LeakyIntegrator

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 global time constant \tau and a local 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(ampa)")

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)")

Equivalent code:

LeakyIntegrator = Neuron(
    parameters=dict(
        tau = 10.0,
        B = ann.Parameter(0.0),
        T = 0.0,
    ), 
    equations=[
        ann.Variable()'tau * dv/dt + v = sum(exc) - sum(inh) + B', method=exponential),
        'r = pos(v - T)',
    ]
)

Parameters

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