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 disabled_test_020_matmul_round_trip():
"""
TODO: Disabled as need to re-design numerical_jacobian for 32 bit float e.g TF.
Objective:
Verify the forward and backward paths at matmul.
Expected:
Forward path:
1. Matmul function(X) == X @ W.T
2. Numerical gradient should be the same with numerical Jacobian
Backward path:
3. Analytical gradient dL/dX == dY @ W
4. Analytical dL/dW == X.T @ dY
5. Analytical gradients are similar to the numerical gradient ones
Gradient descent
6. W is updated via the gradient descent.
7. Objective L is decreasing via the gradient descent.
"""
profiler = cProfile.Profile()
profiler.enable()
for _ in range(NUM_MAX_TEST_TIMES):
# --------------------------------------------------------------------------------
# Instantiate a Matmul layer
# --------------------------------------------------------------------------------
N: int = np.random.randint(1, NUM_MAX_BATCH_SIZE)
M: int = np.random.randint(1, NUM_MAX_NODES)
D: int = np.random.randint(1, NUM_MAX_FEATURES)
W = weights.he(M, D + 1)
name = "test_020_matmul_methods"
def objective(X: np.ndarray) -> Union[float, np.ndarray]:
"""Dummy objective function to calculate the loss L"""
return np.sum(X)
# Test both static instantiation and build()
if TYPE_FLOAT(np.random.uniform()) < 0.5:
matmul = Matmul(name=name,
num_nodes=M,
W=W,
log_level=logging.DEBUG)
else:
matmul_spec = {
_NAME: "test_020_matmul_builder_to_fail_matmul_spec",
_NUM_NODES: M,
_NUM_FEATURES: D,
_WEIGHTS: {
_SCHEME: "he",
},
_OPTIMIZER: {
_SCHEME: "sGd"
}
}
matmul = Matmul.build(matmul_spec)
matmul.objective = objective
# ================================================================================
# Layer forward path
# Calculate the layer output Y=f(X), and get the loss L = objective(Y)
# Test the numerical gradient dL/dX=matmul.gradient_numerical().
#
# Note that bias columns are added inside the matmul layer instance, hence
# matmul.X.shape is (N, 1+D), matmul.W.shape is (M, 1+D)
# ================================================================================
X = np.random.randn(N, D).astype(TYPE_FLOAT)
Logger.debug("%s: X is \n%s", name, X)
# pylint: disable=not-callable
Y = matmul.function(X)
# pylint: disable=not-callable
L = matmul.objective(Y)
# Constraint 1 : Matmul outputs Y should be [email protected]
assert np.array_equal(Y, np.matmul(matmul.X, matmul.W.T))
# Constraint 2: Numerical gradient should be the same with numerical Jacobian
GN = matmul.gradient_numerical() # [dL/dX, dL/dW]
# DO NOT use matmul.function() as the objective function for numerical_jacobian().
# The state of the layer will be modified.
# LX = lambda x: matmul.objective(matmul.function(x))
def LX(x):
y = np.matmul(x, matmul.W.T)
# pylint: disable=not-callable
return matmul.objective(y)
EGNX = numerical_jacobian(LX,
matmul.X) # Numerical dL/dX including bias
EGNX = EGNX[::, 1::] # Remove bias for dL/dX
assert np.array_equal(GN[0], EGNX), \
"GN[0]\n%s\nEGNX=\n%s\n" % (GN[0], EGNX)
# DO NOT use matmul.function() as the objective function for numerical_jacobian().
# The state of the layer will be modified.
# LW = lambda w: matmul.objective(np.matmul(X, w.T))
def LW(w):
Y = np.matmul(matmul.X, w.T)
# pylint: disable=not-callable
return matmul.objective(Y)
EGNW = numerical_jacobian(LW,
matmul.W) # Numerical dL/dW including bias
assert np.array_equal(GN[1], EGNW) # No need to remove bias
# ================================================================================
# Layer backward path
# Calculate the analytical gradient dL/dX=matmul.gradient(dL/dY) with a dummy dL/dY.
# ================================================================================
dY = np.ones_like(Y)
dX = matmul.gradient(dY)
# Constraint 3: Matmul gradient dL/dX should be dL/dY @ W. Use a dummy dL/dY = 1.0.
expected_dX = np.matmul(dY, matmul.W)
expected_dX = expected_dX[::, 1:: # Omit bias
]
assert np.array_equal(dX, expected_dX)
# Constraint 5: Analytical gradient dL/dX close to the numerical gradient GN.
assert np.all(np.abs(dX - GN[0]) < GRADIENT_DIFF_ACCEPTANCE_VALUE), \
"dX need close to GN[0]. dX:\n%s\ndiff \n%s\n" % (dX, dX-GN[0])
# --------------------------------------------------------------------------------
# Gradient update.
# Run the gradient descent to update Wn+1 = Wn - lr * dL/dX.
# --------------------------------------------------------------------------------
# Python passes the reference to W, hence it is directly updated by the gradient-
# descent to avoid a temporary copy. Backup W before to compare before/after.
backup = copy.deepcopy(W)
# Gradient descent and returns analytical dL/dX, dL/dW
dS = matmul.update()
dW = dS[0]
# Constraint 6.: W has been updated by the gradient descent.
assert np.any(backup != matmul.W), "W has not been updated "
# Constraint 5: the numerical gradient (dL/dX, dL/dW) are closer to the analytical ones.
assert validate_against_expected_gradient(GN[0], dX), \
"dX=\n%s\nGN[0]=\n%sdiff=\n%s\n" % (dX, GN[0], (dX-GN[0]))
assert validate_against_expected_gradient(GN[1], dW), \
"dW=\n%s\nGN[1]=\n%sdiff=\n%s\n" % (dW, GN[1], (dW-GN[1]))
# Constraint 7: gradient descent progressing with the new objective L(Yn+1) < L(Yn)
# pylint: disable=not-callable
assert np.all(np.abs(objective(matmul.function(X)) < L))
profiler.disable()
profiler.print_stats(sort="cumtime")
def validate_relu_neuron_training(matmul: Matmul,
activation: ReLU,
loss: CrossEntropyLogLoss,
X: np.ndarray,
T: np.ndarray,
num_epochs: int = 100,
test_numerical_gradient: bool = False,
callback: Callable = None):
activation.objective = loss.function
matmul.objective = compose(activation.function, loss.function)
objective = compose(matmul.function, matmul.objective)
num_no_progress: int = 0 # how many time when loss L not decreased.
history: List[np.ndarray] = []
loss.T = T
for i in range(num_epochs):
L = objective(X)
N = X.shape[0]
P = softmax(relu(np.matmul(matmul.X, matmul.W.T)))
EDA = expected_gradient_from_log_loss(P=P, T=T, N=N)
# ********************************************************************************
# Constraint: Expected gradients must match actual
# ********************************************************************************
validate_relu_neuron_round_trip(matmul=matmul,
activation=activation,
X=X,
dA=EDA)
# --------------------------------------------------------------------------------
# gradient descent and get the analytical dL/dX, dL/dW
# --------------------------------------------------------------------------------
previous_W = copy.deepcopy(matmul.W)
matmul.update() # dL/dX, dL/dW
# ********************************************************************************
# Constraint. W in the matmul has been updated by the gradient descent.
# ********************************************************************************
Logger.debug("W after is \n%s", matmul.W)
if np.array_equal(previous_W, matmul.W):
Logger.warning("W has not been updated")
# ********************************************************************************
# Constraint: Objective/Loss L(Yn+1) after gradient descent < L(Yn)
# ********************************************************************************
if i > 0 and L >= history[-1]:
Logger.warning(
"Iteration [%i]: Loss[%s] has not improved from the previous [%s] for %s times.",
i, L, history[-1], num_no_progress + 1)
# --------------------------------------------------------------------------------
# Reduce the learning rate can make the situation worse.
# When reduced the lr every time L >= history, the (L >= history) became successive
# and eventually exceeded 50 successive non-improvement ending in failure.
# Keep the learning rate make the L>=history more frequent but still up to 3
# successive events, and the training still kept progressing.
# --------------------------------------------------------------------------------
num_no_progress += 1
if num_no_progress > 5:
matmul.lr = matmul.lr * 0.95
if num_no_progress > 50:
Logger.error(
"The training has no progress more than %s times.",
num_no_progress)
break
else:
num_no_progress = 0
history.append(L)
if callback:
callback(W=matmul.W)
return history