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])