LIFRef

LIFRef#

class brainpy.state.LIFRef(in_size, R=Quantity(1., "ohm"), tau=Quantity(5., "ms"), tau_ref=Quantity(5., "ms"), V_th=Quantity(1., "mV"), V_reset=Quantity(0., "mV"), V_rest=Quantity(0., "mV"), V_initializer=Constant(value=0. mV), spk_fun=ReluGrad(alpha=0.3, width=1.0), spk_reset='soft', name=None)#

Leaky Integrate-and-Fire neuron model with refractory period.

This class implements a Leaky Integrate-and-Fire neuron model that includes a refractory period after spiking, during which the neuron cannot fire regardless of input. This better captures the behavior of biological neurons that exhibit a recovery period after action potential generation.

The model is characterized by the following equations:

When not in refractory period:

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

During refractory period:

\[ V = V_{reset} \]

Spike condition: If \(V \geq V_{th}\): emit spike, set \(V = V_{reset}\), and enter refractory period for \(\tau_{ref}\)

Parameters:

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

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

  • tau (ArrayLike, default 5. * u.ms) – Membrane time constant.

  • tau_ref (ArrayLike, default 5. * u.ms) – Refractory period duration.

  • V_th (ArrayLike, default 1. * u.mV) – Firing threshold voltage.

  • V_reset (ArrayLike, default 0. * u.mV) – Reset voltage after spike.

  • V_rest (ArrayLike, default 0. * u.mV) – Resting membrane potential.

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

  • spk_fun (Callable, default surrogate.ReluGrad()) – Surrogate gradient function for the non-differentiable spike generation.

  • spk_reset (str, default 'soft') – Reset mechanism after spike generation: - ‘soft’: subtract threshold V = V - V_th - ‘hard’: strict reset using stop_gradient

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

V#

Membrane potential.

Type:

HiddenState

last_spike_time#

Time of the last spike, used to implement refractory period.

Type:

ShortTermState

See also

LIF

LIF without refractory period.

ALIF

Adaptive LIF with spike-frequency adaptation.

Notes

  • The refractory period is implemented by tracking the time of the last spike and preventing membrane potential updates if the elapsed time is less than tau_ref.

  • During the refractory period, the membrane potential remains at the reset value regardless of input current strength.

  • Refractory periods prevent high-frequency repetitive firing and are critical for realistic neural dynamics [3].

  • The time-dependent dynamics are integrated using an exponential Euler method.

  • The simulation environment time variable ‘t’ is used to track the refractory state.

  • For a comprehensive treatment of LIF models with refractory periods, see [1] and [2].

References

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create a LIFRef neuron layer with 10 neurons
>>> lifref = brainpy.state.LIFRef(10, tau=10*u.ms, tau_ref=5*u.ms,
...                               V_th=0.8*u.mV)
>>> # Initialize the state
>>> lifref.init_state(batch_size=1)
>>> # Apply an input current and update the neuron state
>>> spikes = lifref.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.