adaptive_thresholds_linear_voltage

adaptive_thresholds_linear_voltage(adaptations: Tensor, voltages: Tensor, *, step_time: float | Tensor, rest_v: float | Tensor, adapt_rate: float | Tensor, rebound_rate: float | Tensor, adapt_reset_min: float | Tensor | None = None, spikes: Tensor | None = None, refracs: Tensor | None = None) → Tensor[source]

Update adaptive thresholds based on membrane potential.

Implemented as an approximation using Euler’s method.

\[\theta_k(t + \Delta t) = \Delta t \left[a_k \left[ V_m(t) - V_\text{rest} \right] - b_k \theta_k(t)\right] + \theta_k(t)\]

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

\[\theta_k(t) \leftarrow \max(\theta_k(t), \theta_\text{reset})\]
Parameters:

  • adaptations (torch.Tensor) – last adaptations applied to membrane voltage threshold, \(\theta_k\), in \(\text{mV}\).

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

  • step_time (float | torch.Tensor) – length of a simulation time step, \(\Delta t\), in \(\text{ms}\).

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

  • adapt_rate (float | torch.Tensor) – rate constant of exponential decay for membrane voltage term, \(a_k\), in \(\text{ms}^{-1}\).

  • rebound_rate (float | torch.Tensor) – rate constant of exponential decay for threshold voltage term, \(b_k\), in \(\text{ms}^{-1}\).

  • adapt_reset_min (float | torch.Tensor | None, optional) – lower bound for the threshold adaptation permitted after a postsynaptic potential, \(\theta_\text{reset}\), in \(\text{mV}\). Defaults to None.

  • spikes (torch.Tensor | None, optional) – if the corresponding neuron generated an action potential. Defaults to None.

  • 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:

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

voltages, spikes, refracs:

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

rest_v:

Broadcastable with voltages, spikes, and refracs.

step_time, adapt_rate, rebound_rate, adapt_reset_min:

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.

Note

If either adapt_reset_min or spikes is None, then no lower bound will be applied to threshold adaptations.

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 Threshold, Linear Voltage-Dependent in the zoo.