AdQuaIF

AdQuaIF#

class brainpy.state.AdQuaIF(in_size, R=Quantity(1., "ohm"), tau=Quantity(10., "ms"), tau_w=Quantity(10., "ms"), V_th=Quantity(-30., "mV"), V_reset=Quantity(-68., "mV"), V_rest=Quantity(-65., "mV"), V_c=Quantity(-50., "mV"), c=Quantity(0.07, "1 / mV"), a=Quantity(1., "S"), b=Quantity(0.1, "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 Quadratic Integrate-and-Fire (AdQuaIF) neuron model.

This model extends the QuaIF model by adding an adaptation current that increases after each spike and decays exponentially between spikes. The adaptation mechanism produces spike-frequency adaptation and enables the neuron to exhibit various firing patterns.

The model is characterized by the following differential equations:

\[ \tau \frac{dV}{dt} = c(V - V_{rest})(V - V_c) - w + R \cdot I(t) \]

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

After a spike: \(V \rightarrow V_{reset}\), \(w \rightarrow w + b\)

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 10. * u.ms) – Adaptation current time constant.

  • V_th (ArrayLike, default -30. * u.mV) – Firing threshold voltage.

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

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

  • V_c (ArrayLike, default -50. * u.mV) – Critical voltage for spike initiation.

  • c (ArrayLike, default 0.07 / u.mV) – Coefficient describing membrane potential update.

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

  • b (ArrayLike, default 0.1 * u.mA) – Increment of 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.

  • 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

QuaIF

Quadratic IF without adaptation.

AdQuaIFRef

Adaptive quadratic IF with refractory period.

AdExIF

Adaptive exponential IF (alternative adaptive model).

Notes

  • The adaptation current w provides negative feedback, reducing firing rate.

  • Parameter ‘a’ controls subthreshold adaptation (coupling from V to w).

  • Parameter ‘b’ controls spike-triggered adaptation (increment after spike).

  • With appropriate parameters, can exhibit regular spiking, bursting, etc. [1].

  • The adaptation time constant tau_w determines adaptation speed.

  • For a detailed bifurcation analysis of this model class, see [2].

References

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an AdQuaIF neuron layer with 10 neurons
>>> adquaif = brainpy.state.AdQuaIF(10, tau=10*u.ms, tau_w=100*u.ms,
...                                 a=1.0*u.siemens, b=0.1*u.mA)
>>> # Initialize the state
>>> adquaif.init_state(batch_size=1)
>>> # Apply an input current and observe spike-frequency adaptation
>>> spikes = adquaif.update(x=3.0*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.