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 disabled_test_040_softmax_log_loss_2d(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(softmax_cross_entropy_log_loss) / N.
2. gradient_numerical() == numerical_jacobian(objective, 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_softmax_log_loss_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 = np.random.randint(2, NUM_MAX_NODES) # number of node > 1
_layer = layer.CrossEntropyLogLoss(
name=name,
num_nodes=M,
log_loss_function=softmax_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)] = int(1)
# log_loss function require (X, T) in X(N, M), and T(N, M) in index 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 = softmax(X)
EG = np.copy(A)
EG[np.arange(N), T] -= TYPE_FLOAT(
1) # Shape(N,), subtract from elements for T=1 only
EG /= TYPE_FLOAT(N)
# --------------------------------------------------------------------------------
# Total loss Z = np.sum(J)/N
# Expected loss EL = -sum(T*log(_A))
# (J, P) = softmax_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 = softmax_cross_entropy_log_loss(X, T)
EL = np.array(-np.sum(logarithm(A[np.arange(N), T])) / 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 = softmax_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() == EG == (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])), \
f"dX is \n{G}\nGN[0] is \n{GN[0]}\nRatio * GN[0] is \n{GRADIENT_DIFF_ACCEPTANCE_RATIO * 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_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_020_cross_entropy_log_loss_2d(caplog):
"""
Objective:
Test case for cross_entropy_log_loss(X, T) for X:shape(N,M), T:shape(N,)
Expected:
"""
def f(P: np.ndarray, T: np.ndarray):
"""Loss function"""
# For P.ndim==2 of shape (N, M), cross_entropy_log_loss() returns (N,).
# Each of which has the loss for P[n].
# If divided by P.shape[0] or N, the loss gets 1/N, which is wrong.
# This is not a gradient function but a loss function.
# return np.sum(cross_entropy_log_loss(P, T)) / P.shape[0]
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 _ in range(NUM_MAX_TEST_TIMES):
# --------------------------------------------------------------------------------
# [2D test case]
# P:(N, M) is probability matrix where Pnm = p, 0 <=n<N-1, 0<=m<M-1
# T:(N,) is index label where Tn=m is label as integer k.g. m=3 for 3rd label.
# Pnm = log(P[i][j])
# L = -log(p), -> dlog(P)/dP -> -1 / (p)
#
# Keep p value away from 0. As p gets close to 0, the log(p+/-h) gets large e.g
# -11.512925464970229, hence log(p+/-h) / 2h explodes.
# --------------------------------------------------------------------------------
while not (x := TYPE_FLOAT(
np.random.uniform(low=-BOUNDARY_SIGMOID,
high=BOUNDARY_SIGMOID))):
pass
p = softmax(x)
N = np.random.randint(1, NUM_MAX_BATCH_SIZE)
M = np.random.randint(2, NUM_MAX_NODES)
# label index, not OHE
T = np.random.randint(0, M, N).astype(
TYPE_LABEL) # N rows of labels, max label value is M-1
P = np.zeros((N, M)).astype(TYPE_FLOAT)
P[range(N), # Set p at random row position
T] = p
E = np.zeros_like(P).astype(TYPE_FLOAT)
E[range(N), # Set p at random row position
T] = (TYPE_FLOAT(-1) * logarithm(p + h) +
TYPE_FLOAT(1) * logarithm(p - h)) / (TYPE_FLOAT(2) * h)
G = numerical_jacobian(partial(f, T=T), P)
assert E.shape == G.shape, \
f"Jacobian shape is expected to be {E.shape} but {G.shape}."
assert np.all(np.abs(E-G) < u), \
f"Delta expected to be < {u} but \n{np.abs(E-G)}"
A = np.zeros_like(P).astype(TYPE_FLOAT)
A[range(N), # Set p at random row position
T] = -1 / p
check.equal(np.all(np.abs(A - G) < u), True,
"A-G %s\n" % np.abs(A - G))
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,
"G3-N3 %s\n" % np.abs(G3 - N3))
# --------------------------------------------------------------------------------
# [1D test case]
# For 1D OHE array P [0, 0, ..., 1, 0, ...] where Pi = 1.
# For 1D OHE array T [0, 0, ..., 0, 1, ...] where Tj = 1 and i != j
def test_010_softmax_cross_entropy_log_loss_2d(caplog):
"""
Objective:
Test case for softmax_cross_entropy_log_loss(X, T) = -T * log(softmax(X))
For the input X of shape (N,M) and T in index format of shape (N,),
calculate the softmax log loss and verify the values are as expected.
Expected:
For P = softmax(X) = exp(-X) / sum(exp(-X))
_P = P[
np.arange(N),
T
] selects the probability p for the correct input x.
Then -log(_P) should be almost same with softmax_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]
# N: Batch size, M: Number of features in X
# X:(N,M)=(1, 2). X=(x0, x1) where x0 == x1 == 0.5 by which softmax(X) generates equal
# probability P=(p0, p1) where p0 == p1.
# Expected:
# softmax(X) generates the same with X.
# softmax_cross_entropy_log_loss(X, T) == -log(0.5)
# --------------------------------------------------------------------------------
X = np.array([[0.5, 0.5]]).astype(TYPE_FLOAT)
T = np.array([1]).astype(TYPE_LABEL)
E = -logarithm(np.array([0.5]).astype(TYPE_FLOAT))
P = softmax(X)
assert np.array_equal(X, P)
J, _ = softmax_cross_entropy_log_loss(X, T)
assert (E.shape == J.shape)
assert np.all(np.abs(E - J) < u), \
"Expected abs(E-J) < %s but \n%s\nE=\n%s\nT=%s\nX=\n%s\nJ=\n%s\n" \
% (u, np.abs(E - J), E, T, X, J)
assert np.all(np.abs(P - _) < u)
# --------------------------------------------------------------------------------
# [Test case 01]
# For X:(N,M)
# --------------------------------------------------------------------------------
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 = np.random.randint(2, NUM_MAX_NODES)
X = np.random.randn(N, M).astype(TYPE_FLOAT)
T = np.random.randint(0, M, N).astype(TYPE_LABEL)
Logger.debug("T is %s\nX is \n%s\n", T, X)
# ----------------------------------------------------------------------
# Expected value E = -logarithm(_P)
# ----------------------------------------------------------------------
P = softmax(X)
_P = P[np.arange(
N
), T] # Probability of p for the correct input x, which generates j=-log(p)
E = -logarithm(_P)
# ----------------------------------------------------------------------
# Actual J should be close to E.
# ----------------------------------------------------------------------
J, _ = softmax_cross_entropy_log_loss(X, T)
assert (E.shape == J.shape)
assert np.all(np.abs(E-J) < u), \
"Expected abs(E-J) < %s but \n%s\nE=\n%s\nT=%s\nX=\n%s\nJ=\n%s\n" \
% (u, np.abs(E - J), E, T, X, J)
# ----------------------------------------------------------------------
# L = cross_entropy_log_loss(P, T) should be close to J
# ----------------------------------------------------------------------
L = cross_entropy_log_loss(P, T)
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(E - J), E, T, X, J)