] \times N_0 \times \cdots \times K\)

Where:

Tip

This function doesn’t automatically reduce along the batch dimension, this should generally be done by averaging along the \(0^\text{th}\) dimension.