Integrator

This demo implements a one-dimensional neural integrator.

This example utilizes a recurrent network. It shows how neurons can be used to implement stable dynamics. Such dynamics are important for memory, noise cleanup, statistical inference, and many other dynamic transformations.

[1]:
import matplotlib.pyplot as plt

%matplotlib inline

import nengo
from nengo.processes import Piecewise
import nengo_loihi

nengo_loihi.set_defaults()

Creating the network in Nengo

Our model consists of one recurrently connected ensemble, and an input node. The input node will provide a piecewise step function as input so that we can see the effects of recurrence.

[2]:
with nengo.Network(label="Integrator") as model:
    ens = nengo.Ensemble(n_neurons=120, dimensions=1)
    stim = nengo.Node(Piecewise({0: 0, 0.2: 1, 1: 0, 2: -2, 3: 0, 4: 1, 5: 0}))

    # Connect the population to itself
    tau = 0.1
    nengo.Connection(ens, ens, transform=[[1]], synapse=tau)
    nengo.Connection(stim, ens, transform=[[tau]], synapse=tau)

    # Collect data for plotting
    stim_probe = nengo.Probe(stim)
    ens_probe = nengo.Probe(ens, synapse=0.01)

Running the network in Nengo

We can use Nengo to see the desired model output.

[3]:
with nengo.Simulator(model) as sim:
    sim.run(6)
t = sim.trange()
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[4]:
def plot_decoded(t, data):
    plt.figure()
    plt.plot(t, data[stim_probe], label="Input")
    plt.plot(t, data[ens_probe], "k", label="Integrator output")
    plt.legend()


plot_decoded(t, sim.data)
../_images/loihi_integrator_6_0.png

Running the network with NengoLoihi

[5]:
with nengo_loihi.Simulator(model) as sim:
    sim.run(6)
t = sim.trange()
/home/tbekolay/Code/nengo-loihi/nengo_loihi/builder/discretize.py:481: UserWarning: Lost 2 extra bits in weight rounding
  warnings.warn("Lost %d extra bits in weight rounding" % (-s2,))
[6]:
plot_decoded(t, sim.data)
../_images/loihi_integrator_9_0.png

The network integrates its input, but without input decays quicker than the Nengo model. Likely the same workarounds discussed in the communication channel example will be useful here.