AdExIF

AdExIF#

class brainpy.state.AdExIF(in_size, R=Quantity(1., "ohm"), tau=Quantity(10., "ms"), tau_w=Quantity(30., "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', name=None)#

Adaptive exponential Integrate-and-Fire (AdExIF) neuron model.

This model extends ExpIF by adding an adaptation current w that is incremented after each spike and relaxes with time constant tau_w. The membrane dynamics are governed by two coupled differential equations [1]:

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

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

After each spike the membrane potential is reset and the adaptation current increases by b. This simple mechanism generates rich firing patterns such as spike-frequency adaptation and bursting.

Parameters:

  • in_size (Size) – Size of the input to the neuron.

  • R (ArrayLike, default 1. * u.ohm) – Membrane resistance.

  • tau (ArrayLike, default 10. * u.ms) – Membrane time constant.

  • tau_w (ArrayLike, default 30. * u.ms) – Adaptation current time constant.

  • V_th (ArrayLike, default -55. * u.mV) – Spike threshold used for reset.

  • V_reset (ArrayLike, default -68. * u.mV) – Reset potential after spike.

  • V_rest (ArrayLike, default -65. * u.mV) – Resting membrane potential.

  • V_T (ArrayLike, default -59.9 * u.mV) – Threshold of the exponential term.

  • delta_T (ArrayLike, default 3.48 * u.mV) – Spike slope factor controlling the sharpness of spike initiation.

  • a (ArrayLike, default 1. * u.siemens) – Coupling strength from voltage to adaptation current.

  • b (ArrayLike, default 1. * u.mA) – 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, default surrogate.ReluGrad()) – Surrogate gradient function for the spike generation.

  • spk_reset (str, default 'soft') – Reset mechanism after spike generation.

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

V#

Membrane potential.

Type:

HiddenState

w#

Adaptation current.

Type:

HiddenState

See also

AdExIFRef

AdExIF with absolute refractory period.

ExpIF

Exponential IF without adaptation.

LIF

Simpler leaky integrate-and-fire.

Notes

  • The AdEx model can reproduce a wide variety of neuronal firing patterns including regular spiking, bursting, and spike-frequency adaptation.

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

References

See also

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

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an AdExIF neuron layer with 10 neurons
>>> adexif = brainpy.state.AdExIF(10, tau=10*u.ms)
>>> # Initialize the state
>>> adexif.init_state(batch_size=1)
>>> # Apply an input current and update the neuron state
>>> spikes = adexif.update(x=1.5*u.mA)
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.