def test_040_objective_instance_properties():
"""
Objective:
Verify the layer class validates the parameters have been initialized before accessed.
Expected:
Initialization detects the access to the non-initialized parameters and fails.
"""
msg = "Accessing uninitialized property of the layer must fail."
name = random_string(np.random.randint(1, 10))
for _ in range(NUM_MAX_TEST_TIMES):
M: int = 1
layer = CrossEntropyLogLoss(
name=name,
num_nodes=1,
log_loss_function=sigmoid_cross_entropy_log_loss,
log_level=logging.DEBUG)
# --------------------------------------------------------------------------------
# To pass
# --------------------------------------------------------------------------------
try:
if not layer.name == name:
raise RuntimeError("layer.name == name should be true")
except AssertionError:
raise RuntimeError(
"Access to name should be allowed as already initialized.")
try:
if not layer.M == M:
raise RuntimeError("layer.M == M should be true")
except AssertionError:
raise RuntimeError(
"Access to M should be allowed as already initialized.")
try:
if not isinstance(layer.logger, logging.Logger):
raise RuntimeError(
"isinstance(layer.logger, logging.Logger) should be true")
except AssertionError:
raise RuntimeError(
"Access to logger should be allowed as already initialized.")
# --------------------------------------------------------------------------------
# To fail
# --------------------------------------------------------------------------------
try:
print(layer.X)
raise RuntimeError(msg)
except AssertionError:
pass
try:
layer.X = int(1)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.N)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.dX)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.Y)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.P)
raise RuntimeError(msg)
except AssertionError:
pass
try:
layer._Y = int(1)
print(layer.Y)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.dY)
raise RuntimeError(msg)
except AssertionError:
pass
try:
layer._dY = int(1)
print(layer.dY)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.T)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.L)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(layer.J)
raise RuntimeError(msg)
except AssertionError:
pass
try:
layer.T = float(1)
raise RuntimeError(msg)
except AssertionError:
pass
try:
layer.function(int(1))
raise RuntimeError("Invoke layer.function(int(1)) must fail.")
except AssertionError:
pass
try:
layer.function(TYPE_FLOAT(1.0))
layer.gradient(int(1))
raise RuntimeError("Invoke layer.gradient(int(1)) must fail.")
except AssertionError:
pass
def disabled_test_040_objective_methods_2d_ohe(caplog):
"""
TODO: Disabled as need to redesign numerical_jacobian for 32 bit floating.
Objective:
Verify the forward path constraints:
1. Layer output L/loss is np.sum(sigmoid_cross_entropy_log_loss) / N.
2. gradient_numerical() == numerical Jacobian numerical_jacobian(O, X).
Verify the backward path constraints:
1. Analytical gradient G: gradient() == (P-1)/N
2. Analytical gradient G is close to GN: gradient_numerical().
"""
caplog.set_level(logging.DEBUG)
# --------------------------------------------------------------------------------
# Instantiate a CrossEntropyLogLoss layer
# --------------------------------------------------------------------------------
name = "test_040_objective_methods_2d_ohe"
profiler = cProfile.Profile()
profiler.enable()
for _ in range(NUM_MAX_TEST_TIMES):
N: int = np.random.randint(1, NUM_MAX_BATCH_SIZE)
M: int = 1 # node number is 1 for 0/1 binary classification.
layer = CrossEntropyLogLoss(
name=name,
num_nodes=M,
log_loss_function=sigmoid_cross_entropy_log_loss,
log_level=logging.DEBUG)
# ================================================================================
# Layer forward path
# ================================================================================
X = np.random.randn(N, M).astype(TYPE_FLOAT)
T = np.zeros_like(X, dtype=TYPE_LABEL) # OHE labels.
T[np.arange(N), np.random.randint(0, M, N)] = TYPE_LABEL(1)
# log_loss function require (X, T) in X(N, M), and T(N, M) in OHE label format.
X, T = transform_X_T(X, T)
layer.T = T
Logger.debug("%s: X is \n%s\nT is \n%s", name, X, T)
# --------------------------------------------------------------------------------
# Expected analytical gradient EG = (dX/dL) = (A-T)/N
# --------------------------------------------------------------------------------
A = sigmoid(X)
EG = ((A - T).astype(TYPE_FLOAT) / TYPE_FLOAT(N))
# --------------------------------------------------------------------------------
# Total loss Z = np.sum(J)/N
# Expected loss EL = sum((1-T)X + np.log(1 + np.exp(-X)))
# (J, P) = sigmoid_cross_entropy_log_loss(X, T) and J:shape(N,) where J:shape(N,)
# is loss for each input and P is activation by sigmoid(X).
# --------------------------------------------------------------------------------
L = layer.function(X)
J, P = sigmoid_cross_entropy_log_loss(X, T)
EL = np.array(np.sum((1 - T) * X + logarithm(1 + np.exp(-X))) / N,
dtype=TYPE_FLOAT)
# Constraint: A == P as they are sigmoid(X)
assert np.all(np.abs(A-P) < ACTIVATION_DIFF_ACCEPTANCE_VALUE), \
f"Need A==P==sigmoid(X) but A=\n{A}\n P=\n{P}\n(A-P)=\n{(A-P)}\n"
# Constraint: Log loss layer output L == sum(J) from the log loss function
Z = np.array(np.sum(J) / N, dtype=TYPE_FLOAT)
assert np.array_equal(L, Z), \
f"Need log loss layer output L == sum(J) but L=\n{L}\nZ=\n{Z}."
# Constraint: L/loss is close to expected loss EL.
assert np.all(np.abs(EL-L) < LOSS_DIFF_ACCEPTANCE_VALUE), \
"Need EL close to L but \nEL=\n{EL}\nL=\n{L}\n"
# --------------------------------------------------------------------------------
# constraint: gradient_numerical() == numerical_jacobian(objective, X)
# TODO: compare the diff to accommodate numerical errors.
# --------------------------------------------------------------------------------
GN = layer.gradient_numerical() # [dL/dX] from the layer
def objective(x):
"""Function to calculate the scalar loss L for cross entropy log loss"""
j, p = sigmoid_cross_entropy_log_loss(x, T)
return np.array(np.sum(j) / N, dtype=TYPE_FLOAT)
EGN = numerical_jacobian(objective, X) # Expected numerical dL/dX
assert np.array_equal(GN[0], EGN), \
f"GN[0]==EGN expected but GN[0] is \n%s\n EGN is \n%s\n" % (GN[0], EGN)
# ================================================================================
# Layer backward path
# ================================================================================
# constraint: Analytical gradient G: gradient() == (P-1)/N.
dY = TYPE_FLOAT(1)
G = layer.gradient(dY)
assert np.all(np.abs(G-EG) <= GRADIENT_DIFF_ACCEPTANCE_VALUE), \
f"Layer gradient dL/dX \n{G} \nneeds to be \n{EG}."
# constraint: Analytical gradient G is close to GN: gradient_numerical().
assert \
np.allclose(GN[0], G, atol=GRADIENT_DIFF_ACCEPTANCE_VALUE, rtol=GRADIENT_DIFF_ACCEPTANCE_RATIO), \
f"dX is \n{G}\nGN[0] is \n{GN[0]}\nRDiff is \n{G-GN[0]}.\n"
# constraint: Gradient g of the log loss layer needs -1 < g < 1
# abs(P-T) = abs(sigmoid(X)-T) cannot be > 1.
assert np.all(np.abs(G) < 1), \
f"Log loss layer gradient cannot be < -1 nor > 1 but\n{G}"
assert np.all(np.abs(GN[0]) < (1+GRADIENT_DIFF_ACCEPTANCE_RATIO)), \
f"Log loss layer gradient cannot be < -1 nor > 1 but\n{GN[0]}"
profiler.disable()
profiler.print_stats(sort="cumtime")
def test_040_objective_instantiation():
"""
Objective:
Verify the initialized layer instance provides its properties.
Expected:
* name, num_nodes, M, log_level are the same as initialized.
* X, T, dY, objective returns what is set.
* N, M property are provided after X is set.
* Y, P, L properties are provided after function(X).
* gradient(dL/dY) repeats dL/dY,
* gradient_numerical() returns 1
"""
name = "test_040_objective_instantiation"
for _ in range(NUM_MAX_TEST_TIMES):
N: int = np.random.randint(1, NUM_MAX_BATCH_SIZE)
M: int = 1
# For sigmoid log loss layer, the number of features N in X is the same with node number.
D: int = M
layer = CrossEntropyLogLoss(
name=name,
num_nodes=M,
log_loss_function=sigmoid_cross_entropy_log_loss,
log_level=logging.DEBUG)
# --------------------------------------------------------------------------------
# Properties
# --------------------------------------------------------------------------------
assert layer.name == name
assert layer.num_nodes == layer.M == M
layer._D = D
assert layer.D == D
X = np.random.randn(N, D).astype(TYPE_FLOAT)
layer.X = X
assert np.array_equal(layer.X, X)
assert layer.N == N == X.shape[0]
# For sigmoid log loss layer, the number of features N in X is the same with node number.
assert layer.M == X.shape[1]
layer._dX = X
assert np.array_equal(layer.dX, X)
T = np.random.randint(0, M, N).astype(TYPE_LABEL)
layer.T = T
assert np.array_equal(layer.T, T)
# layer.function() gives the total loss L in shape ().
# log_loss function require (X, T) in X(N, M), and T(N, M) in OHE label format.
X, T = transform_X_T(X, T)
L = layer.function(X)
J, P = sigmoid_cross_entropy_log_loss(X, T)
assert \
L.shape == () and np.allclose(L, (np.sum(J) / N).astype(TYPE_FLOAT)) and L == layer.Y, \
"After setting T, layer.function(X) generates the total loss L but %s" % L
# layer.function(X) sets layer.P to sigmoid_cross_entropy_log_loss(X, T)
# P is nearly equal with sigmoid(X)
assert \
np.array_equal(layer.P, P) and \
np.all(np.abs(layer.P - sigmoid(X)) < LOSS_DIFF_ACCEPTANCE_VALUE), \
"layer.function(X) needs to set P as sigmoid_cross_entropy_log_loss(X, T) " \
"which is close to sigmoid(X) but layer.P=\n%s\nP=\n%s\nsigmoid(X)=%s" \
% (layer.P, P, sigmoid(X))
# gradient of sigmoid cross entropy log loss layer is (P-T)/N
G = layer.gradient()
assert \
np.all(np.abs(G - ((P-T)/N)) < GRADIENT_DIFF_ACCEPTANCE_VALUE), \
"Gradient G needs (P-T)/N but G=\n%s\n(P-T)/N=\n%s\n" % (G, (P-T)/N)
layer.logger.debug("This is a pytest")
# pylint: disable=not-callable
assert \
layer.objective(np.array(1.0, dtype=TYPE_FLOAT)) \
== np.array(1.0, dtype=TYPE_FLOAT), \
"Objective function of the output/last layer is an identity function."
def disabled_test_040_objective_methods_1d_ohe():
"""
TODO: Disabled as need to redesign numerical_jacobian for 32 bit floating.
Objective:
Verify the forward path constraints:
1. Layer output L/loss is np.sum(cross_entropy_log_loss(sigmoid(X), T, f=logistic_log_loss))) / N.
2. gradient_numerical() == numerical Jacobian numerical_jacobian(O, X).
Verify the backward path constraints:
1. Analytical gradient G: gradient() == (P-1)/N
2. Analytical gradient G is close to GN: gradient_numerical().
Expected:
Initialization detects the access to the non-initialized parameters and fails.
For X.ndim > 0, the layer transform X into 2D so as to use the numpy tuple-
like indexing:
P[
(0,3),
(2,4)
]
Hence, the shape of GN, G are 2D.
"""
# --------------------------------------------------------------------------------
# Instantiate a CrossEntropyLogLoss layer
# --------------------------------------------------------------------------------
name = "test_040_objective_methods_1d_ohe"
N = 1
for _ in range(NUM_MAX_TEST_TIMES):
layer = CrossEntropyLogLoss(
name=name,
num_nodes=1,
log_loss_function=sigmoid_cross_entropy_log_loss,
log_level=logging.DEBUG)
# ================================================================================
# Layer forward path
# ================================================================================
X = TYPE_FLOAT(
np.random.uniform(low=-BOUNDARY_SIGMOID, high=BOUNDARY_SIGMOID))
T = TYPE_LABEL(np.random.randint(0, 2)) # OHE labels.
# log_loss function require (X, T) in X(N, M), and T(N, M) in OHE label format.
X, T = transform_X_T(X, T)
layer.T = T
# Expected analytical gradient dL/dX = (P-T)/N of shape (N,M)
A = sigmoid(X)
EG = ((A - T) / N).reshape(1, -1).astype(TYPE_FLOAT)
Logger.debug("%s: X is \n%s\nT is %s\nP is %s\nEG is %s\n", name, X, T,
A, EG)
# --------------------------------------------------------------------------------
# constraint: L/loss == np.sum(J) / N.
# J, P = sigmoid_cross_entropy_log_loss(X, T)
# --------------------------------------------------------------------------------
L = layer.function(X) # L is shape ()
J, P = sigmoid_cross_entropy_log_loss(X, T)
Z = np.array(np.sum(J), dtype=TYPE_FLOAT) / TYPE_FLOAT(N)
assert np.array_equal(L, Z), f"LogLoss output should be {L} but {Z}."
# --------------------------------------------------------------------------------
# constraint: gradient_numerical() == numerical Jacobian numerical_jacobian(O, X)
# Use a dummy layer for the objective function because using the "layer"
# updates the X, Y which can interfere the independence of the layer.
# --------------------------------------------------------------------------------
GN = layer.gradient_numerical() # [dL/dX] from the layer
# --------------------------------------------------------------------------------
# Cannot use CrossEntropyLogLoss.function() to simulate the objective function L.
# because it causes applying transform_X_T multiple times.
# Because internally transform_X_T(X, T) has transformed T into the index label
# in 1D with with length 1 by "T = T.reshape(-1)".
# Then providing X in 1D into "dummy.function(x)" re-run "transform_X_T(X, T)"
# again. The (X.ndim == T.ndim ==1) as an input and T must be OHE label for such
# combination and T.shape == P.shape must be true for OHE labels.
# However, T has been converted into the index format already by transform_X_T
# (applying transform_X_T multiple times) and (T.shape=(1,1), X.shape=(1, > 1)
# that violates the (X.shape == T.shape) constraint.
# --------------------------------------------------------------------------------
# dummy = CrossEntropyLogLoss(
# name="dummy",
# num_nodes=M,
# log_level=logging.DEBUG
# )
# dummy.T = T
# dummy.objective = objective
# dummy.function(X)
# --------------------------------------------------------------------------------
def objective(x):
j, p = sigmoid_cross_entropy_log_loss(x, T)
return np.array(np.sum(j) / N, dtype=TYPE_FLOAT)
EGN = numerical_jacobian(objective,
X).reshape(1, -1) # Expected numerical dL/dX
assert np.array_equal(GN[0], EGN), \
f"Layer gradient_numerical GN \n{GN} \nneeds to be \n{EGN}."
# ================================================================================
# Layer backward path
# ================================================================================
# --------------------------------------------------------------------------------
# constraint: Analytical gradient G: gradient() == (P-1)/N.
# --------------------------------------------------------------------------------
dY = TYPE_FLOAT(1)
G = layer.gradient(dY)
assert np.all(np.abs(G-EG) <= GRADIENT_DIFF_ACCEPTANCE_VALUE), \
f"Layer gradient dL/dX \n{G} \nneeds to be \n{EG}."
# --------------------------------------------------------------------------------
# constraint: Analytical gradient G is close to GN: gradient_numerical().
# --------------------------------------------------------------------------------
assert \
np.all(np.abs(G-GN[0]) <= GRADIENT_DIFF_ACCEPTANCE_VALUE) or \
np.all(np.abs(G-GN[0]) <= np.abs(GRADIENT_DIFF_ACCEPTANCE_RATIO * GN[0])), \
"dX is \n%s\nGN is \n%s\nG-GN is \n%s\n Ratio * GN[0] is \n%s.\n" \
% (G, GN[0], G-GN[0], GRADIENT_DIFF_ACCEPTANCE_RATIO * GN[0])
def train_binary_classifier(N: int,
D: int,
M: int,
X: np.ndarray,
T: np.ndarray,
W: np.ndarray,
log_loss_function: Callable,
optimizer: Optimizer,
num_epochs: int = 100,
test_numerical_gradient: bool = False,
log_level: int = logging.ERROR,
callback: Callable = None):
"""Test case for binary classification with matmul + log loss.
Args:
N: Batch size
D: Number of features
M: Number of nodes. 1 for sigmoid and 2 for softmax
X: train data
T: labels
W: weight
log_loss_function: cross entropy logg loss function
optimizer: Optimizer
num_epochs: Number of epochs to run
test_numerical_gradient: Flag if test the analytical gradient with the numerical one.
log_level: logging level
callback: callback function to invoke at the each epoch end.
"""
name = __name__
assert isinstance(T, np.ndarray) and np.issubdtype(
T.dtype, np.integer) and T.ndim == 1 and T.shape[0] == N
assert isinstance(
X, np.ndarray) and X.dtype == TYPE_FLOAT and X.ndim == 2 and X.shape[
0] == N and X.shape[1] == D
assert isinstance(
W, np.ndarray) and W.dtype == TYPE_FLOAT and W.ndim == 2 and W.shape[
0] == M and W.shape[1] == D + 1
assert num_epochs > 0 and N > 0 and D > 0
assert ((log_loss_function == sigmoid_cross_entropy_log_loss and M == 1) or
(log_loss_function == softmax_cross_entropy_log_loss and M >= 2))
# --------------------------------------------------------------------------------
# Instantiate a CrossEntropyLogLoss layer
# --------------------------------------------------------------------------------
loss = CrossEntropyLogLoss(name="loss",
num_nodes=M,
log_loss_function=log_loss_function,
log_level=log_level)
# --------------------------------------------------------------------------------
# Instantiate a Matmul layer
# --------------------------------------------------------------------------------
matmul = Matmul(name="matmul",
num_nodes=M,
W=W,
optimizer=optimizer,
log_level=log_level)
matmul.objective = loss.function
num_no_progress: int = 0 # how many time when loss L not decreased.
loss.T = T
history: List[np.ndarray] = [loss.function(matmul.function(X))]
for i in range(num_epochs):
# --------------------------------------------------------------------------------
# Layer forward path
# Calculate the matmul output Y=f(X), and get the loss L = objective(Y)
# Test the numerical gradient dL/dX=matmul.gradient_numerical().
# --------------------------------------------------------------------------------
Y = matmul.function(X)
L = loss.function(Y)
if not (i % 50): print(f"iteration {i} Loss {L}")
Logger.info("%s: iteration[%s]. Loss is [%s]", name, i, L)
# --------------------------------------------------------------------------------
# Constraint: 1. Objective/Loss L(Yn+1) after gradient descent < L(Yn)
# --------------------------------------------------------------------------------
if L >= history[-1] and (i % 20) == 1:
Logger.warning(
"Iteration [%i]: Loss[%s] has not improved from the previous [%s].",
i, L, history[-1])
if (num_no_progress := num_no_progress + 1) > 20:
Logger.error(
"The training has no progress more than %s times.",
num_no_progress)
# break
else:
num_no_progress = 0
history.append(L)
# --------------------------------------------------------------------------------
# Expected dL/dW.T = X.T @ dL/dY = X.T @ (P-T) / N, and dL/dX = dL/dY @ W
# P = sigmoid(X) or softmax(X)
# dL/dX = dL/dY * W is to use W BEFORE updating W.
# --------------------------------------------------------------------------------
P = None
if log_loss_function == sigmoid_cross_entropy_log_loss:
# P = sigmoid(np.matmul(X, W.T))
P = sigmoid(np.matmul(matmul.X, matmul.W.T))
P = P - T.reshape(-1, 1) # T(N,) -> T(N,1) to align with P(N,1)
assert P.shape == (
N, 1), "P.shape is %s T.shape is %s" % (P.shape, T.shape)
elif log_loss_function == softmax_cross_entropy_log_loss:
# matmul.X.shape is (N, D+1), matmul.W.T.shape is (D+1, M)
P = softmax(np.matmul(matmul.X, matmul.W.T)) # (N, M)
P[np.arange(N), T] -= 1
EDX = np.matmul(P / N, matmul.W) # (N,M) @ (M, D+1) -> (N, D+1)
EDX = EDX[::, 1:] # Hide the bias -> (N, D)
EDW = np.matmul(matmul.X.T,
P / N).T # ((D+1,N) @ (N, M)).T -> (M, D+1)
# --------------------------------------------------------------------------------
# Layer backward path
# 1. Calculate the analytical gradient dL/dX=matmul.gradient(dL/dY) with a dL/dY.
# 2. Gradient descent to update Wn+1 = Wn - lr * dL/dX.
# --------------------------------------------------------------------------------
before = copy.deepcopy(matmul.W)
dY = loss.gradient(TYPE_FLOAT(1))
dX = matmul.gradient(dY)
# gradient descent and get the analytical gradients dS=[dL/dX, dL/dW]
# dL/dX.shape = (N, D)
# dL/dW.shape = (M, D+1)
dS = matmul.update()
dW = dS[0]
# --------------------------------------------------------------------------------
# Constraint 1. W in the matmul has been updated by the gradient descent.
# --------------------------------------------------------------------------------
Logger.debug("W after is \n%s", matmul.W)
assert not np.array_equal(before, matmul.W), "W has not been updated."
if not validate_against_expected_gradient(EDX, dX):
Logger.warning("Expected dL/dX \n%s\nDiff\n%s", EDX, EDX - dX)
if not validate_against_expected_gradient(EDW, dW):
Logger.warning("Expected dL/dW \n%s\nDiff\n%s", EDW, EDW - dW)
if test_numerical_gradient:
# --------------------------------------------------------------------------------
# Numerical gradients gn=[dL/dX, dL/dW]
# dL/dX.shape = (N, D)
# dL/dW.shape = (M, D+1)
# --------------------------------------------------------------------------------
gn = matmul.gradient_numerical()
validate_against_numerical_gradient([dX] + dS, gn, Logger)
if callback:
# if W.shape[1] == 1 else callback(W=np.average(matmul.W, axis=0))
callback(W=matmul.W[0])