def test_lif(Simulator, plt, rng, dt, allclose):
"""Test that the dynamic model approximately matches the rates."""
n = 5000
x = 0.5
encoders = np.ones((n, 1))
max_rates = rng.uniform(low=10, high=200, size=n)
intercepts = rng.uniform(low=-1, high=1, size=n)
m = nengo.Network()
with m:
ins = nengo.Node(x)
ens = nengo.Ensemble(
n,
dimensions=1,
neuron_type=LIF(),
encoders=encoders,
max_rates=max_rates,
intercepts=intercepts,
)
nengo.Connection(ins,
ens.neurons,
transform=np.ones((n, 1)),
synapse=None)
spike_probe = nengo.Probe(ens.neurons)
voltage_probe = nengo.Probe(ens.neurons, "voltage")
ref_probe = nengo.Probe(ens.neurons, "refractory_time")
t_final = 1.0
with Simulator(m, dt=dt) as sim:
sim.run(t_final)
i = 3
plt.subplot(311)
plt.plot(sim.trange(), sim.data[spike_probe][:, :i])
plt.subplot(312)
plt.plot(sim.trange(), sim.data[voltage_probe][:, :i])
plt.subplot(313)
plt.plot(sim.trange(), sim.data[ref_probe][:, :i])
plt.ylim([-dt, ens.neuron_type.tau_ref + dt])
# check rates against analytic rates
math_rates = ens.neuron_type.rates(
x, *ens.neuron_type.gain_bias(max_rates, intercepts))
spikes = sim.data[spike_probe]
sim_rates = (spikes > 0).sum(0) / t_final
logging.info("ME = %f", (sim_rates - math_rates).mean())
logging.info("RMSE = %f",
rms(sim_rates - math_rates) / (rms(math_rates) + 1e-20))
assert np.sum(
math_rates > 0) > 0.5 * n, "At least 50% of neurons must fire"
assert allclose(sim_rates, math_rates, atol=1, rtol=0.02)
# if voltage and ref time are non-constant, the probe is doing something
assert np.abs(np.diff(sim.data[voltage_probe])).sum() > 1
assert np.abs(np.diff(sim.data[ref_probe])).sum() > 1
# compute spike counts after each timestep
actual_counts = (spikes > 0).cumsum(axis=0)
expected_counts = np.outer(sim.trange(), math_rates)
assert (abs(actual_counts - expected_counts) < 1).all()
def test_lif(Simulator):
"""Test that the dynamic model approximately matches the rates"""
rng = np.random.RandomState(85243)
dt = 0.001
n = 5000
x = 0.5
max_rates = rng.uniform(low=10, high=200, size=n)
intercepts = rng.uniform(low=-1, high=1, size=n)
m = nengo.Network()
with m:
ins = nengo.Node(x)
ens = nengo.Ensemble(nengo.LIF(n),
1,
max_rates=max_rates,
intercepts=intercepts)
nengo.Connection(ins, ens.neurons, transform=np.ones((n, 1)))
spike_probe = nengo.Probe(ens.neurons, "output")
sim = Simulator(m, dt=dt)
t_final = 1.0
sim.run(t_final)
spikes = sim.data[spike_probe].sum(0)
math_rates = ens.neurons.rates(
x, *ens.neurons.gain_bias(max_rates, intercepts))
sim_rates = spikes / t_final
logger.debug("ME = %f", (sim_rates - math_rates).mean())
logger.debug("RMSE = %f",
rms(sim_rates - math_rates) / (rms(math_rates) + 1e-20))
assert np.sum(math_rates > 0) > 0.5 * n, (
"At least 50% of neurons must fire")
assert np.allclose(sim_rates, math_rates, atol=1, rtol=0.02)
def test_pes_error_clip(plt, seed, Simulator):
dims = 2
n_per_dim = 120
tau = 0.01
error_scale = 5. # scale up error signal so it clips
simtime = 0.3
model, probes = pes_network(
n_per_dim, dims, seed, learn_synapse=tau,
learning_rule_type=nengo.PES(learning_rate=1e-2 / error_scale),
input_scale=np.array([1., -1.]),
error_scale=error_scale,
period=simtime)
with pytest.warns(UserWarning, match=r'.*PES error.*Clipping.'):
with Simulator(model) as loihi_sim:
loihi_sim.run(simtime)
t = loihi_sim.trange()
post_tmask = t > simtime - 1.0
dec_tau = loihi_sim.model.decode_tau
y = loihi_sim.data[probes['stim']]
y_dpre = nengo.Lowpass(dec_tau).filt(y)
y_dpost = nengo.Lowpass(tau).combine(nengo.Lowpass(dec_tau)).filt(y_dpre)
y_loihi = loihi_sim.data[probes['post']]
plt.plot(t, y_dpost, 'k', label='target')
plt.plot(t, y_loihi, 'g', label='loihi')
# --- assert that we've learned something, but not everything
error = (rms(y_loihi[post_tmask] - y_dpost[post_tmask])
/ rms(y_dpost[post_tmask]))
assert error < 0.5
assert error > 0.05
def test_decoder_solver(solver):
rng = np.random.RandomState(39408)
dims = 1
n_neurons = 100
n_points = 500
rates = get_rate_function(n_neurons, dims, rng=rng)
E = get_encoders(n_neurons, dims, rng=rng)
train = get_eval_points(n_points, dims, rng=rng)
Atrain = rates(np.dot(train, E))
D, _ = solver(Atrain, train, rng=rng)
test = get_eval_points(n_points, dims, rng=rng, sort=True)
Atest = rates(np.dot(test, E))
est = np.dot(Atest, D)
rel_rmse = rms(est - test) / rms(test)
with Plotter(nengo.Simulator) as plt:
plt.plot(test, np.zeros_like(test), 'k--')
plt.plot(test, test - est)
plt.title("relative RMSE: %0.2e" % rel_rmse)
plt.savefig('test_decoders.test_decoder_solver.%s.pdf'
% solver.__name__)
plt.close()
assert np.allclose(test, est, atol=3e-2, rtol=1e-3)
assert rel_rmse < 0.02
def test_decoder_solver(Solver, plt, rng, allclose):
solver = Solver()
dims = 1
n_neurons = 100
n_points = 1000
rates = get_rate_function(n_neurons, rng=rng)
E = get_encoders(n_neurons, dims, rng=rng)
train = get_eval_points(n_points, dims, rng=rng)
Atrain = rates(np.dot(train, E))
D, _ = solver(Atrain, train, rng=rng)
test = get_eval_points(n_points, dims, rng=rng, sort=True)
Atest = rates(np.dot(test, E))
est = np.dot(Atest, D)
rel_rmse = rms(est - test) / rms(test)
plt.plot(test, np.zeros_like(test), "k--")
plt.plot(test, test - est)
plt.title(f"relative RMSE: {rel_rmse:0.2e}")
atol = (0.1 if isinstance(solver, (LstsqNoise, LstsqDrop,
LstsqMultNoise)) else 1.5e-2)
assert allclose(test, est, atol=atol, rtol=1e-3)
assert rel_rmse < 0.02
def error_plot(dt, prestime, t, ystar, learners, tmin=None, tmax=None, ax=None):
ax = plt.gca() if ax is None else ax
es = [learner['e'] for learner in learners]
if tmin is not None or tmax is not None:
tmin = t[0] if tmin is None else tmin
tmax = t[-1] if tmax is None else tmax
tmask = (t >= tmin) & (t <= tmax)
t = t[tmask]
es = [e[tmask] for e in es]
vsynapse = Alpha(0.01, default_dt=dt)
# esynapse = Alpha(1*prestime, default_dt=dt)
# esynapse = Alpha(1*prestime, default_dt=dt)
esynapse = Alpha(5*prestime, default_dt=dt)
# esynapse = Alpha(20*prestime, default_dt=dt)
# yrms = rms(ystar, axis=1).mean()
yrms = rms(vsynapse.filtfilt(ystar), axis=1).mean()
# yrms = rms(esynapse.filtfilt(ystar), axis=1).mean()
# print(yrms)
for e in es:
# erms = esynapse.filtfilt(rms(e, axis=1) / yrms)
# erms = rms(esynapse.filtfilt(e), axis=1) / yrms
# erms = rms(vsynapse.filtfilt(e), axis=1) / yrms
erms = esynapse.filtfilt(rms(vsynapse.filtfilt(e), axis=1) / yrms)
plt.plot(t, erms)
def test_decoder_solver(Solver, plt, rng):
solver = Solver()
dims = 1
n_neurons = 100
n_points = 500
rates = get_rate_function(n_neurons, dims, rng=rng)
E = get_encoders(n_neurons, dims, rng=rng)
train = get_eval_points(n_points, dims, rng=rng)
Atrain = rates(np.dot(train, E))
D, _ = solver(Atrain, train, rng=rng)
test = get_eval_points(n_points, dims, rng=rng, sort=True)
Atest = rates(np.dot(test, E))
est = np.dot(Atest, D)
rel_rmse = rms(est - test) / rms(test)
plt.plot(test, np.zeros_like(test), 'k--')
plt.plot(test, test - est)
plt.title("relative RMSE: %0.2e" % rel_rmse)
atol = 3.5e-2 if isinstance(solver, LstsqNoise) else 1.5e-2
assert np.allclose(test, est, atol=atol, rtol=1e-3)
assert rel_rmse < 0.02
def test_decay_magnitude(offset, plt, logger):
bits = 12
decays = np.arange(1, 2**bits, 7)
ref = []
emp = []
est = []
for decay in decays:
def empirical_decay_magnitude(decay, x0):
x = x0 * np.ones(decay.shape, dtype=np.int32)
y = x
y_sum = np.zeros(decay.shape, dtype=np.int64)
for i in range(100000):
y_sum += y
if (y <= 0).all():
break
y = decay_int(y, decay, bits=bits, offset=offset)
else:
raise RuntimeError("Exceeded max number of iterations")
return y_sum / x0
x0 = np.arange(2**21 - 1000, 2**21, step=41, dtype=np.int32)
m = empirical_decay_magnitude(decay * np.ones_like(x0), x0)
m0 = m.mean()
emp.append(m0)
# reference (naive) method, not accounting for truncation loss
r = (2**bits - offset - decay) / 2**bits
Sx1 = (1 - r/x0) / (1 - r) # sum_i^n x_i/x_0, where x_n = r**n*x_0 = 1
ref.append(Sx1.mean())
m = decay_magnitude(decay, x0, bits=bits, offset=offset)
m2 = m.mean()
est.append(m2)
ref = np.array(ref)
emp = np.array(emp)
est = np.array(est)
rms_ref = rms(ref - emp) / rms(emp)
rms_est = rms(est - emp) / rms(emp)
logger.info("Ref rel RMSE: %0.3e, decay_magnitude rel RMSE: %0.3e" % (
rms_ref, rms_est))
abs_ref = np.abs(ref - emp)
abs_est = np.abs(est - emp)
# find places where ref is better than est
relative_diff = (abs_est - abs_ref) / emp
ax = plt.subplot(211)
plt.plot(abs_ref, 'b')
plt.plot(abs_est, 'g')
ax.set_yscale('log')
ax = plt.subplot(212)
plt.plot(relative_diff.clip(0, None))
assert np.all(relative_diff < 1e-6)
def test_run(Simulator, seed):
rng = np.random.RandomState(seed)
vocab = spa.Vocabulary(16, rng=rng)
with spa.SPA(seed=seed, vocabs=[vocab]) as model:
model.bind = spa.Bind(dimensions=16)
def inputA(t):
if 0 <= t < 0.1:
return "A"
else:
return "B"
model.input = spa.Input(bind_A=inputA, bind_B="A")
bind, vocab = model.get_module_output("bind")
with model:
p = nengo.Probe(bind, "output", synapse=0.03)
with Simulator(model) as sim:
sim.run(0.2)
error = rms(vocab.parse("B*A").v - sim.data[p][-1])
assert error < 0.1
error = rms(vocab.parse("A*A").v - sim.data[p][100])
assert error < 0.1
def test_decoder_solver(Solver, plt, rng):
if isinstance(Solver, tuple):
Solver, args, kwargs = Solver
else:
args, kwargs = (), {}
dims = 1
n_neurons = 100
n_points = 500
rates = get_rate_function(n_neurons, dims, rng=rng)
E = get_encoders(n_neurons, dims, rng=rng)
train = get_eval_points(n_points, dims, rng=rng)
Atrain = rates(np.dot(train, E))
D, _ = Solver(*args, **kwargs)(Atrain, train, rng=rng)
test = get_eval_points(n_points, dims, rng=rng, sort=True)
Atest = rates(np.dot(test, E))
est = np.dot(Atest, D)
rel_rmse = rms(est - test) / rms(test)
plt.plot(test, np.zeros_like(test), 'k--')
plt.plot(test, test - est)
plt.title("relative RMSE: %0.2e" % rel_rmse)
atol = 3.5e-2 if Solver is LstsqNoise else 1.5e-2
assert np.allclose(test, est, atol=atol, rtol=1e-3)
assert rel_rmse < 0.02
def test_run(Simulator, algebra, seed):
rng = np.random.RandomState(seed)
vocab = spa.Vocabulary(16, pointer_gen=rng, algebra=algebra)
vocab.populate("A; B")
with spa.Network(seed=seed) as model:
model.bind = spa.Bind(vocab)
def inputA(t):
if 0 <= t < 0.1:
return "A"
else:
return "B"
model.input = spa.Transcode(inputA, output_vocab=vocab)
model.input >> model.bind.input_left
spa.sym.A >> model.bind.input_right
with model:
p = nengo.Probe(model.bind.output, synapse=0.03)
with Simulator(model) as sim:
sim.run(0.2)
error = rms(vocab.parse("(B*A).normalized()").v - sim.data[p][-1])
assert error < 0.15
error = rms(vocab.parse("(A*A).normalized()").v - sim.data[p][100])
assert error < 0.15
def test_lif(Simulator):
"""Test that the dynamic model approximately matches the rates"""
rng = np.random.RandomState(85243)
dt = 0.001
n = 5000
x = 0.5
max_rates = rng.uniform(low=10, high=200, size=n)
intercepts = rng.uniform(low=-1, high=1, size=n)
m = nengo.Network()
with m:
ins = nengo.Node(x)
ens = nengo.Ensemble(
nengo.LIF(n), 1, max_rates=max_rates, intercepts=intercepts)
nengo.Connection(ins, ens.neurons, transform=np.ones((n, 1)))
spike_probe = nengo.Probe(ens.neurons, "output")
sim = Simulator(m, dt=dt)
t_final = 1.0
sim.run(t_final)
spikes = sim.data[spike_probe].sum(0)
math_rates = ens.neurons.rates(
x, *ens.neurons.gain_bias(max_rates, intercepts))
sim_rates = spikes / t_final
logger.debug("ME = %f", (sim_rates - math_rates).mean())
logger.debug("RMSE = %f",
rms(sim_rates - math_rates) / (rms(math_rates) + 1e-20))
assert np.sum(math_rates > 0) > 0.5 * n, (
"At least 50% of neurons must fire")
assert np.allclose(sim_rates, math_rates, atol=1, rtol=0.02)
def test_decoder_solver(Solver):
rng = np.random.RandomState(39408)
dims = 1
n_neurons = 100
n_points = 500
rates = get_rate_function(n_neurons, dims, rng=rng)
E = get_encoders(n_neurons, dims, rng=rng)
train = get_eval_points(n_points, dims, rng=rng)
Atrain = rates(np.dot(train, E))
D, _ = Solver()(Atrain, train, rng=rng)
test = get_eval_points(n_points, dims, rng=rng, sort=True)
Atest = rates(np.dot(test, E))
est = np.dot(Atest, D)
rel_rmse = rms(est - test) / rms(test)
with Plotter(nengo.Simulator) as plt:
plt.plot(test, np.zeros_like(test), 'k--')
plt.plot(test, test - est)
plt.title("relative RMSE: %0.2e" % rel_rmse)
plt.savefig('test_decoders.test_decoder_solver.%s.pdf'
% Solver.__name__)
plt.close()
assert np.allclose(test, est, atol=3e-2, rtol=1e-3)
assert rel_rmse < 0.02
def test_fastlif(plt):
"""Test that the dynamic model approximately matches the rates."""
# Based nengo.tests.test_neurons.test_lif
rng = np.random.RandomState(10)
dt = 1e-3
n = 5000
x = 0.5
encoders = np.ones((n, 1))
max_rates = rng.uniform(low=10, high=200, size=n)
intercepts = rng.uniform(low=-1, high=1, size=n)
m = nengo.Network()
with m:
ins = nengo.Node(x)
ens = nengo.Ensemble(n, dimensions=1,
neuron_type=FastLIF(),
encoders=encoders,
max_rates=max_rates,
intercepts=intercepts)
nengo.Connection(
ins, ens.neurons, transform=np.ones((n, 1)), synapse=None)
spike_probe = nengo.Probe(ens.neurons)
voltage_probe = nengo.Probe(ens.neurons, 'voltage')
ref_probe = nengo.Probe(ens.neurons, 'refractory_time')
t_final = 1.0
with nengo.Simulator(m, dt=dt) as sim:
sim.run(t_final)
i = 3
plt.subplot(311)
plt.plot(sim.trange(), sim.data[spike_probe][:, :i])
plt.subplot(312)
plt.plot(sim.trange(), sim.data[voltage_probe][:, :i])
plt.subplot(313)
plt.plot(sim.trange(), sim.data[ref_probe][:, :i])
plt.ylim([-dt, ens.neuron_type.tau_ref + dt])
# check rates against analytic rates
math_rates = ens.neuron_type.rates(
x, *ens.neuron_type.gain_bias(max_rates, intercepts))
spikes = sim.data[spike_probe]
sim_rates = (spikes > 0).sum(0) / t_final
print("ME = %f" % (sim_rates - math_rates).mean())
print("RMSE = %f" % (
rms(sim_rates - math_rates) / (rms(math_rates) + 1e-20)))
assert np.sum(math_rates > 0) > 0.5 * n, (
"At least 50% of neurons must fire")
assert np.allclose(sim_rates, math_rates, atol=1, rtol=0.02)
# if voltage and ref time are non-constant, the probe is doing something
assert np.abs(np.diff(sim.data[voltage_probe])).sum() > 1
assert np.abs(np.diff(sim.data[ref_probe])).sum() > 1
# compute spike counts after each timestep
actual_counts = (spikes > 0).cumsum(axis=0)
expected_counts = np.outer(sim.trange(), math_rates)
assert (abs(actual_counts - expected_counts) < 1).all()
def test_subsolvers(Solver, seed, rng, tol=1e-2):
get_rng = lambda: np.random.RandomState(seed)
A, b = get_system(500, 100, 5, rng=rng)
x0, _ = Solver(solver=lstsq.Cholesky())(A, b, rng=get_rng())
subsolvers = [lstsq.Conjgrad, lstsq.BlockConjgrad]
for subsolver in subsolvers:
x, info = Solver(solver=subsolver(tol=tol))(A, b, rng=get_rng())
rel_rmse = rms(x - x0) / rms(x0)
assert rel_rmse < 4 * tol
def test_subsolvers(Solver, seed, rng, tol=1e-2):
get_rng = lambda: np.random.RandomState(seed)
A, b = get_system(500, 100, 5, rng=rng)
x0, _ = Solver(solver=cholesky)(A, b, rng=get_rng())
subsolvers = [conjgrad, block_conjgrad]
for subsolver in subsolvers:
x, info = Solver(solver=subsolver, tol=tol)(A, b, rng=get_rng())
rel_rmse = rms(x - x0) / rms(x0)
assert rel_rmse < 4 * tol
def test_alif(Simulator):
"""Test ALIF and ALIFRate by comparing them to each other"""
n = 100
max_rates = 50 * np.ones(n)
intercepts = np.linspace(-0.99, 0.99, n)
encoders = np.ones((n, 1))
nparams = dict(tau_n=1, inc_n=10e-3)
eparams = dict(n_neurons=n,
max_rates=max_rates,
intercepts=intercepts,
encoders=encoders)
model = nengo.Network()
with model:
u = nengo.Node(output=0.5)
a = nengo.Ensemble(neuron_type=nengo.AdaptiveLIFRate(**nparams),
dimensions=1,
**eparams)
b = nengo.Ensemble(neuron_type=nengo.AdaptiveLIF(**nparams),
dimensions=1,
**eparams)
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
ap = nengo.Probe(a, "spikes", synapse=0)
bp = nengo.Probe(b, "spikes", synapse=0)
dt = 1e-3
sim = Simulator(model, dt=dt)
sim.run(2.)
t = sim.trange()
a_rates = sim.data[ap] / dt
spikes = sim.data[bp]
b_rates = rates_kernel(t, spikes)
tmask = (t > 0.1) & (t < 1.7)
rel_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
with Plotter(Simulator) as plt:
ax = plt.subplot(311)
implot(plt, t, intercepts[::-1], a_rates.T, ax=ax)
ax.set_ylabel('input')
ax = plt.subplot(312)
implot(plt, t, intercepts[::-1], b_rates.T, ax=ax)
ax.set_ylabel('input')
ax = plt.subplot(313)
implot(plt, t, intercepts[::-1], (b_rates - a_rates)[tmask].T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('input')
plt.savefig('test_neurons.test_alif.pdf')
plt.close()
assert rel_rmse < 0.07
def test_subsolvers(solver, tol=1e-2):
rng = np.random.RandomState(89)
get_rng = lambda: np.random.RandomState(87)
A, b = get_system(500, 100, 5, rng=rng)
x0, _ = solver(A, b, rng=get_rng(), solver=_cholesky)
subsolvers = [_conjgrad, _block_conjgrad]
for subsolver in subsolvers:
x, info = solver(A, b, rng=get_rng(), solver=subsolver, tol=tol)
rel_rmse = rms(x - x0) / rms(x0)
assert rel_rmse < 3 * tol
def _test_rates(Simulator, rates, name=None):
if name is None:
name = rates.__name__
n = 100
max_rates = 50 * np.ones(n)
# max_rates = 200 * np.ones(n)
intercepts = np.linspace(-0.99, 0.99, n)
encoders = np.ones((n, 1))
nparams = dict(n_neurons=n)
eparams = dict(
max_rates=max_rates, intercepts=intercepts, encoders=encoders)
model = nengo.Network()
with model:
u = nengo.Node(output=whitenoise(1, 5, seed=8393))
a = nengo.Ensemble(nengo.LIFRate(**nparams), 1, **eparams)
b = nengo.Ensemble(nengo.LIF(**nparams), 1, **eparams)
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
up = nengo.Probe(u)
ap = nengo.Probe(a.neurons, "output", synapse=None)
bp = nengo.Probe(b.neurons, "output", synapse=None)
dt = 1e-3
sim = Simulator(model, dt=dt)
sim.run(2.)
t = sim.trange()
x = sim.data[up]
a_rates = sim.data[ap] / dt
spikes = sim.data[bp]
b_rates = rates(t, spikes)
with Plotter(Simulator) as plt:
ax = plt.subplot(411)
plt.plot(t, x)
ax = plt.subplot(412)
implot(plt, t, intercepts, a_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(413)
implot(plt, t, intercepts, b_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(414)
implot(plt, t, intercepts, (b_rates - a_rates).T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('intercept')
plt.savefig('utils.test_neurons.test_rates.%s.pdf' % name)
plt.close()
tmask = (t > 0.1) & (t < 1.9)
relative_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
return relative_rmse
def _test_rates(Simulator, rates, name=None):
if name is None:
name = rates.__name__
n = 100
max_rates = 50 * np.ones(n)
# max_rates = 200 * np.ones(n)
intercepts = np.linspace(-0.99, 0.99, n)
encoders = np.ones((n, 1))
model = nengo.Network()
with model:
model.config[nengo.Ensemble].max_rates = max_rates
model.config[nengo.Ensemble].intercepts = intercepts
model.config[nengo.Ensemble].encoders = encoders
u = nengo.Node(output=whitenoise(1, 5, seed=8393))
a = nengo.Ensemble(n, 1, neuron_type=nengo.LIFRate())
b = nengo.Ensemble(n, 1, neuron_type=nengo.LIF())
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
up = nengo.Probe(u)
ap = nengo.Probe(a.neurons)
bp = nengo.Probe(b.neurons)
dt = 1e-3
sim = Simulator(model, dt=dt)
sim.run(2.)
t = sim.trange()
x = sim.data[up]
a_rates = sim.data[ap] / dt
spikes = sim.data[bp]
b_rates = rates(t, spikes)
with Plotter(Simulator) as plt:
ax = plt.subplot(411)
plt.plot(t, x)
ax = plt.subplot(412)
implot(plt, t, intercepts, a_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(413)
implot(plt, t, intercepts, b_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(414)
implot(plt, t, intercepts, (b_rates - a_rates).T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('intercept')
plt.savefig('utils.test_neurons.test_rates.%s.pdf' % name)
plt.close()
tmask = (t > 0.1) & (t < 1.9)
relative_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
return relative_rmse
def test_lif(Simulator):
"""Test that the dynamic model approximately matches the rates"""
rng = np.random.RandomState(85243)
dt = 0.001
n = 5000
x = 0.5
encoders = np.ones((n, 1))
max_rates = rng.uniform(low=10, high=200, size=n)
intercepts = rng.uniform(low=-1, high=1, size=n)
m = nengo.Network()
with m:
ins = nengo.Node(x)
ens = nengo.Ensemble(
n, dimensions=1, neuron_type=nengo.LIF(),
encoders=encoders, max_rates=max_rates, intercepts=intercepts)
nengo.Connection(ins, ens.neurons, transform=np.ones((n, 1)))
spike_probe = nengo.Probe(ens.neurons)
voltage_probe = nengo.Probe(ens.neurons, 'voltage')
ref_probe = nengo.Probe(ens.neurons, 'refractory_time')
sim = Simulator(m, dt=dt)
t_final = 1.0
sim.run(t_final)
with Plotter(Simulator) as plt:
i = 3
plt.subplot(311)
plt.plot(sim.trange(), sim.data[spike_probe][:, :i])
plt.subplot(312)
plt.plot(sim.trange(), sim.data[voltage_probe][:, :i])
plt.subplot(313)
plt.plot(sim.trange(), sim.data[ref_probe][:, :i])
plt.ylim([-dt, ens.neuron_type.tau_ref + dt])
plt.savefig('test_neurons.test_lif.pdf')
plt.close()
# check rates against analytic rates
math_rates = ens.neuron_type.rates(
x, *ens.neuron_type.gain_bias(max_rates, intercepts))
sim_rates = sim.data[spike_probe].sum(0) / t_final
logger.debug("ME = %f", (sim_rates - math_rates).mean())
logger.debug("RMSE = %f",
rms(sim_rates - math_rates) / (rms(math_rates) + 1e-20))
assert np.sum(math_rates > 0) > 0.5 * n, (
"At least 50% of neurons must fire")
assert np.allclose(sim_rates, math_rates, atol=1, rtol=0.02)
# if voltage and ref time are non-constant, the probe is doing something
assert np.abs(np.diff(sim.data[voltage_probe])).sum() > 1
assert np.abs(np.diff(sim.data[ref_probe])).sum() > 1
def test_alif(Simulator):
"""Test ALIF and ALIFRate by comparing them to each other"""
n = 100
max_rates = 50 * np.ones(n)
intercepts = np.linspace(-0.99, 0.99, n)
encoders = np.ones((n, 1))
nparams = dict(tau_n=1, inc_n=10e-3)
eparams = dict(n_neurons=n, max_rates=max_rates,
intercepts=intercepts, encoders=encoders)
model = nengo.Network()
with model:
u = nengo.Node(output=0.5)
a = nengo.Ensemble(neuron_type=nengo.AdaptiveLIFRate(**nparams),
dimensions=1,
**eparams)
b = nengo.Ensemble(neuron_type=nengo.AdaptiveLIF(**nparams),
dimensions=1,
**eparams)
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
ap = nengo.Probe(a, "spikes", synapse=0)
bp = nengo.Probe(b, "spikes", synapse=0)
dt = 1e-3
sim = Simulator(model, dt=dt)
sim.run(2.)
t = sim.trange()
a_rates = sim.data[ap] / dt
spikes = sim.data[bp]
b_rates = rates_kernel(t, spikes)
tmask = (t > 0.1) & (t < 1.7)
rel_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
with Plotter(Simulator) as plt:
ax = plt.subplot(311)
implot(plt, t, intercepts[::-1], a_rates.T, ax=ax)
ax.set_ylabel('input')
ax = plt.subplot(312)
implot(plt, t, intercepts[::-1], b_rates.T, ax=ax)
ax.set_ylabel('input')
ax = plt.subplot(313)
implot(plt, t, intercepts[::-1], (b_rates - a_rates)[tmask].T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('input')
plt.savefig('test_neurons.test_alif.pdf')
plt.close()
assert rel_rmse < 0.07
def test_lif(Simulator, plt, rng, logger):
"""Test that the dynamic model approximately matches the rates"""
dt = 0.001
n = 5000
x = 0.5
encoders = np.ones((n, 1))
max_rates = rng.uniform(low=10, high=200, size=n)
intercepts = rng.uniform(low=-1, high=1, size=n)
m = nengo.Network()
with m:
ins = nengo.Node(x)
ens = nengo.Ensemble(n,
dimensions=1,
neuron_type=nengo.LIF(),
encoders=encoders,
max_rates=max_rates,
intercepts=intercepts)
nengo.Connection(ins, ens.neurons, transform=np.ones((n, 1)))
spike_probe = nengo.Probe(ens.neurons)
voltage_probe = nengo.Probe(ens.neurons, 'voltage')
ref_probe = nengo.Probe(ens.neurons, 'refractory_time')
sim = Simulator(m, dt=dt)
t_final = 1.0
sim.run(t_final)
i = 3
plt.subplot(311)
plt.plot(sim.trange(), sim.data[spike_probe][:, :i])
plt.subplot(312)
plt.plot(sim.trange(), sim.data[voltage_probe][:, :i])
plt.subplot(313)
plt.plot(sim.trange(), sim.data[ref_probe][:, :i])
plt.ylim([-dt, ens.neuron_type.tau_ref + dt])
# check rates against analytic rates
math_rates = ens.neuron_type.rates(
x, *ens.neuron_type.gain_bias(max_rates, intercepts))
spikes = sim.data[spike_probe]
sim_rates = (spikes > 0).sum(0) / t_final
logger.info("ME = %f", (sim_rates - math_rates).mean())
logger.info("RMSE = %f",
rms(sim_rates - math_rates) / (rms(math_rates) + 1e-20))
assert np.sum(math_rates > 0) > 0.5 * n, (
"At least 50% of neurons must fire")
assert np.allclose(sim_rates, math_rates, atol=1, rtol=0.02)
# if voltage and ref time are non-constant, the probe is doing something
assert np.abs(np.diff(sim.data[voltage_probe])).sum() > 1
assert np.abs(np.diff(sim.data[ref_probe])).sum() > 1
def test_alif(Simulator, plt):
"""Test ALIF and ALIFRate by comparing them to each other"""
n = 100
max_rates = 50 * np.ones(n)
intercepts = np.linspace(-0.99, 0.99, n)
encoders = np.ones((n, 1))
nparams = dict(tau_n=1, inc_n=10e-3)
eparams = dict(n_neurons=n,
max_rates=max_rates,
intercepts=intercepts,
encoders=encoders)
model = nengo.Network()
with model:
u = nengo.Node(output=0.5)
a = nengo.Ensemble(neuron_type=AdaptiveLIFRate(**nparams),
dimensions=1,
**eparams)
b = nengo.Ensemble(neuron_type=AdaptiveLIF(**nparams),
dimensions=1,
**eparams)
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
ap = nengo.Probe(a.neurons)
bp = nengo.Probe(b.neurons)
with Simulator(model) as sim:
sim.run(2.0)
t = sim.trange()
a_rates = sim.data[ap]
spikes = sim.data[bp]
b_rates = nengo.Lowpass(0.04).filtfilt(spikes)
tmask = (t > 0.1) & (t < 1.7)
rel_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
ax = plt.subplot(311)
implot(plt, t, intercepts[::-1], a_rates.T, ax=ax)
ax.set_ylabel("input")
ax = plt.subplot(312)
implot(plt, t, intercepts[::-1], b_rates.T, ax=ax)
ax.set_ylabel("input")
ax = plt.subplot(313)
implot(plt, t, intercepts[::-1], (b_rates - a_rates)[tmask].T, ax=ax)
ax.set_xlabel("time [s]")
ax.set_ylabel("input")
assert rel_rmse < 0.07
def _test_rates(Simulator, rates, plt, seed, name=None):
if name is None:
name = rates.__name__
n = 100
intercepts = np.linspace(-0.99, 0.99, n)
model = nengo.Network(seed=seed)
with model:
model.config[nengo.Ensemble].max_rates = Choice([50])
model.config[nengo.Ensemble].encoders = Choice([[1]])
u = nengo.Node(output=WhiteNoise(2., 5).f(
rng=np.random.RandomState(seed=seed)))
a = nengo.Ensemble(n, 1,
intercepts=intercepts, neuron_type=nengo.LIFRate())
b = nengo.Ensemble(n, 1,
intercepts=intercepts, neuron_type=nengo.LIF())
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
up = nengo.Probe(u)
ap = nengo.Probe(a.neurons)
bp = nengo.Probe(b.neurons)
sim = Simulator(model)
sim.run(2.)
t = sim.trange()
x = sim.data[up]
a_rates = sim.data[ap]
spikes = sim.data[bp]
b_rates = rates(t, spikes)
ax = plt.subplot(411)
plt.plot(t, x)
ax = plt.subplot(412)
implot(plt, t, intercepts, a_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(413)
implot(plt, t, intercepts, b_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(414)
implot(plt, t, intercepts, (b_rates - a_rates).T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('intercept')
plt.saveas = 'utils.test_neurons.test_rates.%s.pdf' % name
tmask = (t > 0.1) & (t < 1.9)
relative_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
return relative_rmse
def _test_rates(Simulator, rates, plt, seed):
n = 100
intercepts = np.linspace(-0.99, 0.99, n)
model = nengo.Network(seed=seed)
with model:
model.config[nengo.Ensemble].max_rates = nengo.dists.Choice([50])
model.config[nengo.Ensemble].encoders = nengo.dists.Choice([[1]])
u = nengo.Node(output=nengo.processes.WhiteSignal(2, high=5))
a = nengo.Ensemble(n,
1,
intercepts=intercepts,
neuron_type=nengo.LIFRate())
b = nengo.Ensemble(n,
1,
intercepts=intercepts,
neuron_type=nengo.LIF())
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
up = nengo.Probe(u)
ap = nengo.Probe(a.neurons)
bp = nengo.Probe(b.neurons)
with Simulator(model, seed=seed + 1) as sim:
sim.run(2.)
t = sim.trange()
x = sim.data[up]
a_rates = sim.data[ap]
spikes = sim.data[bp]
b_rates = rates(t, spikes)
if plt is not None:
ax = plt.subplot(411)
plt.plot(t, x)
ax = plt.subplot(412)
implot(plt, t, intercepts, a_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(413)
implot(plt, t, intercepts, b_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(414)
implot(plt, t, intercepts, (b_rates - a_rates).T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('intercept')
tmask = (t > 0.1) & (t < 1.9)
relative_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
return relative_rmse
def test_amplitude(Simulator, seed, rng, plt, allclose, Neuron):
amp = 0.1
neuron0 = Neuron()
neuron = Neuron(amplitude=amp)
# check static
x = np.linspace(-5, 30)
y = amp * neuron0.rates(x, 1.0, 0.0)
y2 = neuron.rates(x, 1.0, 0.0)
assert allclose(y, y2, atol=1e-5)
# check dynamic
n = 100
x = 1.0
encoders = np.ones((n, 1))
max_rates = rng.uniform(low=20, high=200, size=n)
intercepts = rng.uniform(low=-1, high=0.8, size=n)
with nengo.Network(seed=seed) as model:
ins = nengo.Node(x)
ens = nengo.Ensemble(
n,
dimensions=1,
neuron_type=neuron,
encoders=encoders,
max_rates=max_rates,
intercepts=intercepts,
)
nengo.Connection(ins, ens, synapse=None)
spike_probe = nengo.Probe(ens.neurons)
dt = 0.001
t_final = 0.5
with Simulator(model, dt=dt) as sim:
sim.run(t_final)
spikes = sim.data[spike_probe]
r = spikes.sum(axis=0) * (dt / t_final)
gain, bias = neuron0.gain_bias(max_rates, intercepts)
r0 = amp * neuron0.rates(x, gain, bias).squeeze(axis=0)
i = np.argsort(r0)
plt.plot(r0[i])
plt.plot(r[i])
error = rms(r - r0) / rms(r0)
assert (error < 0.02).all()
def test_alif(Simulator, plt):
"""Test ALIF and ALIFRate by comparing them to each other"""
n = 100
max_rates = 50 * np.ones(n)
intercepts = np.linspace(-0.99, 0.99, n)
encoders = np.ones((n, 1))
nparams = dict(tau_n=1, inc_n=10e-3)
eparams = dict(n_neurons=n, max_rates=max_rates,
intercepts=intercepts, encoders=encoders)
model = nengo.Network()
with model:
u = nengo.Node(output=0.5)
a = nengo.Ensemble(neuron_type=AdaptiveLIFRate(**nparams),
dimensions=1,
**eparams)
b = nengo.Ensemble(neuron_type=AdaptiveLIF(**nparams),
dimensions=1,
**eparams)
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
ap = nengo.Probe(a.neurons)
bp = nengo.Probe(b.neurons)
with Simulator(model) as sim:
sim.run(2.)
t = sim.trange()
a_rates = sim.data[ap]
spikes = sim.data[bp]
b_rates = nengo.Lowpass(0.04).filtfilt(spikes)
tmask = (t > 0.1) & (t < 1.7)
rel_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
ax = plt.subplot(311)
implot(plt, t, intercepts[::-1], a_rates.T, ax=ax)
ax.set_ylabel('input')
ax = plt.subplot(312)
implot(plt, t, intercepts[::-1], b_rates.T, ax=ax)
ax.set_ylabel('input')
ax = plt.subplot(313)
implot(plt, t, intercepts[::-1], (b_rates - a_rates)[tmask].T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('input')
assert rel_rmse < 0.07
def solve_HingeLoss(solver, queue, clA, Y, rng=None, E=None):
import scipy.optimize
import pyopencl_blas
pyopencl_blas.setup()
tstart = time.time()
assert clA.shape[0] == Y.shape[0]
m, n = clA.shape
_, d = Y.shape
Xshape = (n, d)
# regularization
sigma = solver.reg * cl.array.max(clA).get()
lamb = m * sigma**2
# --- initialization
X0 = rng.uniform(-1. / n, 1. / n, size=Xshape)
# --- solve with L-BFGS
yinds = Y.argmax(axis=1)
clX = cl.array.Array(queue, (n, d), dtype=np.float32)
clyinds = cl.array.to_device(queue, yinds.astype(np.int32))
clZ = cl.array.Array(queue, (m, d), dtype=np.float32)
clc = cl.array.Array(queue, (m, ), dtype=np.float32)
clE = cl.array.Array(queue, (m, d), dtype=np.float32)
clG = cl.array.Array(queue, (n, d), dtype=np.float32)
hingeloss_plan = plan_hingeloss(queue, clyinds, clZ, clc, clE)
def f_df(x):
clX.set(x.astype(np.float32).reshape(Xshape))
pyopencl_blas.gemm(queue, clA, clX, clZ)
hingeloss_plan()
cost = pyopencl.array.sum(clc).get()
pyopencl_blas.gemm(queue, clA, clE, clG, transA=True)
if lamb > 0:
cost += 0.5 * lamb * pyopencl.array.sum(clX**2).get()
# cost += 0.5 * lamb * sum_square(clX).get()
clG[:] += lamb * clX
G = clG.get().astype(np.float64)
return cost, G.ravel()
x0 = X0.ravel()
x, mincost, info = scipy.optimize.fmin_l_bfgs_b(f_df,
x0,
maxfun=solver.n_epochs,
iprint=solver.verbose)
tend = time.time()
A = clA.get()
X = x.reshape(Xshape)
return solver.mul_encoders(X, E), {
'rmses': npext.rms(np.dot(A, X) - Y, axis=1),
'time': tend - tstart
}
def objective(args):
sargs = arg_string(args)
w_kind = args['w_kind']
w_scale = args['w_scale']
eta = args['eta']
# eta = [args['eta0'], args['eta1'], args['eta2']]
max_cost = -np.inf
for _ in range(5):
f, df = static_f_df(tau_rc=0.05, **args['neuron_type'])
weights = initial_weights(sizes, kind=w_kind, scale=w_scale, rng=rng)
# weights = initial_weights(sizes, kind='ortho', rng=rng)
# lsuv(X, weights, f, target_input=True, target_std=1, verbose=1)
# lsuv(X[:100], weights, f, target_input=True, target_std=1, verbose=1)
# --- learners
network = Network(weights, f=f, df=df, biases=None)
# network = Network(weights, f=f, df=df, biases=None, noise=1.)
learner = Learner(network,
squared_cost,
rms_error,
eta=eta,
alpha=alpha,
momentum=momentum)
learner.train(1, batch_fn, verbose=0)
y = learner.network.predict(Xvalid)
mean_cost = rms(y - Yvalid, axis=1).mean()
max_cost = max(max_cost, mean_cost)
print("%s: %0.3e" % (sargs, max_cost))
return max_cost
def lstsq_L1(A, Y, rng=np.random, E=None, l1=1e-4, l2=1e-6):
"""Least-squares with L1 and L2 regularization (elastic net).
This method is well suited for creating sparse decoders or weight matrices.
"""
import sklearn.linear_model
# TODO: play around with these regularization constants (I just guessed).
# Do we need to scale regularization by number of neurons, to get same
# level of sparsity? esp. with weights? Currently, setting l1=1e-3 works
# well with weights when connecting 1D populations with 100 neurons each.
a = l1 * A.max() # L1 regularization
b = l2 * A.max()**2 # L2 regularization
alpha = a + b
l1_ratio = a / (a + b)
# --- solve least-squares A * X = Y
if E is not None:
Y = np.dot(Y, E)
model = sklearn.linear_model.ElasticNet(
alpha=alpha, l1_ratio=l1_ratio, fit_intercept=False, max_iter=1000)
model.fit(A, Y)
X = model.coef_.T
X.shape = (A.shape[1], Y.shape[1]) if Y.ndim > 1 else (A.shape[1],)
infos = {'rmses': npext.rms(Y - np.dot(A, X), axis=0)}
return X, infos
def run_trial():
model = nengo.Network(seed=rng.randint(maxint))
with model:
model.config[nengo.Ensemble].n_eval_points = n_eval_points
stimulus = nengo.Node(
output=lambda t: stimulus_fn(max(0.0, t - wait_duration)),
size_out=2)
product_net = nengo.networks.Product(n_neurons, 1)
nengo.Connection(stimulus[0], product_net.input_a)
nengo.Connection(stimulus[1], product_net.input_b)
probe_test = nengo.Probe(product_net.output)
ens_direct = nengo.Ensemble(1,
dimensions=2,
neuron_type=nengo.Direct())
result_direct = nengo.Node(size_in=1)
nengo.Connection(stimulus, ens_direct)
nengo.Connection(ens_direct,
result_direct,
function=lambda x: x[0] * x[1],
synapse=None)
probe_direct = nengo.Probe(result_direct)
with Simulator(model) as sim:
sim.run(duration + wait_duration, progress_bar=False)
selection = sim.trange() > wait_duration
test = sim.data[probe_test][selection]
direct = sim.data[probe_direct][selection]
return rms(test - direct)
def __call__(self, A, Y, sigma, rng=None):
Y, m, _, _, matrix_in = format_system(A, Y)
U, s, V = np.linalg.svd(A, full_matrices=0)
si = s / (s**2 + m * sigma**2)
X = np.dot(V.T, si[:, None] * np.dot(U.T, Y))
info = {'rmses': npext.rms(Y - np.dot(A, X), axis=0)}
return X if matrix_in else X.flatten(), info
def make_step(self, size_in, size_out, dt, rng):
assert size_in[0] == 0
assert size_out[0] == 1
rate = 1. / dt
orig_rate, orig = readwav(self.path)
new_size = int(orig.size * (rate / orig_rate))
wave = resample(orig, new_size)
wave -= wave.mean()
# Normalize wave to desired rms
wave_rms = npext.rms(wave)
wave *= (self.rms / wave_rms)
if self.at_end == 'loop':
def step_wavfileloop(t):
idx = int(t * rate) % wave.size
return wave[idx]
return step_wavfileloop
elif self.at_end == 'stop':
def step_wavfilestop(t):
idx = int(t * rate)
if idx > wave.size:
return 0.
else:
return wave[idx]
return step_wavfilestop
def test_eval_point_decoding(Simulator, nl_nodirect, plt, seed):
with nengo.Network(seed=seed) as model:
model.config[nengo.Ensemble].neuron_type = nl_nodirect()
a = nengo.Ensemble(200, 2)
b = nengo.Ensemble(100, 1)
c = nengo.Connection(a, b, function=lambda x: x[0] * x[1])
sim = Simulator(model)
eval_points, targets, decoded = eval_point_decoding(c, sim)
def contour(xy, z):
xi = np.linspace(-1, 1, 101)
yi = np.linspace(-1, 1, 101)
zi = griddata(xy[:, 0], xy[:, 1], z.ravel(), xi, yi, interp="linear")
plt.contourf(xi, yi, zi, cmap=plt.cm.seismic)
plt.colorbar()
plt.figure(figsize=(15, 5))
plt.subplot(131)
contour(eval_points, targets)
plt.title("Target (desired decoding)")
plt.subplot(132)
plt.title("Actual decoding")
contour(eval_points, decoded)
plt.subplot(133)
plt.title("Difference between actual and desired")
contour(eval_points, decoded - targets)
# Generous error check, just to make sure it's in the right ballpark.
# Also make sure error is above zero, i.e. y != z
error = rms(decoded - targets, axis=1).mean()
assert error < 0.1 and error > 1e-8
def randomized_svd(A, Y, sigma, rng=np.random,
n_components=60, n_oversamples=10, **kwargs):
"""Solve the least-squares system using a randomized (partial) SVD.
Parameters
----------
n_components : int (default is 50)
The number of SVD components to compute. A small survey of activity
matrices suggests that the first 50 components capture almost all
the variance.
n_oversamples: int (default is 10)
The number of additional samples on the range of A.
n_iter : int (default is 0)
The number of power iterations to perform (can help with noisy data).
See also
--------
``sklearn.utils.extmath.randomized_svd`` for details about the parameters.
"""
from sklearn.utils.extmath import randomized_svd as sklearn_randomized_svd
Y, m, n, _, matrix_in = _format_system(A, Y)
if min(m, n) <= n_components + n_oversamples:
# more efficient to do a full SVD
return svd(A, Y, sigma, rng=rng)
U, s, V = sklearn_randomized_svd(
A, n_components, random_state=rng, **kwargs)
si = s / (s**2 + m * sigma**2)
X = np.dot(V.T, si[:, None] * np.dot(U.T, Y))
info = {'rmses': npext.rms(Y - np.dot(A, X), axis=0)}
return X if matrix_in else X.flatten(), info
def test_eval_points(Simulator, nl_nodirect, plt, seed, rng):
n = 100
d = 5
filter = 0.08
eval_points = np.logspace(np.log10(300), np.log10(5000), 11)
eval_points = np.round(eval_points).astype('int')
max_points = eval_points.max()
n_trials = 1
rmses = np.nan * np.zeros((len(eval_points), n_trials))
for j in range(n_trials):
points = rng.normal(size=(max_points, d))
points *= (rng.uniform(size=max_points) / norm(points, axis=-1))[:,
None]
rng_j = np.random.RandomState(348 + j)
seed = 903824 + j
# generate random input in unit hypersphere
x = rng_j.normal(size=d)
x *= rng_j.uniform() / norm(x)
for i, n_points in enumerate(eval_points):
model = nengo.Network(seed=seed)
with model:
model.config[nengo.Ensemble].neuron_type = nl_nodirect()
u = nengo.Node(output=x)
a = nengo.Ensemble(n * d,
dimensions=d,
eval_points=points[:n_points])
nengo.Connection(u, a, synapse=0)
up = nengo.Probe(u)
ap = nengo.Probe(a)
with Timer() as timer:
sim = Simulator(model)
sim.run(10 * filter)
t = sim.trange()
xt = nengo.synapses.filtfilt(sim.data[up], filter, dt=sim.dt)
yt = nengo.synapses.filtfilt(sim.data[ap], filter, dt=sim.dt)
t0 = 5 * filter
t1 = 7 * filter
tmask = (t > t0) & (t < t1)
rmses[i, j] = rms(yt[tmask] - xt[tmask])
print("done %d (%d) in %0.3f s" % (n_points, j, timer.duration))
# subtract out mean for each model
rmses_norm = rmses - rmses.mean(0, keepdims=True)
mean = rmses_norm.mean(1)
low = rmses_norm.min(1)
high = rmses_norm.max(1)
plt.semilogx(eval_points, mean, 'k-')
plt.semilogx(eval_points, high, 'r-')
plt.semilogx(eval_points, low, 'b-')
plt.xlim([eval_points[0], eval_points[-1]])
plt.xticks(eval_points, eval_points)
def conjgrad_scipy(A, Y, sigma, tol=1e-4):
"""Solve the least-squares system using Scipy's conjugate gradient."""
import scipy.sparse.linalg
Y, m, n, d, matrix_in = _format_system(A, Y)
damp = m * sigma**2
calcAA = lambda x: np.dot(A.T, np.dot(A, x)) + damp * x
G = scipy.sparse.linalg.LinearOperator(
(n, n), matvec=calcAA, matmat=calcAA, dtype=A.dtype)
B = np.dot(A.T, Y)
X = np.zeros((n, d), dtype=B.dtype)
infos = np.zeros(d, dtype='int')
itns = np.zeros(d, dtype='int')
for i in range(d):
def callback(x):
itns[i] += 1 # use the callback to count the number of iterations
X[:, i], infos[i] = scipy.sparse.linalg.cg(
G, B[:, i], tol=tol, callback=callback)
info = {'rmses': npext.rms(Y - np.dot(A, X), axis=0),
'iterations': itns,
'info': infos}
return X if matrix_in else X.flatten(), info
def test_regularization(Simulator, nl_nodirect, plt):
# TODO: multiple trials per parameter set, with different seeds
Solvers = [LstsqL2, LstsqL2nz]
neurons = np.array([10, 20, 50, 100])
regs = np.linspace(0.01, 0.3, 16)
filters = np.linspace(0, 0.03, 11)
buf = 0.2 # buffer for initial transients
dt = 1e-3
tfinal = 3 + buf
def input_function(t):
return np.interp(t, [1, 3], [-1, 1], left=-1, right=1)
model = nengo.Network('test_regularization')
with model:
model.config[nengo.Ensemble].neuron_type = nl_nodirect()
u = nengo.Node(output=input_function)
up = nengo.Probe(u)
probes = np.zeros(
(len(Solvers), len(neurons), len(regs), len(filters)),
dtype='object')
for j, n_neurons in enumerate(neurons):
a = nengo.Ensemble(n_neurons, dimensions=1)
nengo.Connection(u, a)
for i, Solver in enumerate(Solvers):
for k, reg in enumerate(regs):
for l, synapse in enumerate(filters):
probes[i, j, k, l] = nengo.Probe(
a, solver=Solver(reg=reg), synapse=synapse)
sim = Simulator(model, dt=dt)
sim.run(tfinal)
t = sim.trange()
ref = sim.data[up]
rmse_buf = lambda a, b: rms(a[t > buf] - b[t > buf])
rmses = np.zeros(probes.shape)
for i, probe in enumerate(probes.flat):
rmses.flat[i] = rmse_buf(sim.data[probe], ref)
rmses = rmses - rmses[:, :, [0], :]
plt.figure(figsize=(8, 12))
X, Y = np.meshgrid(filters, regs)
for i, Solver in enumerate(Solvers):
for j, n_neurons in enumerate(neurons):
plt.subplot(len(neurons), len(Solvers), len(Solvers)*j + i + 1)
Z = rmses[i, j, :, :]
plt.contourf(X, Y, Z, levels=np.linspace(Z.min(), Z.max(), 21))
plt.xlabel('filter')
plt.ylabel('reg')
plt.title("%s (N=%d)" % (Solver.__name__, n_neurons))
plt.tight_layout()
def test_sine_waves(Simulator, plt, seed):
radius = 2
dim = 5
product = nengo.networks.Product(200, dim, radius, seed=seed)
func_a = lambda t: np.sqrt(radius) * np.sin(
np.arange(1, dim + 1) * 2 * np.pi * t)
func_b = lambda t: np.sqrt(radius) * np.sin(
np.arange(dim, 0, -1) * 2 * np.pi * t)
with product:
input_a = nengo.Node(func_a)
input_b = nengo.Node(func_b)
nengo.Connection(input_a, product.input_a)
nengo.Connection(input_b, product.input_b)
p = nengo.Probe(product.output, synapse=0.005)
with Simulator(product) as sim:
sim.run(1.0)
t = sim.trange()
ideal = np.asarray([func_a(tt)
for tt in t]) * np.asarray([func_b(tt) for tt in t])
delay = 0.013
offset = np.where(t >= delay)[0]
for i in range(dim):
plt.subplot(dim + 1, 1, i + 1)
plt.plot(t + delay, ideal[:, i])
plt.plot(t, sim.data[p][:, i])
plt.xlim(right=t[-1])
plt.yticks((-2, 0, 2))
assert rms(ideal[:len(offset), :] - sim.data[p][offset, :]) < 0.2
def lstsq_drop(A, Y, rng, E=None, noise_amp=0.1, drop=0.25, solver=lstsq_L2nz):
"""Find sparser decoders/weights by dropping small values.
This solver first solves for coefficients (decoders/weights) with
L2 regularization, drops those nearest to zero, and retrains remaining.
"""
Y, m, n, d, matrix_in = _format_system(A, Y)
# solve for coefficients using standard solver
X, info0 = solver(A, Y, rng=rng, noise_amp=noise_amp)
X = np.dot(X, E) if E is not None else X
# drop weights close to zero, based on `drop` ratio
Xabs = np.sort(np.abs(X.flat))
threshold = Xabs[int(np.round(drop * Xabs.size))]
X[np.abs(X) < threshold] = 0
# retrain nonzero weights
Y = np.dot(Y, E) if E is not None else Y
for i in range(X.shape[1]):
nonzero = X[:, i] != 0
if nonzero.sum() > 0:
X[nonzero, i], info1 = solver(
A[:, nonzero], Y[:, i], rng=rng, noise_amp=0.1 * noise_amp)
info = {'rmses': npext.rms(Y - np.dot(A, X), axis=0),
'info0': info0, 'info1': info1}
return X if matrix_in else X.flatten(), info
def test_high_dimensional_integrator(plt):
d = 32
dt = 1e-3
def f(t, hz):
return np.cos(2 * np.pi * hz * (t - dt)) * (2 * np.pi * hz)
input_functions = [
lambda t, hz=hz: f(t, hz) for hz in np.linspace(1, 2, d)
]
u = stimuli(input_functions)
x = u.integrate()
y = np.asarray(x.run(1, dt=dt))
y_hat = np.asarray(x.decode().filter(5e-3).run(1, dt=dt))
assert y.shape == y_hat.shape
t = (1 + np.arange(y.shape[1])) * dt
y_check = np.cumsum(np.asarray([f(t)
for f in input_functions]), axis=1) * dt
assert np.allclose(y.squeeze(axis=2)[:, 1:], y_check[:, :-1])
assert rms(y - y_hat) < 0.1
for y_i, y_hat_i in zip(y, y_hat):
plt.plot(y_i.squeeze(axis=1), linestyle="--")
plt.plot(y_hat_i.squeeze(axis=1), alpha=0.7)
plt.xlabel("Time-step")
def make_step(self, size_in, size_out, dt, rng):
assert size_in[0] == 0
assert size_out[0] == 1
rate = 1. / dt
orig_rate, orig = readwav(self.path)
new_size = int(orig.size * (rate / orig_rate))
wave = resample(orig, new_size)
wave -= wave.mean()
# Normalize wave to desired rms
wave_rms = npext.rms(wave)
wave *= (self.rms / wave_rms)
if self.at_end == 'loop':
def step_wavfileloop(t):
idx = int(t * rate) % wave.size
return wave[idx]
return step_wavfileloop
elif self.at_end == 'stop':
def step_wavfilestop(t):
idx = int(t * rate)
if idx > wave.size:
return 0.
else:
return wave[idx]
return step_wavfilestop
def cholesky(A, y, sigma, transpose=None):
"""Solve the least-squares system using the Cholesky decomposition."""
m, n = A.shape
if transpose is None:
# transpose if matrix is fat, but not if we have sigmas for each neuron
transpose = m < n and sigma.size == 1
if transpose:
# substitution: x = A'*xbar, G*xbar = b where G = A*A' + lambda*I
G = np.dot(A, A.T)
b = y
else:
# multiplication by A': G*x = A'*b where G = A'*A + lambda*I
G = np.dot(A.T, A)
b = np.dot(A.T, y)
# add L2 regularization term 'lambda' = m * sigma**2
np.fill_diagonal(G, G.diagonal() + m * sigma**2)
try:
import scipy.linalg
factor = scipy.linalg.cho_factor(G, overwrite_a=True)
x = scipy.linalg.cho_solve(factor, b)
except ImportError:
L = np.linalg.cholesky(G)
L = np.linalg.inv(L.T)
x = np.dot(L, np.dot(L.T, b))
x = np.dot(A.T, x) if transpose else x
info = {'rmses': npext.rms(y - np.dot(A, x), axis=0)}
return x, info
def __call__(self, A, Y, rng=None, E=None):
Y = self.mul_encoders(Y, E)
X, residuals2, rank, s = np.linalg.lstsq(A, Y, rcond=self.rcond)
return X, {'rmses': npext.rms(Y - np.dot(A, X), axis=0),
'residuals': np.sqrt(residuals2),
'rank': rank,
'singular_values': s}
def cholesky(A, y, sigma, transpose=None):
"""Solve the least-squares system using the Cholesky decomposition."""
m, n = A.shape
if transpose is None:
# transpose if matrix is fat, but not if we have sigmas for each neuron
transpose = m < n and sigma.size == 1
if transpose:
# substitution: x = A'*xbar, G*xbar = b where G = A*A' + lambda*I
G = np.dot(A, A.T)
b = y
else:
# multiplication by A': G*x = A'*b where G = A'*A + lambda*I
G = np.dot(A.T, A)
b = np.dot(A.T, y)
# add L2 regularization term 'lambda' = m * sigma**2
np.fill_diagonal(G, G.diagonal() + m * sigma**2)
try:
import scipy.linalg
factor = scipy.linalg.cho_factor(G, overwrite_a=True)
x = scipy.linalg.cho_solve(factor, b)
except ImportError:
L = np.linalg.cholesky(G)
L = np.linalg.inv(L.T)
x = np.dot(L, np.dot(L.T, b))
x = np.dot(A.T, x) if transpose else x
info = {'rmses': npext.rms(y - np.dot(A, x), axis=0)}
return x, info
def __call__(self, A, Y, rng=None, E=None):
Y, m, n, d, matrix_in = _format_system(A, Y)
# solve for coefficients using standard solver
X, info0 = self.solver1(A, Y, rng=rng)
X = self.mul_encoders(X, E)
# drop weights close to zero, based on `drop` ratio
Xabs = np.sort(np.abs(X.flat))
threshold = Xabs[int(np.round(self.drop * Xabs.size))]
X[np.abs(X) < threshold] = 0
# retrain nonzero weights
Y = self.mul_encoders(Y, E)
for i in range(X.shape[1]):
nonzero = X[:, i] != 0
if nonzero.sum() > 0:
X[nonzero, i], info1 = self.solver2(A[:, nonzero],
Y[:, i],
rng=rng)
info = {
'rmses': npext.rms(Y - np.dot(A, X), axis=0),
'info0': info0,
'info1': info1
}
return X if matrix_in else X.flatten(), info
def conjgrad_scipy(A, Y, sigma, tol=1e-4):
"""Solve the least-squares system using Scipy's conjugate gradient."""
import scipy.sparse.linalg
Y, m, n, d, matrix_in = _format_system(A, Y)
damp = m * sigma**2
calcAA = lambda x: np.dot(A.T, np.dot(A, x)) + damp * x
G = scipy.sparse.linalg.LinearOperator((n, n),
matvec=calcAA,
matmat=calcAA,
dtype=A.dtype)
B = np.dot(A.T, Y)
X = np.zeros((n, d), dtype=B.dtype)
infos = np.zeros(d, dtype='int')
itns = np.zeros(d, dtype='int')
for i in range(d):
def callback(x):
itns[i] += 1 # use the callback to count the number of iterations
X[:, i], infos[i] = scipy.sparse.linalg.cg(G,
B[:, i],
tol=tol,
callback=callback)
info = {
'rmses': npext.rms(Y - np.dot(A, X), axis=0),
'iterations': itns,
'info': infos
}
return X if matrix_in else X.flatten(), info
def __call__(self, A, Y, sigma, rng=None):
Y, m, _, _, matrix_in = format_system(A, Y)
U, s, V = np.linalg.svd(A, full_matrices=0)
si = s / (s**2 + m * sigma**2)
X = np.dot(V.T, si[:, None] * np.dot(U.T, Y))
info = {'rmses': npext.rms(Y - np.dot(A, X), axis=0)}
return X if matrix_in else X.ravel(), info
def lstsq(A, Y, rng=np.random, E=None, rcond=0.01):
"""Unregularized least-squares."""
Y = np.dot(Y, E) if E is not None else Y
X, residuals2, rank, s = np.linalg.lstsq(A, Y, rcond=rcond)
return X, {'rmses': npext.rms(Y - np.dot(A, X), axis=0),
'residuals': np.sqrt(residuals2),
'rank': rank,
'singular_values': s}
def svd(A, Y, sigma, rng=None):
"""Solve the least-squares system using a full SVD."""
Y, m, _, _, matrix_in = _format_system(A, Y)
U, s, V = np.linalg.svd(A, full_matrices=0)
si = s / (s**2 + m * sigma**2)
X = np.dot(V.T, si[:, None] * np.dot(U.T, Y))
info = {'rmses': npext.rms(Y - np.dot(A, X), axis=0)}
return X if matrix_in else X.flatten(), info
def _test_rates(Simulator, rates, plt, seed):
n = 100
intercepts = np.linspace(-0.99, 0.99, n)
model = nengo.Network(seed=seed)
with model:
model.config[nengo.Ensemble].max_rates = Choice([50])
model.config[nengo.Ensemble].encoders = Choice([[1]])
u = nengo.Node(output=WhiteSignal(2, high=5))
a = nengo.Ensemble(n, 1,
intercepts=intercepts, neuron_type=nengo.LIFRate())
b = nengo.Ensemble(n, 1,
intercepts=intercepts, neuron_type=nengo.LIF())
nengo.Connection(u, a, synapse=0)
nengo.Connection(u, b, synapse=0)
up = nengo.Probe(u)
ap = nengo.Probe(a.neurons)
bp = nengo.Probe(b.neurons)
with Simulator(model, seed=seed+1) as sim:
sim.run(2.)
t = sim.trange()
x = sim.data[up]
a_rates = sim.data[ap]
spikes = sim.data[bp]
b_rates = rates(t, spikes)
if plt is not None:
ax = plt.subplot(411)
plt.plot(t, x)
ax = plt.subplot(412)
implot(plt, t, intercepts, a_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(413)
implot(plt, t, intercepts, b_rates.T, ax=ax)
ax.set_ylabel('intercept')
ax = plt.subplot(414)
implot(plt, t, intercepts, (b_rates - a_rates).T, ax=ax)
ax.set_xlabel('time [s]')
ax.set_ylabel('intercept')
tmask = (t > 0.1) & (t < 1.9)
relative_rmse = rms(b_rates[tmask] - a_rates[tmask]) / rms(a_rates[tmask])
return relative_rmse
def test_amplitude(Simulator, seed, rng, plt, Neuron):
amp = 0.1
neuron0 = Neuron()
neuron = Neuron(amplitude=amp)
# check static
x = np.linspace(-5, 30)
y = amp * neuron0.rates(x, 1., 0.)
y2 = neuron.rates(x, 1., 0.)
assert np.allclose(y, y2, atol=1e-5)
# check dynamic
n = 100
x = 1.0
encoders = np.ones((n, 1))
max_rates = rng.uniform(low=20, high=200, size=n)
intercepts = rng.uniform(low=-1, high=0.8, size=n)
with nengo.Network(seed=seed) as model:
ins = nengo.Node(x)
ens = nengo.Ensemble(
n, dimensions=1, neuron_type=neuron,
encoders=encoders, max_rates=max_rates, intercepts=intercepts)
nengo.Connection(ins, ens, synapse=None)
spike_probe = nengo.Probe(ens.neurons)
dt = 0.001
t_final = 0.5
with Simulator(model, dt=dt) as sim:
sim.run(t_final)
spikes = sim.data[spike_probe]
r = spikes.sum(axis=0) * (dt / t_final)
gain, bias = neuron0.gain_bias(max_rates, intercepts)
r0 = amp * neuron0.rates(x, gain, bias).squeeze(axis=0)
i = np.argsort(r0)
plt.plot(r0[i])
plt.plot(r[i])
error = rms(r - r0) / rms(r0)
assert (error < 0.02).all()
def test_nnls(Solver, plt):
rng = np.random.RandomState(39408)
A, x = get_system(500, 100, 1, rng=rng, sort=True)
y = x**2
d, _ = Solver()(A, y, rng)
yest = np.dot(A, d)
rel_rmse = rms(yest - y) / rms(y)
plt.subplot(211)
plt.plot(x, y, 'k--')
plt.plot(x, yest)
plt.ylim([-0.1, 1.1])
plt.subplot(212)
plt.plot(x, np.zeros_like(x), 'k--')
plt.plot(x, yest - y)
plt.saveas = 'test_solvers.test_nnls.%s.pdf' % Solver.__name__
assert np.allclose(yest, y, atol=3e-2, rtol=1e-3)
assert rel_rmse < 0.02
def test_nnls(Solver, plt, rng):
pytest.importorskip('scipy')
A, x = get_system(500, 100, 1, rng=rng, sort=True)
y = x**2
d, _ = Solver()(A, y, rng)
yest = np.dot(A, d)
rel_rmse = rms(yest - y) / rms(y)
plt.subplot(211)
plt.plot(x, y, 'k--')
plt.plot(x, yest)
plt.ylim([-0.1, 1.1])
plt.subplot(212)
plt.plot(x, np.zeros_like(x), 'k--')
plt.plot(x, yest - y)
assert np.allclose(yest, y, atol=3e-2, rtol=1e-3)
assert rel_rmse < 0.02
def _get_samples(self, path, labels, rms=0.5):
data, fs = sf.read("%s.WAV" % self.path)
assert fs == TIMIT.fs, "fs (%s) != 16000" % fs
# Normalize data to desired rms (or do this per sample?)
data_rms = npext.rms(data)
data *= (rms / data_rms)
info = self._parse_text(path)
samples = {lbl: [] for lbl in labels}
for inf in info:
if inf['lbl'] in samples:
samples[inf['lbl']].append(data[inf['start']: inf['end']])
return samples
def __call__(self, A, Y, rng=None, E=None):
Y = self.mul_encoders(Y, E)
X, residuals2, rank, s = np.linalg.lstsq(A, Y, rcond=self.rcond)
return (
X,
{
"rmses": npext.rms(Y - np.dot(A, X), axis=0),
"residuals": np.sqrt(residuals2),
"rank": rank,
"singular_values": s,
},
)
def __call__(self, A, Y, rng=None, E=None):
import scipy.optimize
Y, m, n, d, matrix_in = _format_system(A, Y)
Y = self.mul_encoders(Y, E)
X = np.zeros((n, d))
residuals = np.zeros(d)
for i in range(d):
X[:, i], residuals[i] = scipy.optimize.nnls(A, Y[:, i])
info = {"rmses": npext.rms(Y - np.dot(A, X), axis=0), "residuals": residuals}
return X if matrix_in else X.flatten(), info
def test_nnls(solver):
rng = np.random.RandomState(39408)
A, x = get_system(500, 100, 1, rng=rng, sort=True)
y = x**2
d, _ = solver(A, y, rng)
yest = np.dot(A, d)
rel_rmse = rms(yest - y) / rms(y)
with Plotter(nengo.Simulator) as plt:
plt.subplot(211)
plt.plot(x, y, 'k--')
plt.plot(x, yest)
plt.ylim([-0.1, 1.1])
plt.subplot(212)
plt.plot(x, np.zeros_like(x), 'k--')
plt.plot(x, yest - y)
plt.savefig('test_decoders.test_nnls.%s.pdf' % solver.__name__)
plt.close()
assert np.allclose(yest, y, atol=3e-2, rtol=1e-3)
assert rel_rmse < 0.02
