Neuron to neuron connections

While Nengo is often used with deep learning and NEF style networks, it can also be used for lower level models in which each neuron to neuron connection is explicitly specified.

In these examples, we connect a pre population to a post population with different sets of specified connection weights.

import matplotlib.pyplot as plt

%matplotlib inline
import numpy as np

import nengo
from nengo.utils.matplotlib import rasterplot
import nengo_loihi

1. Simple fan-out

In this example, a neuron is connected to several downstream neurons with increasing synaptic strength.

Synaptic strengths are defined through the transform of a nengo.Connection. While a Connection between two ensembles operates on their vector representations, a connection between two ensemble’s neuron values operates directly on neural activities (i.e., spikes).

with nengo.Network() as model:
    pre = nengo.Ensemble(1, dimensions=1, gain=[1], bias=[1.05])
    post = nengo.Ensemble(6, dimensions=1, gain=np.ones(6), bias=np.zeros(6))

    transform = np.linspace(0.01, 0.15, post.n_neurons)
    transform = transform.reshape((post.n_neurons, pre.n_neurons))
    nengo.Connection(pre.neurons, post.neurons, transform=transform)

    pre_probe = nengo.Probe(pre.neurons)
    post_probe = nengo.Probe(post.neurons)

Running the network in Nengo

with nengo.Simulator(model) as sim:
    sim.run(1)
t = sim.trange()

/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:580: RuntimeWarning: divide by zero encountered in log1p
  self.tau_ref - self.tau_rc * np.log1p(1.0 / (gain * (intercepts - 1) - 1))

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def plot_rasters(t, data):
    plt.figure(figsize=(10, 8))
    plt.subplot(2, 1, 1)
    rasterplot(t, data[pre_probe])
    plt.xticks(())
    plt.ylabel("pre neuron number")
    plt.subplot(2, 1, 2)
    rasterplot(t, data[post_probe])
    plt.ylabel("post neuron number")
    plt.xlabel("Time (s)")
    plt.tight_layout()


plot_rasters(t, sim.data)

Running the network with NengoLoihi

with nengo_loihi.Simulator(model) as sim:
    sim.run(1)
t = sim.trange()

/home/travis/build/nengo/nengo-loihi/nengo_loihi/builder/ensemble.py:157: UserWarning: NengoLoihi does not support initial values for 'voltage' being non-zero on LIF neurons. On the chip, all values will be initialized to zero.
  % (key, type(neuron_type).__name__)
/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:580: RuntimeWarning: divide by zero encountered in log1p
  self.tau_ref - self.tau_rc * np.log1p(1.0 / (gain * (intercepts - 1) - 1))

plot_rasters(t, sim.data)

2. One-to-one connections

In this example, two populations of equal size are connected one-to-one with random biases in the pre population and random excitatory connection weights.

rng = np.random.RandomState(seed=10)
n_neurons = 5

with nengo.Network() as model:
    pre = nengo.Ensemble(
        n_neurons,
        1,
        gain=np.ones(n_neurons),
        bias=rng.uniform(low=1.0, high=1.5, size=n_neurons),
    )
    post = nengo.Ensemble(
        n_neurons, 1, gain=np.ones(n_neurons), bias=np.zeros(n_neurons)
    )

    transform = np.zeros((n_neurons, n_neurons))
    di = np.diag_indices(n_neurons)
    transform[di] = rng.uniform(low=0.0, high=0.2, size=n_neurons)
    nengo.Connection(pre.neurons, post.neurons, transform=transform)

    pre_probe = nengo.Probe(pre.neurons)
    post_probe = nengo.Probe(post.neurons)

Running the network in Nengo

with nengo.Simulator(model) as sim:
    sim.run(1)
t = sim.trange()
plot_rasters(t, sim.data)

/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:580: RuntimeWarning: divide by zero encountered in log1p
  self.tau_ref - self.tau_rc * np.log1p(1.0 / (gain * (intercepts - 1) - 1))

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Running the network with NengoLoihi

with nengo_loihi.Simulator(model) as sim:
    sim.run(1)
t = sim.trange()
plot_rasters(t, sim.data)

/home/travis/build/nengo/nengo-loihi/nengo_loihi/builder/ensemble.py:157: UserWarning: NengoLoihi does not support initial values for 'voltage' being non-zero on LIF neurons. On the chip, all values will be initialized to zero.
  % (key, type(neuron_type).__name__)
/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:580: RuntimeWarning: divide by zero encountered in log1p
  self.tau_ref - self.tau_rc * np.log1p(1.0 / (gain * (intercepts - 1) - 1))

3. Fixed probability connections

In this example, two populations are recurrently connected (i.e., post is also connected back to pre). There is a fixed probability of two neurons being connected in either direction, a fixed probability of an inhibitory connection, and all connections have the same weight.

rng = np.random.RandomState(seed=100)
inhibitory = 0.5  # 50% inhibitory connections
connection_prob = 0.6  # 60% probability of being connected
n_neurons = 25

with nengo.Network() as model:
    pre = nengo.Ensemble(
        n_neurons,
        1,
        gain=np.ones(n_neurons),
        bias=rng.uniform(low=-2, high=2, size=n_neurons),
    )
    post = nengo.Ensemble(
        n_neurons,
        1,
        gain=np.ones(n_neurons),
        bias=rng.uniform(low=-2, high=2, size=n_neurons),
    )

    pre_post = np.ones((n_neurons, n_neurons)) * 0.05
    # Make some inhibitory
    pre_post[rng.rand(n_neurons, n_neurons) <= inhibitory] *= -1
    # Remove 1 - connection_prob connections
    pre_post[rng.rand(n_neurons, n_neurons) > connection_prob] = 0
    nengo.Connection(pre.neurons, post.neurons, transform=pre_post)

    post_pre = np.ones((n_neurons, n_neurons)) * 0.05
    post_pre[rng.rand(n_neurons, n_neurons) <= inhibitory] *= -1
    post_pre[rng.rand(n_neurons, n_neurons) > connection_prob] = 0
    nengo.Connection(post.neurons, pre.neurons, transform=post_pre)

    pre_probe = nengo.Probe(pre.neurons)
    post_probe = nengo.Probe(post.neurons)

Running the network in Nengo

with nengo.Simulator(model) as sim:
    sim.run(1)
t = sim.trange()
plot_rasters(t, sim.data)

/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:580: RuntimeWarning: invalid value encountered in log1p
  self.tau_ref - self.tau_rc * np.log1p(1.0 / (gain * (intercepts - 1) - 1))
/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:584: UserWarning: Non-finite values detected in `max_rates`; this probably means that `gain` was too small.
  "Non-finite values detected in `max_rates`; this "

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Running the network with NengoLoihi

with nengo_loihi.Simulator(model) as sim:
    sim.run(1)
t = sim.trange()
plot_rasters(t, sim.data)

/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:580: RuntimeWarning: invalid value encountered in log1p
  self.tau_ref - self.tau_rc * np.log1p(1.0 / (gain * (intercepts - 1) - 1))
/home/travis/virtualenv/python3.6.7/lib/python3.6/site-packages/nengo/neurons.py:584: UserWarning: Non-finite values detected in `max_rates`; this probably means that `gain` was too small.
  "Non-finite values detected in `max_rates`; this "
/home/travis/build/nengo/nengo-loihi/nengo_loihi/builder/ensemble.py:157: UserWarning: NengoLoihi does not support initial values for 'voltage' being non-zero on LIF neurons. On the chip, all values will be initialized to zero.
  % (key, type(neuron_type).__name__)