def test_adam_optimizer_univar(self, x_start, tol):
"""Tests that adam optimizer takes one and two steps correctly
for univariate functions."""
stepsize, gamma, delta = 0.1, 0.5, 0.8
adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
univariate_funcs = [np.sin, lambda x: np.exp(x / 10.0), lambda x: x ** 2]
grad_uni_fns = [
lambda x: (np.cos(x),),
lambda x: (np.exp(x / 10.0) / 10.0,),
lambda x: (2 * x,),
]
for gradf, f in zip(grad_uni_fns, univariate_funcs):
adam_opt.reset()
x_onestep = adam_opt.step(f, x_start)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 - gamma)
firstmoment = (1 - gamma) * gradf(x_start)[0]
secondmoment = (1 - delta) * gradf(x_start)[0] * gradf(x_start)[0]
x_onestep_target = x_start - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8
)
assert np.allclose(x_onestep, x_onestep_target, atol=tol)
x_twosteps = adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta ** 2) / (1 - gamma ** 2)
firstmoment = gamma * firstmoment + (1 - gamma) * gradf(x_onestep)[0]
secondmoment = (
delta * secondmoment + (1 - delta) * gradf(x_onestep)[0] * gradf(x_onestep)[0]
)
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8
)
assert np.allclose(x_twosteps, x_twosteps_target, atol=tol)
def test_adam_optimizer_multivar(self, tol):
"""Tests that adam optimizer takes one and two steps correctly
for multivariate functions."""
stepsize, gamma, delta = 0.1, 0.5, 0.8
adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_ ** 2 for x_ in x]),
]
grad_multi_funcs = [
lambda x: (np.array([np.cos(x[0]), -np.sin(x[1])]),),
lambda x: (
np.array(
[
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1]) ** 2),
]
),
),
lambda x: (np.array([2 * x_ for x_ in x]),),
]
x_vals = np.linspace(-10, 10, 16, endpoint=False)
for gradf, f in zip(grad_multi_funcs, multivariate_funcs):
for jdx in range(len(x_vals[:-1])):
adam_opt.reset()
x_vec = x_vals[jdx : jdx + 2]
x_onestep = adam_opt.step(f, x_vec)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 - gamma)
firstmoment = (1 - gamma) * gradf(x_vec)[0]
secondmoment = (1 - delta) * gradf(x_vec)[0] * gradf(x_vec)[0]
x_onestep_target = x_vec - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8
)
assert np.allclose(x_onestep, x_onestep_target, atol=tol)
x_twosteps = adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta ** 2) / (1 - gamma ** 2)
firstmoment = gamma * firstmoment + (1 - gamma) * gradf(x_onestep)[0]
secondmoment = (
delta * secondmoment + (1 - delta) * gradf(x_onestep)[0] * gradf(x_onestep)[0]
)
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8
)
assert np.allclose(x_twosteps, x_twosteps_target, atol=tol)
def train(X=[], Y=[], iterations=25, num_of_layers=NUM_OF_LAYERS):
opt = AdamOptimizer(0.01, beta1=0.9, beta2=0.999)
var = weight_init(num_of_layers)
for it in range(iterations):
var = opt.step(lambda v: cost(v, X, Y), var)
# print("Iter: {:5d} | Cost: {:0.7f} ".format(it + 1, cost(var, X, Y)))
return var
def test_adam_optimizer_properties(self):
"""Test the adam property interfaces"""
stepsize, gamma, delta = 0.1, 0.5, 0.8
adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
# check if None is returned when accumulation is empty
assert adam_opt.fm == None
assert adam_opt.sm == None
assert adam_opt.t == None
# Do some calculations to fill accumulation
adam_opt.step(np.sin, np.random.rand(1))
# Check the properties return the same values, stored in accumulation
assert adam_opt.fm == adam_opt.accumulation["fm"]
assert adam_opt.sm == adam_opt.accumulation["sm"]
assert adam_opt.t == adam_opt.accumulation["t"]
def train(self, iterations=25):
opt = AdamOptimizer(0.01, beta1=0.9, beta2=0.999)
var_init = 0.05 * np.random.randn(
self.num_of_layers,
5) # initialise network weights at a Normal Distribution
self.weights = var_init # initialise network weights at a Normal Distribution
for it in range(iterations):
self.weights = opt.step(lambda v: self.cost(v, X, Y), self.weights)
print("Iter: {:5d} | Cost: {:0.7f} ".format(
it + 1, self.cost(self.weights, X, Y)))
accuracy_test = accuracy_score(y_test, predicted_test)
# save predictions with random weights for comparison
initial_predictions = predicted_test
loss = cost(params, X_test, y_test, state_labels)
print(
"Epoch: {:2d} | Cost: {:3f} | Train accuracy: {:3f} | Test Accuracy: {:3f}"
.format(0, loss, accuracy_train, accuracy_test))
for it in range(epochs):
for Xbatch, ybatch in iterate_minibatches(X_train,
y_train,
batch_size=batch_size):
params = opt.step(lambda v: cost(v, Xbatch, ybatch, state_labels),
params)
predicted_train, states_train = test(params, X_train, y_train,
state_labels)
accuracy_train = accuracy_score(y_train, predicted_train)
loss = cost(params, X_train, y_train, state_labels)
predicted_test, states_test = test(params, X_test, y_test, state_labels)
accuracy_test = accuracy_score(y_test, predicted_test)
res = [it + 1, loss, accuracy_train, accuracy_test]
print(
"Epoch: {:2d} | Loss: {:3f} | Train accuracy: {:3f} | Test accuracy: {:3f}"
.format(*res))
##############################################################################
# Results
var (array[float]): array of variables
features (array[float]): 2-d array of input vectors
labels (array[float]): 1-d array of targets
Returns:
float: loss
"""
# Compute prediction for each input in data batch
preds = [quantum_neural_net(var, x=x) for x in features]
return square_loss(labels, preds)
# load function data
data = np.loadtxt("sine.txt")
X = data[:, 0]
Y = data[:, 1]
# initialize weights
np.random.seed(0)
num_layers = 4
var_init = 0.05 * np.random.randn(num_layers, 5)
# create optimizer
opt = AdamOptimizer(0.01, beta1=0.9, beta2=0.999)
# train
var = var_init
for it in range(500):
var = opt.step(lambda v: cost(v, X, Y), var)
print("Iter: {:5d} | Cost: {:0.7f} ".format(it + 1, cost(var, X, Y)))
BATCH_SIZE = 5
EPOCH = 10
LR = 1e-3
opt = AdamOptimizer(LR)
for epoch in tqdm(range(EPOCH), desc="Epoch"):
with tqdm(range(0,
len(X_train) - BATCH_SIZE, BATCH_SIZE),
desc="Train") as pbar:
for batch in pbar:
X_train_batch = X_train[batch:batch + BATCH_SIZE]
y_train_batch = y_train[batch:batch + BATCH_SIZE]
weights = opt.step(lambda v: cost(v, X_train_batch, y_train_batch),
weights)
#Compute loss and accuracy
predictions = [circuit(weights, x) for x in X_train]
acc = accuracy(predictions, y_train)
loss = cross_entropy(predictions, y_train)
pbar.set_postfix(loss=f"{loss:.4f}", accuracy=f"{acc*100:.2f}%")
with tqdm(range(0,
len(X_test) - BATCH_SIZE, BATCH_SIZE),
desc="Test") as pbar:
for batch in pbar:
X_test_batch = X_test[batch:batch + BATCH_SIZE]
y_test_batch = y_test[batch:batch + BATCH_SIZE]
ZZ = (1.-XX)**2 + 100.*(YY-XX*XX)**2
ZZ = ZZ/np.max(ZZ)
# final inputs and labels
inputs = list(zip(XX.flatten(),YY.flatten()))
labels = ZZ.flatten()
# sets initial variable value and optimizer
var = inits
opt = AdamOptimizer(0.01, beta1=0.9, beta2=0.999)
losses = []
for it in range(500):
# update variable with optimizer and get loss
var = opt.step(lambda v: cost(v, inputs,labels), var)
losses.append(cost.loss._value)
# get the final predictions
preds = np.array([pred._value for pred in cost.preds])
ZZ_NN = preds.reshape(ZZ.shape)
# plot
ax = fig.gca(projection='3d')
ax.view_init(30, 35)
ax.dist = 13
surf = ax.plot_surface(XX, YY, ZZ_NN, rstride=1, cstride=1,
cmap='coolwarm', edgecolor=None, antialiased=True) #Try coolwarm vs jet
ax.set_xlabel('x', rotation=0, labelpad=10, size=22)
ax.set_ylabel('y', rotation=0, labelpad=10, size=22)
ax.set_zlabel('f(x)', rotation=0, labelpad=10, size=22)
class BasicTest(BaseTest):
"""Basic optimizer tests.
"""
def setUp(self):
self.sgd_opt = GradientDescentOptimizer(stepsize)
self.mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
self.nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
self.adag_opt = AdagradOptimizer(stepsize)
self.rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
self.adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
self.fnames = ['test_function_1', 'test_function_2', 'test_function_3']
self.univariate_funcs = [
np.sin, lambda x: np.exp(x / 10.), lambda x: x**2
]
self.grad_uni_fns = [
np.cos, lambda x: np.exp(x / 10.) / 10., lambda x: 2 * x
]
self.multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x])
]
self.grad_multi_funcs = [
lambda x: np.array([np.cos(x[0]), -np.sin(x[1])]),
lambda x: np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2)
]), lambda x: np.array([2 * x_ for x_ in x])
]
self.mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1], lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x])
]
self.grad_mvar_mdim_funcs = [
lambda x: np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.]]),
lambda x: np.array([[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2)
], [0., 0.]]), lambda x: np.array([[2 * x_[0], 0.] for x_ in x])
]
self.class_fun = class_fun
self.quant_fun = quant_fun
self.hybrid_fun = hybrid_fun
self.hybrid_fun_nested = hybrid_fun_nested
self.hybrid_fun_flat = hybrid_fun_flat
self.hybrid_fun_mdarr = hybrid_fun_mdarr
self.hybrid_fun_mdlist = hybrid_fun_mdlist
self.mixed_list = [(0.2, 0.3), np.array([0.4, 0.2, 0.4]), 0.1]
self.mixed_tuple = (np.array([0.2, 0.3]), [0.4, 0.2, 0.4], 0.1)
self.nested_list = [[[0.2], 0.3], [0.1, [0.4]], -0.1]
self.flat_list = [0.2, 0.3, 0.1, 0.4, -0.1]
self.multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
self.multid_list = [[0.1, 0.2], [-0.1, -0.4]]
def test_mixed_inputs_for_hybrid_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for hybrid optimization tasks."""
self.logTestName()
hybrid_list = self.sgd_opt.step(self.hybrid_fun, self.mixed_list)
hybrid_tuple = self.sgd_opt.step(self.hybrid_fun, self.mixed_tuple)
self.assertAllAlmostEqual(hybrid_list[0],
hybrid_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[1],
hybrid_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[2],
hybrid_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_classical_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely classical optimization tasks."""
self.logTestName()
class_list = self.sgd_opt.step(self.class_fun, self.mixed_list)
class_tuple = self.sgd_opt.step(self.class_fun, self.mixed_tuple)
self.assertAllAlmostEqual(class_list[0],
class_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(class_list[1],
class_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(class_list[2],
class_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_quantum_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely quantum optimization tasks."""
self.logTestName()
quant_list = self.sgd_opt.step(self.quant_fun, self.mixed_list)
quant_tuple = self.sgd_opt.step(self.quant_fun, self.mixed_tuple)
self.assertAllAlmostEqual(quant_list[0],
quant_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[1],
quant_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[2],
quant_tuple[2],
delta=self.tol)
def test_nested_and_flat_returns_same_update(self):
"""Tests that gradient descent optimizer has the same output for
nested and flat lists."""
self.logTestName()
nested = self.sgd_opt.step(self.hybrid_fun_nested, self.nested_list)
flat = self.sgd_opt.step(self.hybrid_fun_flat, self.flat_list)
self.assertAllAlmostEqual(flat, list(_flatten(nested)), delta=self.tol)
def test_array_and_list_return_same_update(self):
"""Tests that gradient descent optimizer has the same output for
lists and arrays."""
self.logTestName()
array = self.sgd_opt.step(self.hybrid_fun_mdarr, self.multid_array)
list = self.sgd_opt.step(self.hybrid_fun_mdlist, self.multid_list)
self.assertAllAlmostEqual(array, list, delta=self.tol)
def test_gradient_descent_optimizer_univar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
x_vec = x_vals[jdx:jdx + 2]
x_new = self.sgd_opt.step(f, x_vec)
x_correct = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar_multidim(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions and with higher dimensional inputs."""
self.logTestName()
for gradf, f, name in zip(self.grad_mvar_mdim_funcs,
self.mvar_mdim_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-3])):
x_vec = x_vals[jdx:jdx + 4]
x_vec_multidim = np.reshape(x_vec, (2, 2))
x_new = self.sgd_opt.step(f, x_vec_multidim)
x_correct = x_vec_multidim - gradf(
x_vec_multidim) * stepsize
x_new_flat = x_new.flatten()
x_correct_flat = x_correct.flatten()
self.assertAllAlmostEqual(x_new_flat,
x_correct_flat,
delta=self.tol)
def test_gradient_descent_optimizer_usergrad(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start, grad_fn=gradf)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_momentum_optimizer_univar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.mom_opt.reset()
x_onestep = self.mom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_momentum_optimizer_multivar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.mom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.mom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_univar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_multivar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.nesmom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.nesmom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_usergrad(self):
"""Tests that nesterov momentum optimizer takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start, grad_fn=gradf)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f,
x_onestep,
grad_fn=gradf)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_univar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adag_opt.reset()
x_onestep = self.adag_opt.step(f, x_start)
past_grads = gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_start) * gradf(x_start) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_multivar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adag_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adag_opt.step(f, x_vec)
past_grads = gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_vec) * gradf(x_vec) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_univar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.rms_opt.reset()
x_onestep = self.rms_opt.step(f, x_start)
past_grads = (1 - gamma) * gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_start)*gradf(x_start) \
+ (1 - gamma) * gradf(x_onestep)*gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_multivar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.rms_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.rms_opt.step(f, x_vec)
past_grads = (1 - gamma) * gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_vec) * gradf(x_vec) \
+ (1 - gamma) * gradf(x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_univar(self):
"""Tests that adam optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adam_opt.reset()
x_onestep = self.adam_opt.step(f, x_start)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_start)
secondmoment = gradf(x_start) * gradf(x_start)
x_onestep_target = x_start - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_start) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_start) * gradf(x_start) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_multivar(self):
"""Tests that adam optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adam_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adam_opt.step(f, x_vec)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_vec)
secondmoment = gradf(x_vec) * gradf(x_vec)
x_onestep_target = x_vec - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_vec) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_vec) * gradf(x_vec) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def classify_data(X_train, Y_train, X_test):
"""Develop and train variational quantum classifier.
Args:
X_train (np.ndarray): An array of floats of size (250, 3) to be used as training data.
Y_train (np.ndarray): An array of size (250,) which are the categorical labels
associated to the training data. The categories are labeled by -1, 0, and 1.
X_test (np.ndarray): An array of floats of (50, 3) to serve as testing data.
Returns:
str: The predicted categories of X_test, converted from a list of ints to a
comma-separated string.
"""
# Use this array to make a prediction for the labels of the data in X_test
predictions = []
NUM_WIRES = 3
NUM_LAYERS = 2
dev = qml.device("default.qubit", wires=NUM_WIRES)
@qml.qnode(dev)
def circuit(params, x):
xEmbeded = [i * np.pi for i in x]
for i in range(NUM_WIRES):
qml.RX(xEmbeded[i], wires=i)
qml.Rot(*params[0, i], wires=i)
qml.CZ(wires=[1, 0])
qml.CZ(wires=[1, 2])
qml.CZ(wires=[0, 2])
for i in range(NUM_WIRES):
qml.Rot(*params[1, i], wires=i)
return qml.expval(qml.PauliZ(0)), qml.expval(
qml.PauliZ(1)), qml.expval(qml.PauliZ(2))
def prediction(weigths, x_train):
predictions = [circuit(weigths, f) for f in x_train]
for i, p in enumerate(predictions):
maxi = p[0]
indexMax = 0
for k in range(3):
if p[k] > maxi:
maxi = p[k]
indexMax = k
predictions[i] = indexMax - 1
return predictions
def cost(weights, x_train, labels):
predictions = [circuit(weights, f) for f in x_train]
loss = 0
for i in range(len(predictions)):
min = predictions[i][0]
max = predictions[i][0]
for k in range(3):
if predictions[i][k] > max:
max = predictions[i][k]
if predictions[i][k] < min:
min = predictions[i][k]
x = (predictions[i][labels[i] + 1] - min) / (max - min)
loss += (1 - x)**2 # [0.4,0.3,0.3]
return loss / len(predictions)
def accuracy(weights, x_train, labels):
predictions = prediction(weights, x_train)
loss = 0
for i in range(len(predictions)):
if predictions[i] == labels[i]:
loss += 1
loss = loss / len(predictions)
return loss
params = (0.01 * np.random.randn(2, NUM_WIRES, 3))
bestparams = (0.01 * np.random.randn(2, NUM_WIRES, 3))
bestcost = 1
opt = AdamOptimizer(0.425)
batch_size = 10
Diag_Cost = []
Diag_Acc = []
for it in range(30):
# Update the weights by one optimizer step
batch_index = np.random.randint(0, 250, (batch_size, ))
X_train_batch = X_train[batch_index]
Y_train_batch = Y_train[batch_index]
params = opt.step(lambda v: cost(v, X_train_batch, Y_train_batch),
params)
# Compute predictions on train and validation set
#predictions_train = prediction(params,X_train)
cosT = cost(params, X_train, Y_train)
# Compute accuracy on train and validation set
acc = accuracy(params, X_train, Y_train)
if cosT < bestcost:
bestcost = cosT
bestparams = params
Diag_Cost.append(cosT.numpy())
Diag_Acc.append(acc)
print("Iter: {:5d} | Cost: {:0.7f} | Accuracy: {:0.2f}% ".format(
it + 1, cosT, acc * 100))
predictions = prediction(bestparams, X_test)
results = [
1, 0, -1, 0, -1, 1, -1, -1, 0, -1, 1, -1, 0, 1, 0, -1, -1, 0, 0, 1, 1,
0, -1, 0, 0, -1, 0, -1, 0, 0, 1, 1, -1, -1, -1, 0, -1, 0, 1, 0, -1, 1,
1, 0, -1, -1, -1, -1, 0, 0
]
accResult = accuracy(bestparams, X_test, results)
print()
print("FINAL ACCURACY: {:0.2f}%".format(accResult * 100))
circuit(bestparams, X_train[0])
print()
print(circuit.draw())
return array_to_concatenated_string(predictions), Diag_Cost, Diag_Acc