class snntorch._neurons.lapicque.Lapicque(beta=False, R=False, C=False, time_step=1, threshold=1.0, spike_grad=None, surrogate_disable=False, init_hidden=False, inhibition=False, learn_beta=False, learn_threshold=False, reset_mechanism='subtract', state_quant=False, output=False)[source]

Bases: LIF

An extension of Lapicque’s experimental comparison between extracellular nerve fibers and an RC circuit. It is qualitatively equivalent to Leaky but defined using RC circuit parameters. Input stimulus is integrated by membrane potential which decays exponentially with a rate of beta. For \(U[T] > U_{\rm thr} ⇒ S[T+1] = 1\).

If reset_mechanism = “subtract”, then \(U[t+1]\) will have threshold subtracted from it whenever the neuron emits a spike:

\[U[t+1] = I_{\rm in}[t+1] (\frac{T}{C}) + (1- \frac{T}{\tau})U[t] - RU_{\rm thr}\]

If reset_mechanism = “zero”, then \(U[t+1]\) will be set to 0 whenever the neuron emits a spike:

\[U[t+1] = I_{\rm in}[t+1] (\frac{T}{\tau}) + (1- \frac{T}{\tau})U[t] - R(I_{\rm in}[t+1] (\frac{T}{C}) + (1- \frac{T}{\tau})U[t])\]
  • \(I_{\rm in}\) - Input current

  • \(U\) - Membrane potential

  • \(U_{\rm thr}\) - Membrane threshold

  • \(T\)- duration of each time step

  • \(R\) - Reset mechanism: if active, \(R = 1\), otherwise \(R = 0\)

  • \(β\) - Membrane potential decay rate. Alternatively, the membrane potential decay rate β can be specified instead:

\[β = e^{-1/RC}\]
  • \(R\) - Parallel resistance of passive membrane (note: distinct from the reset \(R\))

  • \(C\) - Parallel capacitance of passive membrane


  • If only β is defined, then R will default to 1, and C will be inferred.

  • If RC is defined, β will be automatically calculated.

  • If (β and R) or (β and C) are defined, the missing variable will be automatically calculated.

  • Note that β, R and C are treated as ‘hard-wired’ physically plausible parameters, and are therefore not learnable. For a single-state neuron with a learnable decay rate β, use snn.Leaky instead.


import torch
import torch.nn as nn
import snntorch as snn

beta = 0.5

R = 1
C = 1.44

# Define Network
class Net(nn.Module):
    def __init__(self):

        # initialize layers
        self.fc1 = nn.Linear(num_inputs, num_hidden)
        self.lif1 = snn.Lapicque(beta=beta)
        self.fc2 = nn.Linear(num_hidden, num_outputs)
        self.lif2 = snn.Lapicque(R=R, C=C)  # lif1 and lif2 are
        approximately equivalent

    def forward(self, x, mem1, spk1, mem2):
        cur1 = self.fc1(x)
        spk1, mem1 = self.lif1(cur1, mem1)
        cur2 = self.fc2(spk1)
        spk2, mem2 = self.lif2(cur2, mem2)
        return mem1, spk1, mem2, spk2

For further reading, see:

L. Lapicque (1907) Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation. J. Physiol. Pathol. Gen. 9, pp. 620-635. (French)

N. Brunel and M. C. Van Rossum (2007) Lapicque’s 1907 paper: From frogs to integrate-and-fire. Biol. Cybern. 97, pp. 337-339. (English)

Although Lapicque did not formally introduce this as an integrate-and-fire neuron model, we pay homage to his discovery of an RC circuit mimicking the dynamics of synaptic current.

  • beta (float or torch.tensor, Optional) – RC potential decay rate. Clipped between 0 and 1 during the forward-pass. May be a single-valued tensor (i.e., equal decay rate for all neurons in a layer), or multi-valued (one weight per neuron).

  • R (int or torch.tensor, Optional) – Resistance of RC circuit

  • C (int or torch.tensor, Optional) – Capacitance of RC circuit

  • time_step (float, Optional) – time step precision. Defaults to 1

  • threshold (float, optional) – Threshold for \(mem\) to reach in order to generate a spike S=1. Defaults to 1

  • spike_grad (surrogate gradient function from snntorch.surrogate, optional) – Surrogate gradient for the term dS/dU. Defaults to None (corresponds to ATan surrogate gradient. See snntorch.surrogate for more options)

  • surrogate_disable (bool, Optional) – Disables surrogate gradients regardless of spike_grad argument. Useful for ONNX compatibility. Defaults to False

  • init_hidden (bool, optional) – Instantiates state variables as instance variables. Defaults to False

  • inhibition (bool, optional) – If True, suppresses all spiking other than the neuron with the highest state. Defaults to False

  • learn_beta (bool, optional) – Option to enable learnable beta. Defaults to False

  • learn_threshold (bool, optional) – Option to enable learnable threshold. Defaults to False

  • reset_mechanism (str, optional) – Defines the reset mechanism applied to \(mem\) each time the threshold is met. Reset-by-subtraction: “subtract”, reset-to-zero: “zero”, none: “none”. Defaults to “none”

  • state_quant (quantization function from snntorch.quant, optional) – If specified, hidden state \(mem\) is quantized to a valid state for the forward pass. Defaults to False

  • output (bool, optional) – If True as well as init_hidden=True, states are returned when neuron is called. Defaults to False

Inputs: input_, mem_0
  • input_ of shape (batch, input_size): tensor containing

input features - mem_0 of shape (batch, input_size): tensor containing the initial membrane potential for each element in the batch.

Outputs: spk, mem_1
  • spk of shape (batch, input_size): tensor containing the

output spikes. - mem_1 of shape (batch, input_size): tensor containing the next membrane potential for each element in the batch

Learnable Parameters:
  • Lapcique.beta (torch.Tensor) - optional learnable weights must

be manually passed in, of shape 1 or (input_size). - Lapcique.threshold (torch.Tensor) - optional learnable thresholds must be manually passed in, of shape 1 or`` (input_size).

classmethod detach_hidden()[source]

Returns the hidden states, detached from the current graph. Intended for use in truncated backpropagation through time where hidden state variables are instance variables.

forward(input_, mem=None)[source]

Define the computation performed at every call.

Should be overridden by all subclasses.


Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.


Deprecated, use Lapicque.reset_mem instead

classmethod reset_hidden()[source]

Used to clear hidden state variables to zero. Intended for use where hidden state variables are instance variables.