from nengo.neurons import LIFRate
from nengo.params import NumberParam
import numpy as np
[docs]class SoftLIFRate(LIFRate):
"""LIF neuron with smoothing around the firing threshold.
This is a rate version of the LIF neuron whose tuning curve has a
continuous first derivative, due to the smoothing around the firing
threshold. It can be used as a substitute for LIF neurons in deep networks
during training, and then replaced with LIF neurons when running
the network [1]_.
Parameters
----------
sigma : float
Amount of smoothing around the firing threshold. Larger values mean
more smoothing.
tau_rc : float
Membrane RC time constant, in seconds. Affects how quickly the membrane
voltage decays to zero in the absence of input (larger = slower decay).
tau_ref : float
Absolute refractory period, in seconds. This is how long the
membrane voltage is held at zero after a spike.
amplitude : float
Scaling factor on the neuron output. Corresponds to the relative
amplitude of the output spikes of the neuron.
References
----------
.. [1] Eric Hunsberger and Chris Eliasmith (2015): Spiking deep networks
with LIF neurons. https://arxiv.org/abs/1510.08829.
Notes
-----
Adapted from
https://github.com/nengo/nengo-extras/blob/master/nengo_extras/neurons.py
"""
sigma = NumberParam('sigma', low=0, low_open=True)
def __init__(self, sigma=1.0, **lif_args):
super(SoftLIFRate, self).__init__(**lif_args)
self.sigma = sigma
self._epsilon = 1e-15
@property
def _argreprs(self):
args = super(SoftLIFRate, self)._argreprs
if self.sigma != 1.0:
args.append("sigma=%s" % self.sigma)
return args
[docs] def rates(self, x, gain, bias):
J = gain * x
J += bias
out = np.zeros_like(J)
self.step_math(dt=1, J=J, output=out)
return out
[docs] def step_math(self, dt, J, output):
"""Compute rates in Hz for input current (incl. bias)"""
j = J - 1
js = j / self.sigma
j_valid = js > -20
z = np.where(js > 30, js, np.log1p(np.exp(js))) * self.sigma
q = np.where(j_valid, np.log1p(1 / z), -js - np.log(self.sigma))
output[:] = self.amplitude / (self.tau_ref + self.tau_rc * q)