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)