ExpIF

ExpIF#

class brainpy.state.ExpIF(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_T=Quantity(-59.9, "mV"), delta_T=Quantity(3.48, "mV"), V_initializer=Constant(value=-65. mV), spk_fun=ReluGrad(alpha=0.3, width=1.0), spk_reset='soft', name=None)#

Exponential Integrate-and-Fire (ExpIF) neuron model.

This model augments the LIF neuron by adding an exponential spike-initiation term, which provides a smooth approximation of the action potential onset and improves biological plausibility for cortical pyramidal cells.

The membrane potential dynamics follow:

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

Spike condition: If \(V \geq V_{th}\): emit spike and reset \(V = V_{reset}\) (hard reset) or \(V = V - (V_{th} - V_{reset})\) (soft 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) – Numerical 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_T (ArrayLike, default -59.9 * u.mV) – Threshold potential of the exponential term.

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

  • 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

ExpIFRef

ExpIF with absolute refractory period.

AdExIF

Adaptive exponential integrate-and-fire.

LIF

Simpler leaky integrate-and-fire without exponential term.

Notes

  • The model was first introduced by Nicolas Fourcaud-Trocmé, David Hansel, Carl van Vreeswijk and Nicolas Brunel [1]. The exponential nonlinearity was later confirmed by Badel et al. [3]. It is one of the prominent examples of a precise theoretical prediction in computational neuroscience that was later confirmed by experimental neuroscience.

  • The right-hand side of the above equation contains a nonlinearity that can be directly extracted from experimental data [3]. In this sense the exponential nonlinearity is not an arbitrary choice but directly supported by experimental evidence.

  • Even though it is a nonlinear model, it is simple enough to calculate the firing rate for constant input, and the linear response to fluctuations, even in the presence of input noise [4].

  • For a comprehensive treatment of this model, see [2] and [5].

References

Examples

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