Two neurons

This demo shows how to construct and manipulate a complementary pair of neurons.

These are leaky integrate-and-fire (LIF) neurons. The neuron tuning properties have been selected so there is one ‘on’ and one ‘off’ neuron.

One neuron will increase for positive input, and the other will decrease. This can be thought of as the simplest population that is able to give a reasonable representation of a scalar value.

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

import nengo
from nengo.dists import Uniform
from nengo.utils.matplotlib import rasterplot

Step 1: Create the neurons

model = nengo.Network(label='Two Neurons')
with model:
    neurons = nengo.Ensemble(
        2, dimensions=1,  # Representing a scalar
        intercepts=Uniform(-.5, -.5),  # Set the intercepts at .5
        max_rates=Uniform(100, 100),  # Set the max firing rate at 100hz
        encoders=[[1], [-1]])  # One 'on' and one 'off' neuron

Step 2: Create input for the model

Create an input node generating a sine wave.

with model:
    sin = nengo.Node(lambda t: np.sin(8 * t))

Step 3: Connect the network elements

with model:
    nengo.Connection(sin, neurons, synapse=0.01)

Step 4: Probe outputs

Anything that is probed will collect the data it produces over time, allowing us to analyze and visualize it later.

with model:
    sin_probe = nengo.Probe(sin)  # The original input
    spikes = nengo.Probe(neurons.neurons)  # Raw spikes from each neuron
    # Subthreshold soma voltages of the neurons
    voltage = nengo.Probe(neurons.neurons, 'voltage')
    # Spikes filtered by a 10ms post-synaptic filter
    filtered = nengo.Probe(neurons, synapse=0.01)

Step 5: Run the model

with nengo.Simulator(model) as sim:  # Create a simulator
    sim.run(1)  # Run it for 1 second

Step 6: Plot the results

t = sim.trange()

# Plot the decoded output of the ensemble
plt.figure()
plt.plot(t, sim.data[filtered])
plt.plot(t, sim.data[sin_probe])
plt.xlim(0, 1)

# Plot the spiking output of the ensemble
plt.figure(figsize=(10, 8))
plt.subplot(2, 2, 1)
rasterplot(t, sim.data[spikes], colors=[(1, 0, 0), (0, 0, 0)])
plt.yticks((1, 2), ("On neuron", "Off neuron"))
plt.ylim(2.5, 0.5)

# Plot the soma voltages of the neurons
plt.subplot(2, 2, 2)
plt.plot(t, sim.data[voltage][:, 0] + 1, 'r')
plt.plot(t, sim.data[voltage][:, 1], 'k')
plt.yticks(())
plt.axis([0, 1, 0, 2])
plt.subplots_adjust(wspace=0.05);

The top graph shows the input signal in green and the filtered output spikes from the two neurons population in blue. The spikes (that are filtered) from the ‘on’ and ‘off’ neurons are shown in the bottom graph on the left. On the right are the subthreshold voltages for the neurons.