adaptive_currents_linear

adaptive_currents_linear(adaptations: Tensor, voltages: Tensor, spikes: Tensor, *, step_time: float | Tensor, rest_v: float | Tensor, time_constant: float | Tensor, voltage_coupling: float | Tensor, spike_increment: float | Tensor, refracs: Tensor | None = None) → Tensor[source]

Update adaptive currents based on membrane potential and postsynaptic spikes.

Implemented as an approximation using Euler’s method.

\[w_k(t + \Delta t) = \frac{\Delta t}{\tau_k} \left[ a_k \left[ V_m(t) - V_\text{rest} \right] - w_k(t) \right] + w_k(t)\]

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

\[w_k(t) \leftarrow w_k(t) + b_k\]
Parameters:

  • adaptations (torch.Tensor) – last adaptations applied to input current, \(w_k\), in \(\text{nA}\).

  • voltages (torch.Tensor) – membrane voltages \(V_m(t)\), 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, in \(\text{ms}\).

  • rest_v (float | torch.Tensor) – membrane potential difference at equilibrium, \(V_\text{rest}\), in \(\text{mV}\).

  • time_constant (float | torch.Tensor) – time constant of exponential decay, \(\tau_k\), in \(\text{ms}\).

  • voltage_coupling (float | torch.Tensor) – strength of coupling to membrane voltage, \(a_k\), in \(\mu\text{S}\).

  • spike_increment (float | torch.Tensor) – amount by which the adaptive current is increased after a spike, \(b_k\), in \(\text{nA}\).

  • 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 input currents, in \(\text{nA}\).

Return type:

torch.Tensor

Shape

adaptations:

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

voltages, spikes, refracs:

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

rest_v:

Broadcastable with voltages, spikes, and refracs.

step_time, voltage_coupling, spike_increment, time_constant:

Broadcastable with adaptations.

return:

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

Where:

  • \(B\) is the batch size.

  • \(N_0, \ldots\) are dimensions of the group of neurons simulated.

  • \(K\) is the number of sets of adaptation parameters.

Tip

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

See also

For more details and references, visit Adaptive Current, Linear in the zoo.