def test_010_sigmoid_cross_entropy_log_loss_2d(caplog):
"""
Objective:
Test case for sigmoid_cross_entropy_log_loss(X, T) =
-( T * log(sigmoid(X)) + (1 -T) * log(1-sigmoid(X)) )
For the input X of shape (N,1) and T in index format of shape (N,1),
calculate the sigmoid log loss and verify the values are as expected.
Expected:
For Z = sigmoid(X) = 1 / (1 + exp(-X)) and T=[[1]]
Then -log(Z) should be almost same with sigmoid_cross_entropy_log_loss(X, T).
Almost because finite float precision always has rounding errors.
"""
# caplog.set_level(logging.DEBUG, logger=Logger.name)
u = REFORMULA_DIFF_ACCEPTANCE_VALUE
# --------------------------------------------------------------------------------
# [Test case 01]
# X:(N,M)=(1, 1). X=(x0) where x0=0 by which sigmoid(X) generates 0.5.
# Expected:
# sigmoid_cross_entropy_log_loss(X, T) == -log(0.5)
# --------------------------------------------------------------------------------
X = np.array([[TYPE_FLOAT(0.0)]])
T = np.array([TYPE_LABEL(1)])
X, T = transform_X_T(X, T)
E = -logarithm(np.array([TYPE_FLOAT(0.5)]))
J, P = sigmoid_cross_entropy_log_loss(X, T)
assert E.shape == J.shape
assert np.all(E == J), \
"Expected (E==J) but \n%s\nE=\n%s\nT=%s\nX=\n%s\nJ=\n%s\n" \
% (np.abs(E - J), E, T, X, J)
assert P == 0.5
# --------------------------------------------------------------------------------
# [Test case 02]
# For X:(N,1)
# --------------------------------------------------------------------------------
for _ in range(NUM_MAX_TEST_TIMES):
# X(N, M), and T(N,) in index label format
N = np.random.randint(1, NUM_MAX_BATCH_SIZE)
M = 1 # always 1 for binary classification 0 or 1.
X = np.random.randn(N, M).astype(TYPE_FLOAT)
T = np.random.randint(0, M, N).astype(TYPE_LABEL)
X, T = transform_X_T(X, T)
Logger.debug("T is %s\nX is \n%s\n", T, X)
# ----------------------------------------------------------------------
# Expected value EJ for J and Z for P
# Note:
# To handle both index label format and OHE label format in the
# Loss layer(s), X and T are transformed into (N,1) shapes in
# transform_X_T(X, T) for logistic log loss.
# DO NOT squeeze Z nor P.
# ----------------------------------------------------------------------
Z = sigmoid(X)
EJ = np.squeeze(-(T * logarithm(Z) + TYPE_FLOAT(1-T) * logarithm(TYPE_FLOAT(1-Z))), axis=-1)
# **********************************************************************
# Constraint: Actual J should be close to EJ.
# **********************************************************************
J, P = sigmoid_cross_entropy_log_loss(X, T)
assert EJ.shape == J.shape
assert np.all(np.abs(EJ-J) < u), \
"Expected abs(EJ-J) < %s but \n%s\nEJ=\n%s\nT=%s\nX=\n%s\nJ=\n%s\n" \
% (u, np.abs(EJ-J), EJ, T, X, J)
# **********************************************************************
# Constraint: Actual P should be close to Z.
# **********************************************************************
assert np.all(np.abs(Z-P) < u), \
"EP \n%s\nP\n%s\nEP-P \n%s\n" % (Z, P, Z-P)
# ----------------------------------------------------------------------
# L = cross_entropy_log_loss(P, T) should be close to J
# ----------------------------------------------------------------------
L = cross_entropy_log_loss(P=Z, T=T, f=logistic_log_loss)
assert L.shape == J.shape
assert np.all(np.abs(L-J) < u), \
"Expected abs(L-J) < %s but \n%s\nL=\n%s\nT=%s\nX=\n%s\nJ=\n%s\n" \
% (u, np.abs(L-J), L, T, X, J)
def test_030_objective_methods_1d_ohe():
"""
Objective:
Verify the forward path constraints:
1. Layer output L/loss is np.sum(cross_entropy_log_loss(softmax(X), T)) / 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_030_objective_methods_1d_ohe"
N = 1
for _ in range(NUM_MAX_TEST_TIMES):
M: int = np.random.randint(2, NUM_MAX_NODES)
assert M >= 2, "Softmax is for multi label classification. "\
" Use Sigmoid for binary classification."
_layer = layer.CrossEntropyLogLoss(name=name,
num_nodes=M,
log_level=logging.DEBUG)
# ================================================================================
# Layer forward path
# ================================================================================
X = np.random.randn(M).astype(TYPE_FLOAT)
T = np.zeros_like(X, dtype=TYPE_LABEL) # OHE labels.
T[np.random.randint(0, M)] = TYPE_LABEL(1)
_layer.T = T
P = softmax(X)
EG = ((P - T) / N).reshape(1, -1).astype(
TYPE_FLOAT) # Expected analytical gradient dL/dX = (P-T)/N
Logger.debug("%s: X is \n%s\nT is %s\nP is %s\nEG is %s\n", name, X, T,
P, EG)
# --------------------------------------------------------------------------------
# constraint: L/loss == np.sum(cross_entropy_log_loss(softmax(X), T)) / N.
# --------------------------------------------------------------------------------
L = _layer.function(X)
Z = np.array(np.sum(cross_entropy_log_loss(softmax(X), T)),
dtype=TYPE_FLOAT) / TYPE_FLOAT(N)
assert np.array_equal(
L, Z), f"SoftmaxLogLoss 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)
# --------------------------------------------------------------------------------
# O = lambda x: dummy.objective(dummy.function(x)) # Objective function
O = lambda x: np.sum(cross_entropy_log_loss(softmax(x), T),
dtype=TYPE_FLOAT) / TYPE_FLOAT(N)
# --------------------------------------------------------------------------------
EGN = numerical_jacobian(O, 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} but G-EG \n{np.abs(G-EG)}\n"
# --------------------------------------------------------------------------------
# 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])), \
f"dX is \n{G}\nGN[0] is \n{GN[0]}\nRatio * GN[0] is \n{GRADIENT_DIFF_ACCEPTANCE_RATIO * GN[0]}.\n"
def disabled_test_030_objective_methods_2d_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(softmax(X), T)) / 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.
"""
def objective(X: np.ndarray) -> Union[float, np.ndarray]:
"""Dummy objective function to calculate the loss L"""
assert X.ndim == 0, "The output of the log loss should be of shape ()"
return X
# --------------------------------------------------------------------------------
# Instantiate a CrossEntropyLogLoss layer
# --------------------------------------------------------------------------------
name = "test_030_objective_methods_2d_ohe"
for _ in range(NUM_MAX_TEST_TIMES):
N: int = np.random.randint(1, NUM_MAX_BATCH_SIZE)
M: int = np.random.randint(2, NUM_MAX_NODES)
assert M >= 2, "Softmax is for multi label classification. "\
" Use Sigmoid for binary classification."
_layer = layer.CrossEntropyLogLoss(name=name,
num_nodes=M,
log_level=logging.DEBUG)
_layer.objective = objective
# ================================================================================
# 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)
_layer.T = T
Logger.debug("%s: X is \n%s\nT is \n%s", name, X, T)
P = softmax(X)
EG = (P - T) / N # Expected analytical gradient dL/dX = (P-T)/N
# --------------------------------------------------------------------------------
# constraint: L/loss == np.sum(cross_entropy_log_loss(softmax(X), T)) / N.
# --------------------------------------------------------------------------------
L = _layer.function(X)
Z = np.array(np.sum(cross_entropy_log_loss(softmax(X), T))) / N
assert np.array_equal(
L, Z), f"SoftmaxLogLoss output should be {L} but {Z}."
# --------------------------------------------------------------------------------
# constraint: gradient_numerical() == numerical Jacobian numerical_jacobian(O, X)
# --------------------------------------------------------------------------------
GN = _layer.gradient_numerical() # [dL/dX] from the _layer
# --------------------------------------------------------------------------------
# DO not use CrossEntropyLogLoss.function() to simulate the objective function for
# the expected GN. See the same part in test_030_objective_methods_1d_ohe().
# --------------------------------------------------------------------------------
# dummy= CrossEntropyLogLoss(
# name=name,
# num_nodes=M,
# log_level=logging.DEBUG
# )
# dummy.T = T
# dummy.objective = objective
# O = lambda x: dummy.objective(dummy.function(x)) # Objective function
O = lambda x: np.sum(cross_entropy_log_loss(softmax(x), T)) / N
# --------------------------------------------------------------------------------
EGN = numerical_jacobian(O, 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 = float(1)
G = _layer.gradient(dY)
assert np.all(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])), \
f"dX is \n{G}\nGN[0] is \n{GN[0]}\nRatio * GN[0] is \n{GRADIENT_DIFF_ACCEPTANCE_RATIO * GN[0]}.\n"
# P:[0, 0, ..., 1, 0, ...] where Pi = 1
# T:[0, 0, ..., 1, 0, ...] is OHE label where Ti=1
# sum(-t * log(p+k)) -> log(1+k)
# dlog(P+k)/dP -> -1 / (1+k)
# --------------------------------------------------------------------------------
M = np.random.randint(2, NUM_MAX_NODES) # M > 1
index = np.random.randint(0, M) # location of the truth
while not (x := TYPE_FLOAT(
np.random.uniform(low=-BOUNDARY_SIGMOID,
high=BOUNDARY_SIGMOID))):
pass
p = softmax(x)
P3 = np.zeros(M, dtype=TYPE_FLOAT)
P3[index] = p
T3 = np.zeros(M).astype(TYPE_LABEL) # OHE index
T3[index] = TYPE_LABEL(1)
# --------------------------------------------------------------------------------
# The Jacobian G shape is the same with P.shape.
# --------------------------------------------------------------------------------
N3 = np.zeros_like(P3, dtype=TYPE_FLOAT)
N3[index] = TYPE_FLOAT(-1 * logarithm(p + h) +
1 * logarithm(p - h)) / TYPE_FLOAT(2 * h)
N3 = numerical_jacobian(partial(f, T=T3), P3)
assert N3.shape == N3.shape
assert np.all(np.abs(N3-N3) < u), \
f"Delta expected to be < {u} but \n{np.abs(N3-N3)}"
G3 = np.zeros_like(P3, dtype=TYPE_FLOAT)
G3[index] = -1 / p
check.equal(np.all(np.abs(G3 - N3) < u), True,
def test_020_cross_entropy_log_loss_1d(caplog):
"""
Objective:
Test the categorical log loss values for P in 1 dimension.
Constraints:
1. The numerical gradient gn = (-t * logarithm(p+h) + t * logarithm(p-h)) / 2h.
2. The numerical gradient gn is within +/- u within the analytical g = -T/P.
P: Probabilities from softmax of shape (M,)
M: Number of nodes in the cross_entropy_log_loss layer.
T: Labels
Note:
log(P=1) -> 0
dlog(x)/dx = 1/x
"""
def f(P: np.ndarray, T: np.ndarray):
return np.sum(cross_entropy_log_loss(P, T))
# caplog.set_level(logging.DEBUG, logger=Logger.name)
h: TYPE_FLOAT = OFFSET_DELTA
u: TYPE_FLOAT = GRADIENT_DIFF_ACCEPTANCE_VALUE
# --------------------------------------------------------------------------------
# For (P, T): P[index] = True/1, OHE label T[index] = 1 where
# P=[0,0,0,...,1,...0], T = [0,0,0,...1,...0]. T[i] == 1
#
# Do not forget the Jacobian shape is (N,) and calculate each element.
# 1. For T=1, loss L = -log(Pi) = 0 and dL/dP=(1/Pi)= -1 is expected.
# 2. For T=0, Loss L = (-log(0+offset+h)-log(0+offset-h)) / 2h = 0 is expected.
# --------------------------------------------------------------------------------
M: TYPE_INT = np.random.randint(2, NUM_MAX_NODES)
index: TYPE_INT = TYPE_INT(np.random.randint(
0, M)) # Position of the true label in P
P1 = np.zeros(M, dtype=TYPE_FLOAT)
P1[index] = TYPE_FLOAT(1.0)
T1 = np.zeros(M, dtype=TYPE_LABEL)
T1[index] = TYPE_LABEL(1)
# Analytica correct gradient for P=1, T=1
AG = np.zeros_like(P1, dtype=TYPE_FLOAT)
AG[index] = TYPE_FLOAT(-1) # dL/dP = -1
EGN1 = np.zeros_like(P1, dtype=TYPE_FLOAT) # Expected numerical gradient
EGN1[index] = (-1 * logarithm(TYPE_FLOAT(1.0 + h)) + TYPE_FLOAT(1) *
logarithm(TYPE_FLOAT(1.0 - h))) / TYPE_FLOAT(2 * h)
assert np.all(np.abs(EGN1-AG) < u), \
"Expected EGN-1<%s but %s\nEGN=\n%s" % (u, (EGN1-AG), EGN1)
GN1 = numerical_jacobian(partial(f, T=T1), P1)
assert np.all(np.abs(GN1-AG) < u), \
"Expected GN-1<%s but %s\nGN=\n%s" % (u, (GN1-AG), GN1)
# The numerical gradient gn = (-t * logarithm(p+h) + t * logarithm(p-h)) / 2h
assert GN1.shape == EGN1.shape
assert np.all(np.abs(EGN1-GN1) < u), \
"Expected GN1==EGN1 but GN1-EGN1=\n%sP=\n%s\nT=%s\nEGN=\n%s\nGN=\n%s\n" \
% (np.abs(GN1-EGN1), P1, T1, EGN1, GN1)
# The numerical gradient gn is within +/- u within the analytical g = -T/P
G1 = np.zeros_like(P1, dtype=TYPE_FLOAT)
G1[T1 == 1] = -1 * (T1[index] / P1[index])
# G1[T1 != 0] = 0
check.equal(np.all(np.abs(G1 - GN1) < u), True,
"G1-GN1 %s\n" % np.abs(G1 - GN1))
# --------------------------------------------------------------------------------
# For (P, T): P[index] = np uniform(), index label T=index
# --------------------------------------------------------------------------------
for _ in range(NUM_MAX_TEST_TIMES):
M = np.random.randint(2, NUM_MAX_NODES) # M > 1
T2 = TYPE_LABEL(np.random.randint(0, M)) # location of the truth
P2 = np.zeros(M, dtype=TYPE_FLOAT)
while not (x := TYPE_FLOAT(
np.random.uniform(low=-BOUNDARY_SIGMOID,
high=BOUNDARY_SIGMOID))):
pass
p = softmax(x)
P2[T2] = p
# --------------------------------------------------------------------------------
# The Jacobian G shape is the same with P.shape.
# G:[0, 0, ...,g, 0, ...] where Gi is numerical gradient close to -1/(1+k).
# --------------------------------------------------------------------------------
N2 = np.zeros_like(P2, dtype=TYPE_FLOAT)
N2[T2] = TYPE_FLOAT(-1) * (logarithm(p + h) -
logarithm(p - h)) / TYPE_FLOAT(2 * h)
N2 = numerical_jacobian(partial(f, T=T2), P2)
# The numerical gradient gn = (-t * logarithm(p+h) + t * logarithm(p-h)) / 2h
assert N2.shape == N2.shape
assert np.all(np.abs(N2-N2) < u), \
f"Delta expected to be < {u} but \n{np.abs(N2-N2)}"
G2 = np.zeros_like(P2, dtype=TYPE_FLOAT)
G2[T2] = -1 / p
# The numerical gradient gn is within +/- u within the analytical g = -T/P
check.equal(np.all(np.abs(G2 - N2) < u), True,
"G2-N2 %s\n" % np.abs(G2 - N2))
def test_010_base_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."
M: int = np.random.randint(1, NUM_MAX_NODES)
name = "test_010_base"
_layer = Layer(name=name, num_nodes=M, 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.D)
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(_layer.X)
raise RuntimeError(msg)
except AssertionError:
pass
try:
_layer.X = int(1)
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:
_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:
_layer.T = TYPE_LABEL(1)
raise RuntimeError(msg)
except AssertionError:
pass
try:
# pylint: disable=not-callable
_layer.objective(np.array(1.0, dtype=TYPE_FLOAT))
raise RuntimeError(msg)
except AssertionError:
pass
try:
print(_layer.N)
raise RuntimeError(msg)
except AssertionError:
pass
assert _layer.name == name
assert _layer.num_nodes == M
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 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 test_020_adapt_embedding_loss_adapter_gradient_to_succeed(caplog):
"""
Objective:
Verify the Adapter gradient method handles dY in shape (N, 1+SL)
Adapter.function(Y) returns
- For Y:(N, 1+SL), the return is in shape (N*(1+SL),1).
Log loss T is set to the same shape
Expected:
"""
caplog.set_level(logging.DEBUG)
name = "test_020_adapt_embedding_logistic_loss_function_multi_lines"
sentences = """
Verify the EventIndexing function can handle multi line sentences
the asbestos fiber <unk> is unusually <unk> once it enters the <unk>
with even brief exposures to it causing symptoms that show up decades later researchers said
"""
dictionary: EventIndexing = _instantiate_event_indexing()
profiler = cProfile.Profile()
profiler.enable()
for _ in range(NUM_MAX_TEST_TIMES):
# First validate the correct configuration, then change parameter one by one.
E = target_size = TYPE_INT(np.random.randint(1, 3))
C = context_size = TYPE_INT(2 * np.random.randint(1, 5))
SL = negative_sample_size = TYPE_INT(np.random.randint(1, 5))
event_vector_size: TYPE_INT = TYPE_INT(np.random.randint(5, 20))
W: TYPE_TENSOR = np.random.rand(dictionary.vocabulary_size,
event_vector_size)
loss, adapter, embedding, event_context = _instantiate(
name=name,
num_nodes=TYPE_INT(1),
target_size=target_size,
context_size=context_size,
negative_sample_size=negative_sample_size,
event_vector_size=event_vector_size,
dictionary=dictionary,
W=W,
log_level=logging.DEBUG,
)
# ================================================================================
# Forward path
# ================================================================================
# --------------------------------------------------------------------------------
# Event indexing
# --------------------------------------------------------------------------------
sequences = dictionary.function(sentences)
# --------------------------------------------------------------------------------
# Event context pairs
# --------------------------------------------------------------------------------
target_context_pairs = event_context.function(sequences)
# --------------------------------------------------------------------------------
# Embedding
# --------------------------------------------------------------------------------
Y = embedding.function(target_context_pairs)
N, _ = embedding.tensor_shape(Y)
batch_size = TYPE_FLOAT(N * (1 + SL))
# --------------------------------------------------------------------------------
# Adapter
# --------------------------------------------------------------------------------
Z = adapter.function(Y)
# --------------------------------------------------------------------------------
# Loss
# --------------------------------------------------------------------------------
L = loss.function(Z)
# ********************************************************************************
# Constraint:
# loss.T is set to the T by adapter.function()
# ********************************************************************************
T = np.zeros(shape=(N, (1 + SL)), dtype=TYPE_LABEL)
T[::, 0] = TYPE_LABEL(1)
assert embedding.all_equal(T.reshape(-1, 1), loss.T), \
"Expected T must equals loss.T. Expected\n%s\nLoss.T\n%s\n" % (T, loss.T)
# ********************************************************************************
# Constraint:
# Expected loss is sum(sigmoid_cross_entropy_log_loss(Y, T)) / (N*(1+SL))
# The batch size for the Log Loss is (N*(1+SL))
# ********************************************************************************
EJ, EP = sigmoid_cross_entropy_log_loss(X=Z, T=T.reshape(-1, 1))
EL = np.sum(EJ, dtype=TYPE_FLOAT) / batch_size
assert embedding.all_close(EL, L), \
"Expected EL=L but EL=\n%s\nL=\n%s\nDiff=\n%s\n" % (EL, L, (EL-L))
# ================================================================================
# Backward path
# ================================================================================
# ********************************************************************************
# Constraint:
# Expected dL/dY from the Log Loss is (P-T)/N
# ********************************************************************************
EDY = (sigmoid(Y) - T.astype(TYPE_FLOAT)) / batch_size
assert EDY.shape == Y.shape
dY = adapter.gradient(loss.gradient(TYPE_FLOAT(1)))
assert dY.shape == Y.shape
assert embedding.all_close(EDY, dY), \
"Expected EDY==dY. EDY=\n%s\nDiff\n%s\n" % (EDY, (EDY-dY))
profiler.disable()
profiler.print_stats(sort="cumtime")
def test_020_adapt_embedding_loss_adapter_function_Y_to_succeed(caplog):
"""
Objective:
Verify the Adapter function handles Y in shape
- Y:(N, 1+SL)
- ys:(N,SL)
- ye:(N,1)
Expected:
Adapter.function(Y) returns
- For Y:(N, 1+SL), the return is in shape (N*(1+SL),1).
Log loss T is set to the same shape
- For Y:(N, SL), the return is in shape (N*SL,1).
Log loss T is set to the same shape
- For Y:(N,), the return is in shape (N,1).
Log loss T is set to the same shape
"""
caplog.set_level(logging.DEBUG)
name = "test_020_adapt_embedding_logistic_loss_function_multi_lines"
sentences = """
Verify the EventIndexing function can handle multi line sentences
the asbestos fiber <unk> is unusually <unk> once it enters the <unk>
with even brief exposures to it causing symptoms that show up decades later researchers said
"""
dictionary: EventIndexing = _instantiate_event_indexing()
profiler = cProfile.Profile()
profiler.enable()
for _ in range(NUM_MAX_TEST_TIMES):
# First validate the correct configuration, then change parameter one by one.
E = target_size = TYPE_INT(np.random.randint(1, 3))
C = context_size = TYPE_INT(2 * np.random.randint(1, 5))
SL = negative_sample_size = TYPE_INT(np.random.randint(1, 5))
event_vector_size: TYPE_INT = TYPE_INT(np.random.randint(5, 20))
W: TYPE_TENSOR = np.random.randn(dictionary.vocabulary_size,
event_vector_size)
loss, adapter, embedding, event_context = _instantiate(
name=name,
num_nodes=TYPE_INT(1),
target_size=target_size,
context_size=context_size,
negative_sample_size=negative_sample_size,
event_vector_size=event_vector_size,
dictionary=dictionary,
W=W,
log_level=logging.DEBUG,
)
sequences = dictionary.function(sentences)
target_context_pairs = event_context.function(sequences)
Y = embedding.function(target_context_pairs)
N, _ = embedding.tensor_shape(Y)
# ********************************************************************************
# Constraint:
# - Adapter function returns (N*(SL+1),1) with the same values of Y
# - Adapter function has set T:(N*(SL+1),1) in the loss layer
# ********************************************************************************
msg = "Y must succeed"
EZ = expected_Z = embedding.reshape(Y, shape=(N * (SL + 1), 1))
Z = _function_must_succeed(adapter=adapter, Y=Y, msg=msg)
assert embedding.all_close(
Z, EZ,
"Z must close to EZ. Z:\n%s\nEZ\n%s\nDiff\n%s\n" % (Z, EZ,
(EZ - Z)))
T = np.zeros(shape=(N, (1 + SL)), dtype=TYPE_LABEL)
T[::, 0] = TYPE_LABEL(1)
T = embedding.reshape(T, shape=(-1, 1))
assert embedding.all_equal(T, loss.T), \
"Expected T must equals loss.T. Expected\n%s\nLoss.T\n%s\n" % (T, loss.T)
profiler.disable()
profiler.print_stats(sort="cumtime")