Nengo Example: Squaring the Input

This demo shows you how to construct a network that squares the value encoded in a first population in the output of a second population.

Step 1: Create the Model

The model is comprised of an input ensemble ('A') and an output ensemble ('B'), from which the squared value of the input signal can be decoded.



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# Create the model object
import nengo
model = nengo.Network(label='Squaring')
with model:
    # Create two ensembles of 100 leaky-integrate-and-fire neurons
    A = nengo.Ensemble(nengo.LIF(100), dimensions=1)
    B = nengo.Ensemble(nengo.LIF(100), dimensions=1)

Step 2: Provide Input to the Model

A single input signal (a sine wave) will be used to drive the neural activity in ensemble A.



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import numpy as np
with model:
    # Create an input node that represents a sine wave
    sin = nengo.Node(output=np.sin)
    
    # Connect the input node to ensemble A
    nengo.Connection(sin, A)
    
    # Define the squaring function
    def square(x):
        return x[0] * x[0]
    
    # Connection ensemble A to ensemble B
    nengo.Connection(A, B, function=square)

Step 3: Probe the Output

Let's collect output data from each ensemble and output.



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with model:
    sin_probe = nengo.Probe(sin, 'output')
    A_probe = nengo.Probe(A, 'decoded_output', synapse=0.01)
    B_probe = nengo.Probe(B, 'decoded_output', synapse=0.01)

Step 4: Run the Model



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# Create the simulator
sim = nengo.Simulator(model)
# Run the simulator for 5 seconds
sim.run(5)



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import matplotlib.pyplot as plt

# Plot the input signal and decoded ensemble values
plt.plot(sim.trange(), sim.data[A_probe],  label='Decoded Ensemble A')
plt.plot(sim.trange(), sim.data[B_probe], label='Decoded Ensemble B')
plt.plot(sim.trange(), sim.data[sin_probe], label='Input Sine Wave', color='k', linewidth=2.0)
plt.legend(loc='best')
plt.ylim(-1.2, 1.2)

The plotted ouput of ensemble B should show the decoded squared value of the input sine wave.