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()

/home/travis/build/nengo/nengo-loihi/nengo_loihi/version.py:23: UserWarning: This version of `nengo_loihi` has not been tested with your `nengo` version (3.0.1.dev0). The latest fully supported version is 3.0.0
  "supported version is %s" % (nengo.__version__, latest_nengo_version)
/home/travis/virtualenv/python3.6.3/lib/python3.6/site-packages/nengo_dl/version.py:42: UserWarning: This version of `nengo_dl` has not been tested with your `nengo` version (3.0.1.dev0). The latest fully supported version is 3.0.0.
  % ((nengo.version.version,) + latest_nengo_version)

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()

[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)

Running the network with Nengo Loihi¶

[5]:

with nengo_loihi.Simulator(model) as sim:
    sim.run(6)
t = sim.trange()

/home/travis/build/nengo/nengo-loihi/nengo_loihi/discretize.py:471: UserWarning: Lost 2 extra bits in weight rounding
  warnings.warn("Lost %d extra bits in weight rounding" % (-s2,))

[6]:

plot_decoded(t, sim.data)

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.