AdExIFRef

AdExIFRef#

class brainpy.state.AdExIFRef(in_size, R=Quantity(1., "ohm"), tau=Quantity(10., "ms"), tau_w=Quantity(30., "ms"), tau_ref=Quantity(1.7, "ms"), V_th=Quantity(-55., "mV"), V_reset=Quantity(-68., "mV"), V_rest=Quantity(-65., "mV"), V_T=Quantity(-59.9, "mV"), delta_T=Quantity(3.48, "mV"), a=Quantity(1., "S"), b=Quantity(1., "mA"), V_initializer=Constant(value=-65. mV), w_initializer=Constant(value=0. mA), spk_fun=ReluGrad(alpha=0.3, width=1.0), spk_reset='soft', ref_var=False, name=None)#

Adaptive exponential Integrate-and-Fire neuron model with refractory mechanism.

This model extends AdExIF by adding an absolute refractory period. While the exponential spike-initiation term and adaptation current keep the membrane potential dynamics biologically realistic, the refractory mechanism prevents the neuron from firing within tau_ref after a spike.

The membrane dynamics are governed by two coupled differential equations:

\[ \tau \frac{dV}{dt} = -(V - V_{rest}) + \Delta_T \exp\left(\frac{V - V_T}{\Delta_T}\right) - R w + R \cdot I(t) \]

\[ \tau_w \frac{dw}{dt} = a (V - V_{rest}) - w \]

After each spike the membrane potential is reset and the adaptation current increases by b. During the refractory period, the membrane potential remains at the reset value.

Parameters:

  • in_size (Union[int, Sequence[int], integer, Sequence[integer]]) – Size of the input to the neuron.

  • R (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Membrane resistance.

  • tau (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Membrane time constant.

  • tau_w (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Adaptation current time constant.

  • tau_ref (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Absolute refractory period duration.

  • V_th (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Spike threshold used for reset.

  • V_reset (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Reset potential after spike.

  • V_rest (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Resting membrane potential.

  • V_T (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Threshold of the exponential term.

  • delta_T (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Spike slope factor controlling the sharpness of spike initiation.

  • a (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Coupling strength from voltage to adaptation current.

  • b (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Increment of the adaptation current after a spike.

  • V_initializer (Callable) – Initializer for the membrane potential state.

  • w_initializer (Callable) – Initializer for the adaptation current.

  • spk_fun (Callable) – Surrogate gradient function for the spike generation.

  • spk_reset (str) – Reset mechanism after spike generation.

  • ref_var (bool) – Whether to expose a boolean refractory state variable.

  • name (str) – Name of the neuron layer.

V#

Membrane potential.

Type:

HiddenState

w#

Adaptation current.

Type:

HiddenState

last_spike_time#

Last spike time recorder.

Type:

ShortTermState

refractory#

Neuron refractory state (if ref_var=True).

Type:

HiddenState

See also

AdExIF

AdExIF without refractory period.

ExpIFRef

ExpIF with refractory period but no adaptation.

Notes

  • The AdExIF model with refractory period combines adaptation dynamics with an absolute refractory period for more biologically realistic behavior.

  • For detailed information about this model, see [1] and [2].

References

See also

brainpy.dyn.AdExIFRef for the dynamical-system counterpart.

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an AdExIFRef neuron layer with 10 neurons
>>> adexif_ref = brainpy.state.AdExIFRef(10, tau=10*u.ms, tau_ref=2*u.ms)
>>> # Initialize the state
>>> adexif_ref.init_state(batch_size=1)
get_spike(V=None)[source]#

Generate spikes based on neuron state variables.

This abstract method must be implemented by subclasses to define the spike generation mechanism. The method should use the surrogate gradient function self.spk_fun to enable gradient-based learning.

Parameters:

  • *args – Positional arguments (typically state variables like membrane potential)

  • **kwargs – Keyword arguments

Returns:

Binary spike tensor where 1 indicates a spike and 0 indicates no spike.

Return type:

ArrayLike

Raises:

NotImplementedError – If the subclass does not implement this method.

init_state(batch_size=None, **kwargs)[source]#

State initialization function.

reset_state(batch_size=None, **kwargs)[source]#

State resetting function.