def predict(network, x): W1, W2, W3 = network['W1'], network['W2'], network['W3'] b1, b2, b3 = network['b1'], network['b2'], network['b3'] a1 = np.dot(x, W1) + b1 z1 = sigmoid(a1) a2 = np.dot(z1, W2) + b2 z2 = sigmoid(a2) a3 = np.dot(z2, W3) + b3 y = softmax(a3) return y
def test_010_sigmoid(): """Test Case for sigmoid """ u = ACTIVATION_DIFF_ACCEPTANCE_VALUE assert sigmoid(np.array(TYPE_FLOAT(0), dtype=TYPE_FLOAT)) == TYPE_FLOAT(0.5) x = np.array([0.0, 0.6, 0., -0.5]).reshape((2, 2)).astype(TYPE_FLOAT) t = np.array( [0.5, 0.6456563062257954529091, 0.5, 0.3775406687981454353611]).reshape((2, 2)).astype(TYPE_FLOAT) assert np.all(np.abs(t - sigmoid(x)) < u), \ f"delta (t-x) is expected < {u} but {x-t}"
def forward(self, x, t): self.t = t self.y = sigmoid(x) self.loss = cross_entropy_error(np.c_[1 - self.y, self.y], self.t) return self.loss
def predict(self, x): w1, w2 = self.params['w1'], self.params['w2'] b1, b2 = self.params['b1'], self.params['b2'] a1 = np.dot(x, w1) + b1 z1 = sigmoid(a1) a2 = np.dot(z1, w2) + b2 y = softmax(a2) return y
def grad(self, x, t): w1, w2 = self.params['w1'], self.params['w2'] b1, b2 = self.params['b1'], self.params['b2'] grads = {} # forward a1 = np.dot(x, w1) + b1 z1 = sigmoid(a1) a2 = np.dot(z1, w2) + b2 y = softmax(a2) # backward dy = (y - t) / x.shape[0] # softmax with entropy loss's gradient, dL/dy grads['w2'] = np.dot(z1.T, dy) grads['b2'] = np.sum(dy, axis=0) da1 = np.dot(dy, w2.T) dz1 = (1.0 - sigmoid(a1)) * sigmoid(a1) * da1 # sigmoid's gradient grads['w1'] = np.dot(x.T, dz1) grads['b1'] = np.sum(dz1, axis=0) return grads
def function( self, X: Union[TYPE_FLOAT, np.ndarray]) -> Union[TYPE_FLOAT, np.ndarray]: X = np.array(X).reshape((1, -1)) if isinstance(X, TYPE_FLOAT) else X assert X.shape[1] == self.M, \ f"Number of node X {X.shape[1] } does not match {self.M}." self.X = X if self._Y.size <= 0 or self.Y.shape[0] != self.N: self._Y = np.empty(X.shape, dtype=TYPE_FLOAT) self._Y = sigmoid(X, out=self._Y) return self.Y
def test_020_numerical_jacobian_sigmoid(caplog): """Test Case for numerical gradient calculation The domain of X is -BOUNDARY_SIGMOID < x < BOUNDARY_SIGMOID Args: u: Acceptable threshold value """ u: TYPE_FLOAT = GRADIENT_DIFF_ACCEPTANCE_VALUE # y=sigmoid(x) -> dy/dx = y(1-y) # 0.5 = sigmoid(0) -> dy/dx = 0.25 for _ in range(NUM_MAX_TEST_TIMES): x = np.random.uniform(low=-BOUNDARY_SIGMOID, high=BOUNDARY_SIGMOID, size=1).astype(TYPE_FLOAT) y = sigmoid(x) analytical = np.multiply(y, (1 - y)) numerical = numerical_jacobian(sigmoid, x) difference = np.abs(analytical - numerical) acceptance = np.abs(analytical * GRADIENT_DIFF_ACCEPTANCE_RATIO) assert np.all(difference < max(u, acceptance)), \ f"Needs difference < {max(u, acceptance)} but {difference}\nx is {x}"
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 forward(self, x, **kwargs): self.out = sigmoid(x) return self.out
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_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 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])
def forward(self, x): self.out = sigmoid(x) return self.out
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")