def test_nrmse():
assert np.allclose(nrmse(np.ones(100), np.ones(100)), 0)
assert np.allclose(nrmse([0, 0, 0], [42, 9000, 0]), 1)
ideal = sphere.sample(100, 3)
r = np.asarray([1, 2, 3])
assert np.allclose(nrmse(ideal, r * ideal, axis=0), 1 - 1. / r)
def test_hetero_neurons(Simulator, rng, seed):
n_neurons = 100
dt = 0.001
T = 0.1
dims_in = 2
taus = nengo.dists.Uniform(0.001, 0.1).sample(n_neurons, rng=rng)
synapses = [Lowpass(tau) for tau in taus]
encoders = sphere.sample(n_neurons, dims_in, rng=rng)
hs = HeteroSynapse(synapses, dt)
def embed_encoders(x):
# Reshapes the vectors to be the same dimensionality as the
# encoders, and then takes the dot product row by row.
# See http://stackoverflow.com/questions/26168363/ for a more
# efficient solution.
return np.sum(encoders * hs.from_vector(x), axis=1)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed)),
stim[i],
synapse=None)
# HeteroSynapse node
syn = nengo.Node(size_in=dims_in, output=hs)
# For comparing results
x = [
nengo.Ensemble(n_neurons, dims_in, seed=0, encoders=encoders)
for _ in range(2)
] # expected, actual
# Expected
for i, synapse in enumerate(synapses):
t = np.zeros_like(encoders)
t[i, :] = encoders[i, :]
nengo.Connection(stim, x[0].neurons, transform=t, synapse=synapse)
# Actual
nengo.Connection(stim, syn, synapse=None)
nengo.Connection(syn,
x[1].neurons,
function=embed_encoders,
synapse=None)
# Probes
p_exp = nengo.Probe(x[0].neurons, synapse=None)
p_act = nengo.Probe(x[1].neurons, synapse=None)
# Check correctness
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_act], sim.data[p_exp])
def test_hetero_neurons(Simulator, rng, seed):
n_neurons = 100
dt = 0.001
T = 0.1
dims_in = 2
taus = nengo.dists.Uniform(0.001, 0.1).sample(n_neurons, rng=rng)
synapses = [Lowpass(tau) for tau in taus]
encoders = sphere.sample(n_neurons, dims_in, rng=rng)
hs = HeteroSynapse(synapses, dt)
def embed_encoders(x):
# Reshapes the vectors to be the same dimensionality as the
# encoders, and then takes the dot product row by row.
# See http://stackoverflow.com/questions/26168363/ for a more
# efficient solution.
return np.sum(encoders * hs.from_vector(x), axis=1)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(
nengo.Node(output=nengo.processes.WhiteSignal(T, high=10)),
stim[i], synapse=None)
# HeteroSynapse node
syn = nengo.Node(size_in=dims_in, output=hs)
# For comparing results
x = [nengo.Ensemble(n_neurons, dims_in, seed=0, encoders=encoders)
for _ in range(2)] # expected, actual
# Expected
for i, synapse in enumerate(synapses):
t = np.zeros_like(encoders)
t[i, :] = encoders[i, :]
nengo.Connection(stim, x[0].neurons, transform=t, synapse=synapse)
# Actual
nengo.Connection(stim, syn, synapse=None)
nengo.Connection(
syn, x[1].neurons, function=embed_encoders, synapse=None)
# Probes
p_exp = nengo.Probe(x[0].neurons, synapse=None)
p_act = nengo.Probe(x[1].neurons, synapse=None)
# Check correctness
sim = Simulator(model, dt=dt, seed=seed)
sim.run(T)
assert np.allclose(sim.data[p_act], sim.data[p_exp])
def test_hetero_multi_vector(Simulator, rng, seed):
n_neurons = 20
dt = 0.0005
T = 0.1
dims_in = 2
synapses = [Alpha(0.1), Lowpass(0.005), Alpha(0.02)]
dims_out = len(synapses)*dims_in
encoders = sphere.sample(n_neurons, dims_out, rng=rng)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(
nengo.Node(output=nengo.processes.WhiteSignal(T, high=10)),
stim[i], synapse=None)
# HeteroSynapse Nodes
syn_dot = nengo.Node(
size_in=dims_in, output=HeteroSynapse(synapses, dt))
syn_elemwise = nengo.Node(
size_in=dims_out, output=HeteroSynapse(
np.repeat(synapses, dims_in), dt, elementwise=True))
# For comparing results
x = [nengo.Ensemble(n_neurons, dims_out, seed=0, encoders=encoders)
for _ in range(3)] # expected, actual 1, actual 2
# Expected
for j, synapse in enumerate(synapses):
nengo.Connection(
stim, x[0][j*dims_in:(j+1)*dims_in], synapse=synapse)
# Actual (method #1 = matrix multiplies)
nengo.Connection(stim, syn_dot, synapse=None)
nengo.Connection(syn_dot, x[1], synapse=None)
# Actual (method #2 = elementwise)
for j in range(len(synapses)):
nengo.Connection(
stim, syn_elemwise[j*dims_in:(j+1)*dims_in], synapse=None)
nengo.Connection(syn_elemwise, x[2], synapse=None)
# Probes
p_exp = nengo.Probe(x[0], synapse=None)
p_act_dot = nengo.Probe(x[1], synapse=None)
p_act_elemwise = nengo.Probe(x[2], synapse=None)
# Check correctness
sim = Simulator(model, dt=dt, seed=seed)
sim.run(T)
assert np.allclose(sim.data[p_act_dot], sim.data[p_exp])
assert np.allclose(sim.data[p_act_elemwise], sim.data[p_exp])
def test_hetero_vector(Simulator, rng, seed):
n_neurons = 20
dt = 0.0005
T = 0.1
dims_in = 2
synapses = [Alpha(0.1), Lowpass(0.005)]
assert dims_in == len(synapses)
encoders = sphere.sample(n_neurons, dims_in, rng=rng)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed)),
stim[i],
synapse=None)
# HeteroSynapse Nodes
syn_elemwise = nengo.Node(size_in=dims_in,
output=HeteroSynapse(synapses,
dt,
elementwise=True))
# For comparing results
x = [
nengo.Ensemble(n_neurons, dims_in, seed=0, encoders=encoders)
for _ in range(2)
] # expected, actual
# Expected
for j, synapse in enumerate(synapses):
nengo.Connection(stim[j], x[0][j], synapse=synapse)
# Actual
nengo.Connection(stim, syn_elemwise, synapse=None)
nengo.Connection(syn_elemwise, x[1], synapse=None)
# Probes
p_exp = nengo.Probe(x[0], synapse=None)
p_act_elemwise = nengo.Probe(x[1], synapse=None)
# Check correctness
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_act_elemwise], sim.data[p_exp])
def test_hetero_vector(Simulator, rng, seed):
n_neurons = 20
dt = 0.0005
T = 0.1
dims_in = 2
synapses = [Alpha(0.1), Lowpass(0.005)]
assert dims_in == len(synapses)
encoders = sphere.sample(n_neurons, dims_in, rng=rng)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(
nengo.Node(output=nengo.processes.WhiteSignal(T, high=10)),
stim[i], synapse=None)
# HeteroSynapse Nodes
syn_elemwise = nengo.Node(
size_in=dims_in,
output=HeteroSynapse(synapses, dt, elementwise=True))
# For comparing results
x = [nengo.Ensemble(n_neurons, dims_in, seed=0, encoders=encoders)
for _ in range(2)] # expected, actual
# Expected
for j, synapse in enumerate(synapses):
nengo.Connection(stim[j], x[0][j], synapse=synapse)
# Actual
nengo.Connection(stim, syn_elemwise, synapse=None)
nengo.Connection(syn_elemwise, x[1], synapse=None)
# Probes
p_exp = nengo.Probe(x[0], synapse=None)
p_act_elemwise = nengo.Probe(x[1], synapse=None)
# Check correctness
sim = Simulator(model, dt=dt, seed=seed)
sim.run(T)
assert np.allclose(sim.data[p_act_elemwise], sim.data[p_exp])
def test_hetero_multi_vector(Simulator, rng, seed):
n_neurons = 20
dt = 0.0005
T = 0.1
dims_in = 2
synapses = [Alpha(0.1), Lowpass(0.005), Alpha(0.02)]
dims_out = len(synapses) * dims_in
encoders = sphere.sample(n_neurons, dims_out, rng=rng)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed)),
stim[i],
synapse=None)
# HeteroSynapse Nodes
syn_dot = nengo.Node(size_in=dims_in,
output=HeteroSynapse(synapses, dt))
syn_elemwise = nengo.Node(size_in=dims_out,
output=HeteroSynapse(np.repeat(
synapses, dims_in),
dt,
elementwise=True))
# For comparing results
x = [
nengo.Ensemble(n_neurons, dims_out, seed=0, encoders=encoders)
for _ in range(3)
] # expected, actual 1, actual 2
# Expected
for j, synapse in enumerate(synapses):
nengo.Connection(stim,
x[0][j * dims_in:(j + 1) * dims_in],
synapse=synapse)
# Actual (method #1 = matrix multiplies)
nengo.Connection(stim, syn_dot, synapse=None)
nengo.Connection(syn_dot, x[1], synapse=None)
# Actual (method #2 = elementwise)
for j in range(len(synapses)):
nengo.Connection(stim,
syn_elemwise[j * dims_in:(j + 1) * dims_in],
synapse=None)
nengo.Connection(syn_elemwise, x[2], synapse=None)
# Probes
p_exp = nengo.Probe(x[0], synapse=None)
p_act_dot = nengo.Probe(x[1], synapse=None)
p_act_elemwise = nengo.Probe(x[2], synapse=None)
# Check correctness
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_act_dot], sim.data[p_exp])
assert np.allclose(sim.data[p_act_elemwise], sim.data[p_exp])
def figure_time_cells(targets, order):
npfile = np.load(TIME_CELLS_SIM % order)
t = npfile['t']
x = npfile['x']
spikes = npfile['a']
mus = []
stds = []
for i in range(spikes.shape[1]):
spike_times = t[spikes[:, i] > 0]
spike_times = spike_times[(spike_times >= 1)] - 1
total = len(spike_times)
if total > 0:
within = len(np.where(spike_times < 4.784)[0])
if within / float(total) >= 0.9:
mus.append(np.mean(spike_times))
stds.append(np.std(spike_times))
logging.info("Remaining: %d", len(mus))
logging.info("Pearson's correlation: %s", pearsonr(mus, stds))
model = sm.OLS(stds, sm.add_constant(mus))
res = model.fit()
logging.info("Intercept / Slope: %s", res.params)
logging.info("Standard errors: %s", res.bse)
logging.info("p-values: %s", res.pvalues)
sample_rate = 10
t = t[::sample_rate] # downsample PDFs to avoid reader lag
x = x[::sample_rate]
n_cells = 73
intercept = -1
rng = np.random.RandomState(seed=2) # chosen to get a good spread
encoders = []
while len(encoders) < n_cells:
e = sphere.sample(1, x.shape[1], rng=rng).squeeze()
s = np.dot(x, e)
if np.max(s) > intercept and 1.1 <= t[np.argmax(s)] <= 5.5:
encoders.append(e)
encoders = np.asarray(encoders)
# Compute heat plot (right subfigure)
a = np.dot(x[t >= 1.0], encoders.T)
a = a.clip(intercept)
a -= np.min(a, axis=0)
assert np.all(np.sum(a, axis=0) > 0)
normed_a = a / np.max(a, axis=0)
assert np.allclose(np.min(normed_a, axis=0), 0)
assert np.allclose(np.max(normed_a, axis=0), 1)
t_peak = np.argmax(normed_a, axis=0)
order = np.argsort(t_peak)
heat = normed_a[:, order]
# Compute cosine similarities (left subfigure)
sorted_a = a[:, order]
norms = np.linalg.norm(sorted_a, axis=1)
assert np.isfinite(norms).all()
cos = sorted_a.dot(sorted_a.T) / norms[:, None] / norms[None, :]
cos -= np.min(cos) # normalize the color map
cos /= np.max(cos)
cmap = 'jet' # bad, but consistent with Zoran's figure
with sns.axes_style('white'):
with sns.plotting_context('paper', font_scale=3.0):
aspect = 0.790
t_ticks = ['', 0, 1, 2, 3, 4, '']
pylab.figure(figsize=(22, 7.4))
gs = gridspec.GridSpec(1, 2)
ax1 = plt.subplot(gs[0])
ax2 = plt.subplot(gs[1])
ax1.imshow(cos, cmap=cmap, aspect=aspect, interpolation='none')
ax1.set_xticklabels(t_ticks)
ax1.set_yticklabels(t_ticks)
ax1.set_xlabel("Time [s]", labelpad=20)
ax1.set_ylabel("Time [s]", labelpad=20)
ax1.set_anchor('S')
ax2.imshow(heat.T,
cmap=cmap,
aspect=aspect * heat.shape[0] / float(heat.shape[1]),
interpolation='none')
ax2.set_xticklabels(t_ticks)
ax2.set_xlabel("Time [s]", labelpad=20)
ax2.set_ylabel(r"Cell \#", labelpad=20)
ax2.set_anchor('S')
savefig(targets[0])
def figure_delay_example(targets):
npfile = np.load(DELAY_EXAMPLE_SIM)
theta = npfile['theta']
dt = npfile['dt']
t = npfile['t']
u = npfile['u']
x = npfile['x']
a = npfile['a']
y = npfile['y']
T = t[-1]
ideal = ideal_delay(u, theta, dt)
logging.info("Paper constant: NRMSE: %s", nrmse(y, target=ideal))
n_encoders = 1000
rng = np.random.RandomState(seed=0)
encoders = sphere.sample(n_encoders, x.shape[1], rng=rng)
sims = np.dot(x, encoders.T)
order = np.argsort(np.argmax(sims, axis=0))
intercept = -1
sims = sims.clip(intercept)
sims -= np.min(sims, axis=0)
sims /= np.max(sims, axis=0)
a = sims[:, order]
assert np.isfinite(a).all()
sample_rate = 50 # downsample PDFs to avoid reader lag
t = t[::sample_rate]
u = u[::sample_rate]
x = x[::sample_rate]
a = a[::sample_rate]
y = y[::sample_rate]
ideal = ideal[::sample_rate]
cmap = sns.diverging_palette(220, 20, as_cmap=True)
with sns.axes_style('ticks'):
with sns.plotting_context('paper', font_scale=2.8):
f, (ax1, ax2, ax3) = pylab.subplots(3, 1, figsize=(18, 16))
cpal = sns.color_palette(None, 2)
ax1.plot(t, u, label=r"$u(t)$", c=cpal[0], lw=4, alpha=0.8)
ax1.plot(t,
ideal,
label=r"$u(t - %s)$" % theta,
c=cpal[0],
lw=4,
linestyle='--',
zorder=2) # on top
ax1.plot(t, y, c=cpal[1], lw=4, label=r"$y(t)$", zorder=1)
ax1.set_xlim(t[0], t[-1])
ax1.set_ylim(-1, 1)
ax1.set_xticks([])
ax1.set_ylabel("Input / Output", labelpad=20)
ax1.legend(bbox_to_anchor=(1.02, 1), loc=2, borderaxespad=0.)
for i in range(x.shape[1]):
ax2.plot(t,
x[:, -i],
label=r"$\hat{x}_%d(t)$" % (i + 1),
lw=2,
alpha=0.8)
ax2.set_xlim(t[0], t[-1])
ax2.set_ylim(-1, 1)
ax2.set_xticks([])
ax2.set_ylabel("Decoded State", labelpad=20)
ax2.legend(bbox_to_anchor=(1.02, 1), loc=2, borderaxespad=0.)
ax3.imshow(a.T, cmap=cmap, aspect='auto', interpolation='none')
ax3.set_xlim(0, len(t))
ax3.set_xticklabels(np.linspace(0, T, 9))
ax3.set_xlabel("Time [s]", labelpad=20)
ax3.set_ylabel(r"Cell \#", labelpad=20)
segs = 100
lc = LineCollection(segs * [[(0, 0)]],
lw=10,
colors=cmap(np.linspace(0, 1, segs)))
ax3.legend([lc], ['Activity'],
handlelength=2,
handler_map={type(lc): HandlerDashedLines()},
bbox_to_anchor=(1.02, 1),
loc=2,
borderaxespad=0.)
sns.despine(offset=15)
savefig(targets[0])