QuaIF

QuaIF#

class brainpy.state.QuaIF(in_size, R=Quantity(1., "ohm"), tau=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"), V_initializer=Constant(value=-65. mV), spk_fun=ReluGrad(alpha=0.3, width=1.0), spk_reset='soft', name=None)#

Quadratic Integrate-and-Fire (QuaIF) neuron model.

This model extends the basic integrate-and-fire neuron by adding a quadratic nonlinearity in the voltage dynamics. The quadratic term creates a soft spike initiation, making the model more biologically realistic than the linear IF model.

The model is characterized by the following differential equation:

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

Spike condition: If \(V \geq V_{th}\): emit spike and reset \(V = V_{reset}\)

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.

  • 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. Must be larger than V_rest.

  • c (ArrayLike, default 0.07 / u.mV) – Coefficient describing membrane potential update. Larger than 0.

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

  • 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

See also

AdQuaIF

Adaptive quadratic integrate-and-fire.

AdQuaIFRef

Adaptive quadratic IF with refractory period.

ExpIF

Exponential integrate-and-fire (alternative nonlinear model).

Notes

  • The quadratic nonlinearity provides a more realistic spike initiation compared to LIF.

  • The critical voltage V_c determines the onset of spike generation.

  • When V approaches V_c, the quadratic term causes rapid acceleration toward threshold.

  • This model can exhibit Type I excitability (continuous f-I curve) [1].

References

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create a QuaIF neuron layer with 10 neurons
>>> quaif = brainpy.state.QuaIF(10, tau=10*u.ms, V_th=-30*u.mV,
...                             V_c=-50*u.mV)
>>> # Initialize the state
>>> quaif.init_state(batch_size=1)
>>> # Apply an input current and update the neuron state
>>> spikes = quaif.update(x=2.5*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.