LIF

class brainpy.state.LIF(in_size, R=Quantity(1., "ohm"), tau=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 (LIF) neuron model.

This class implements the Leaky Integrate-and-Fire neuron model, which extends the basic Integrate-and-Fire model by adding a leak term. The leak causes the membrane potential to decay towards a resting value in the absence of input, making the model more biologically plausible.

The model is characterized by the following differential equation:

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

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 5. * u.ms) – Membrane time constant.

• 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

See also

IF

Perfect integrator without leak.

LIFRef

LIF with absolute refractory period.

ALIF

Adaptive LIF with spike-frequency adaptation.

ExpIF

LIF with exponential spike initiation.

Notes

• The leak term causes the membrane potential to decay exponentially towards V_rest with time constant tau when no input is present.

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

• Spike generation is non-differentiable, so surrogate gradients are used for backpropagation during training.

• For a detailed treatment of LIF models, see [1] and [2].

References

[1]

Gerstner, W., Kistler, W. M., Naud, R., & Paninski, L. (2014). Neuronal dynamics: From single neurons to networks and models of cognition. Cambridge University Press.

[2]

Burkitt, A. N. (2006). A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biological cybernetics, 95(1), 1-19.

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create a LIF neuron layer with 10 neurons
>>> lif = brainpy.state.LIF(10, tau=10*u.ms, V_th=0.8*u.mV)
>>> # Initialize the state
>>> lif.init_state(batch_size=1)
>>> # Apply an input current and update the neuron state
>>> spikes = lif.update(x=1.5*u.mA)

get_spike(V=None)

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)

State initialization function.

reset_state(batch_size=None, **kwargs)

State resetting function.