LeakyIntegrator

models.Neurons.LeakyIntegrator(
    self,
    tau=10.0,
    B=0.0,
    T=0.0,
    sum='sum(exc) - sum(inh)',
    noise=None,
)

Leaky-integrator rate-coded neuron, optionally noisy.

This simple rate-coded neuron defines an internal variable v(t) which integrates the inputs I(t) with a time constant \tau and a baseline B. An additive noise N(t) can be optionally defined:

\tau \cdot \frac{dv(t)}{dt} + v(t) = I(t) + B + N(t)

The transfer function is the positive (or rectified linear ReLU) function with a threshold T:

r(t) = (v(t) - T)^+

By default, the input I(t) to this neuron is “sum(exc) - sum(inh)”, but this can be changed by setting the sum argument:

neuron = ann.LeakyIntegrator(sum="sum('exc')")

By default, there is no additive noise, but the noise argument can be passed with a specific distribution:

neuron = ann.LeakyIntegrator(noise="Normal(0.0, 1.0)")

Parameters:

• tau = 10.0 : Time constant in ms of the neuron.
• B = 0.0 : Baseline value for v.
• T = 0.0 : Threshold for the positive transfer function.

Variables:

• v : internal variable (init = 0.0):

  tau * dv/dt + v = sum(exc) - sum(inh) + B + N

• r : firing rate (init = 0.0):

  r = pos(v - T)

The ODE is solved using the exponential Euler method.

Equivalent code:

LeakyIntegrator = Neuron(
    parameters='''
        tau = 10.0 : population
        B = 0.0
        T = 0.0 : population
    ''', 
    equations='''
        tau * dv/dt + v = sum(exc) - sum(inh) + B : exponential
        r = pos(v - T)
    '''
)

Parameters

Name	Type	Description	Default
tau	float	Time constant.	10.0
B	float	Baseline.	0.0
T	float	Threshold.	0.0
sum	str	Input sums.	'sum(exc) - sum(inh)'