def init_train_updates(self):
step = self.variables.step
min_eigval = self.min_eigval
parameters = list(iter_parameters(self))
param_vector = parameters2vector(self)
gradients = T.grad(self.variables.error_func, wrt=parameters)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
second_derivatives = []
for parameter, gradient in zip(parameters, gradients):
second_derivative = T.grad(gradient.sum(), wrt=parameter)
second_derivatives.append(second_derivative.flatten())
hessian_diag = T.concatenate(second_derivatives)
hessian_diag = T.switch(
T.abs_(hessian_diag) < min_eigval,
T.switch(
hessian_diag < 0,
-min_eigval,
min_eigval,
), hessian_diag)
# We divide gradient by Hessian diagonal elementwise is the same
# as we just took diagonal Hessian inverse (which is
# reciprocal for each diagonal element) and mutliply
# by gradient. This operation is less clear, but works faster.
updated_parameters = (param_vector -
step * full_gradient / hessian_diag)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
step = self.variables.step
previous_delta = self.variables.prev_delta
previous_gradient = self.variables.prev_gradient
n_parameters = count_parameters(self)
parameters = list(iter_parameters(self))
param_vector = parameters2vector(self)
gradients = T.grad(self.variables.error_func, wrt=parameters)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
beta = self.update_function(previous_gradient, full_gradient,
previous_delta)
parameter_delta = ifelse(
T.eq(T.mod(self.variables.epoch, n_parameters), 1),
-full_gradient,
-full_gradient + beta * previous_delta
)
updated_parameters = param_vector + step * parameter_delta
updates = [
(previous_gradient, full_gradient),
(previous_delta, parameter_delta),
]
parameter_updates = setup_parameter_updates(parameters,
updated_parameters)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
step = self.variables.step
previous_delta = self.variables.prev_delta
previous_gradient = self.variables.prev_gradient
n_parameters = count_parameters(self.connection)
parameters = parameter_values(self.connection)
param_vector = T.concatenate([param.flatten() for param in parameters])
gradients = T.grad(self.variables.error_func, wrt=parameters)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
beta = self.update_function(previous_gradient, full_gradient,
previous_delta)
parameter_delta = ifelse(
T.eq(T.mod(self.variables.epoch, n_parameters), 1), -full_gradient,
-full_gradient + beta * previous_delta)
updated_parameters = param_vector + step * parameter_delta
updates = [
(previous_gradient, full_gradient),
(previous_delta, parameter_delta),
]
parameter_updates = setup_parameter_updates(parameters,
updated_parameters)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
network_output = self.variables.network_output
prediction_func = self.variables.train_prediction_func
last_error = self.variables.last_error
error_func = self.variables.error_func
mu = self.variables.mu
new_mu = ifelse(
T.lt(last_error, error_func),
mu * self.mu_update_factor,
mu / self.mu_update_factor,
)
se_for_each_sample = (
(network_output - prediction_func) ** 2
).ravel()
params = parameter_values(self.connection)
param_vector = parameters2vector(self)
J = compute_jacobian(se_for_each_sample, params)
n_params = J.shape[1]
updated_params = param_vector - slinalg.solve(
J.T.dot(J) + new_mu * T.eye(n_params),
J.T.dot(se_for_each_sample)
)
updates = [(mu, new_mu)]
parameter_updates = setup_parameter_updates(params, updated_params)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
network_output = self.variables.network_output
prediction_func = self.variables.train_prediction_func
last_error = self.variables.last_error
error_func = self.variables.error_func
mu = self.variables.mu
new_mu = ifelse(
T.lt(last_error, error_func),
mu * self.mu_update_factor,
mu / self.mu_update_factor,
)
mse_for_each_sample = T.mean((network_output - prediction_func)**2,
axis=1)
params = list(iter_parameters(self))
param_vector = parameters2vector(self)
J = compute_jaccobian(mse_for_each_sample, params)
n_params = J.shape[1]
updated_params = param_vector - T.nlinalg.matrix_inverse(
J.T.dot(J) + new_mu * T.eye(n_params)).dot(
J.T).dot(mse_for_each_sample)
updates = [(mu, new_mu)]
parameter_updates = setup_parameter_updates(params, updated_params)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
network_output = self.variables.network_output
prediction_func = self.variables.train_prediction_func
last_error = self.variables.last_error
error_func = self.variables.error_func
mu = self.variables.mu
new_mu = tf.where(
tf.less(last_error, error_func),
mu * self.mu_update_factor,
mu / self.mu_update_factor,
)
err_for_each_sample = flatten((network_output - prediction_func) ** 2)
params = parameter_values(self.connection)
param_vector = make_single_vector(params)
J = compute_jacobian(err_for_each_sample, params)
J_T = tf.transpose(J)
n_params = J.shape[1]
parameter_update = tf.matrix_solve(
tf.matmul(J_T, J) + new_mu * tf.eye(n_params.value),
tf.matmul(J_T, tf.expand_dims(err_for_each_sample, 1))
)
updated_params = param_vector - flatten(parameter_update)
updates = [(mu, new_mu)]
parameter_updates = setup_parameter_updates(params, updated_params)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
step = self.variables.step
inv_min_eigval = 1 / self.min_eigval
parameters = parameter_values(self.connection)
param_vector = make_single_vector(parameters)
gradients = tf.gradients(self.variables.error_func, parameters)
full_gradient = make_single_vector(gradients)
second_derivatives = []
for parameter, gradient in zip(parameters, gradients):
second_derivative, = tf.gradients(gradient, parameter)
second_derivatives.append(flatten(second_derivative))
hessian_diag = tf.concat(second_derivatives, axis=0)
# it's easier to clip inverse hessian rather than the hessian,.
inv_hessian_diag = tf.clip_by_value(
# inverse for diagonal matrix easy to compute with
# elementwise inverse operation.
1 / hessian_diag,
-inv_min_eigval,
inv_min_eigval,
)
updates = setup_parameter_updates(
parameters, param_vector - step * full_gradient * inv_hessian_diag)
return updates
def init_train_updates(self):
network_output = self.variables.network_output
prediction_func = self.variables.train_prediction_func
last_error = self.variables.last_error
error_func = self.variables.error_func
mu = self.variables.mu
new_mu = ifelse(
T.lt(last_error, error_func),
mu * self.mu_update_factor,
mu / self.mu_update_factor,
)
se_for_each_sample = ((network_output - prediction_func)**2).ravel()
params = parameter_values(self.connection)
param_vector = T.concatenate([param.flatten() for param in params])
J = compute_jacobian(se_for_each_sample, params)
n_params = J.shape[1]
updated_params = param_vector - slinalg.solve(
J.T.dot(J) + new_mu * T.eye(n_params), J.T.dot(se_for_each_sample))
updates = [(mu, new_mu)]
parameter_updates = setup_parameter_updates(params, updated_params)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
network_output = self.variables.network_output
prediction_func = self.variables.train_prediction_func
last_error = self.variables.last_error
error_func = self.variables.error_func
mu = self.variables.mu
new_mu = ifelse(
T.lt(last_error, error_func),
mu * self.mu_update_factor,
mu / self.mu_update_factor,
)
mse_for_each_sample = T.mean(
(network_output - prediction_func) ** 2,
axis=1
)
params = list(iter_parameters(self))
param_vector = parameters2vector(self)
J = compute_jaccobian(mse_for_each_sample, params)
n_params = J.shape[1]
updated_params = param_vector - T.nlinalg.matrix_inverse(
J.T.dot(J) + new_mu * T.eye(n_params)
).dot(J.T).dot(mse_for_each_sample)
updates = [(mu, new_mu)]
parameter_updates = setup_parameter_updates(params, updated_params)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
network_inputs = self.variables.network_inputs
network_output = self.variables.network_output
inv_hessian = self.variables.inv_hessian
prev_params = self.variables.prev_params
prev_full_gradient = self.variables.prev_full_gradient
params = parameter_values(self.connection)
param_vector = T.concatenate([param.flatten() for param in params])
gradients = T.grad(self.variables.error_func, wrt=params)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
new_inv_hessian = ifelse(
T.eq(self.variables.epoch, 1), inv_hessian,
self.update_function(inv_hessian, param_vector - prev_params,
full_gradient - prev_full_gradient))
param_delta = -new_inv_hessian.dot(full_gradient)
layers_and_parameters = list(iter_parameters(self.layers))
def prediction(step):
updated_params = param_vector + step * param_delta
# This trick allow us to replace shared variables
# with theano variables and get output from the network
start_pos = 0
for layer, attrname, param in layers_and_parameters:
end_pos = start_pos + param.size
updated_param_value = T.reshape(
updated_params[start_pos:end_pos], param.shape)
setattr(layer, attrname, updated_param_value)
start_pos = end_pos
output = self.connection.output(*network_inputs)
# Restore previous parameters
for layer, attrname, param in layers_and_parameters:
setattr(layer, attrname, param)
return output
def phi(step):
return self.error(network_output, prediction(step))
def derphi(step):
error_func = self.error(network_output, prediction(step))
return T.grad(error_func, wrt=step)
step = asfloat(line_search(phi, derphi))
updated_params = param_vector + step * param_delta
updates = setup_parameter_updates(params, updated_params)
updates.extend([
(inv_hessian, new_inv_hessian),
(prev_params, param_vector),
(prev_full_gradient, full_gradient),
])
return updates
def init_train_updates(self):
network_input = self.variables.network_input
network_output = self.variables.network_output
inv_hessian = self.variables.inv_hessian
prev_params = self.variables.prev_params
prev_full_gradient = self.variables.prev_full_gradient
params = list(iter_parameters(self))
param_vector = parameters2vector(self)
gradients = T.grad(self.variables.error_func, wrt=params)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
new_inv_hessian = ifelse(
T.eq(self.variables.epoch, 1),
inv_hessian,
self.update_function(inv_hessian,
param_vector - prev_params,
full_gradient - prev_full_gradient)
)
param_delta = -new_inv_hessian.dot(full_gradient)
def prediction(step):
# TODO: I need to update this ugly solution later
updated_params = param_vector + step * param_delta
layer_input = network_input
start_pos = 0
for layer in self.layers:
for param in layer.parameters:
end_pos = start_pos + param.size
parameter_name, parameter_id = param.name.split('_')
setattr(layer, parameter_name, T.reshape(
updated_params[start_pos:end_pos],
param.shape
))
start_pos = end_pos
layer_input = layer.output(layer_input)
return layer_input
def phi(step):
return self.error(network_output, prediction(step))
def derphi(step):
error_func = self.error(network_output, prediction(step))
return T.grad(error_func, wrt=step)
step = asfloat(line_search(phi, derphi))
updated_params = param_vector + step * param_delta
updates = setup_parameter_updates(params, updated_params)
updates.extend([
(inv_hessian, new_inv_hessian),
(prev_params, param_vector),
(prev_full_gradient, full_gradient),
])
return updates
def init_train_updates(self):
n_parameters = count_parameters(self.connection)
parameters = parameter_values(self.connection)
param_vector = T.concatenate([param.flatten() for param in parameters])
penalty_const = asfloat(self.penalty_const)
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters)
updated_parameters = param_vector - slinalg.solve(
hessian_matrix + penalty_const * T.eye(n_parameters),
full_gradient)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
penalty_const = asfloat(self.penalty_const)
n_parameters = count_parameters(self.connection)
parameters = parameter_values(self.connection)
param_vector = make_single_vector(parameters)
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters)
parameter_update = tf.matrix_solve(
hessian_matrix + penalty_const * tf.eye(n_parameters),
tf.reshape(full_gradient, [-1, 1]))
updated_parameters = param_vector - flatten(parameter_update)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
n_parameters = count_parameters(self.connection)
parameters = parameter_values(self.connection)
param_vector = T.concatenate([param.flatten() for param in parameters])
penalty_const = asfloat(self.penalty_const)
print n_parameters
self.variables.hessian = theano.shared(value=asfloat(
np.zeros((n_parameters, n_parameters))),
name='hessian_inverse')
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters)
updated_parameters = hessian_matrix
updates = setup_parameter_updates([self.variables.hessian],
updated_parameters)
return updates
def init_train_updates(self):
n_parameters = count_parameters(self)
parameters = list(iter_parameters(self))
param_vector = parameters2vector(self)
penalty_const = asfloat(self.penalty_const)
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters)
hessian_inverse = T.nlinalg.matrix_inverse(hessian_matrix +
penalty_const *
T.eye(n_parameters))
updated_parameters = param_vector - hessian_inverse.dot(full_gradient)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
n_parameters = count_parameters(self)
parameters = list(iter_parameters(self))
param_vector = parameters2vector(self)
penalty_const = asfloat(self.penalty_const)
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters
)
hessian_inverse = T.nlinalg.matrix_inverse(
hessian_matrix + penalty_const * T.eye(n_parameters)
)
updated_parameters = param_vector - hessian_inverse.dot(full_gradient)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
n_parameters = count_parameters(self.connection)
parameters = parameter_values(self.connection)
param_vector = parameters2vector(self)
penalty_const = asfloat(self.penalty_const)
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters
)
updated_parameters = param_vector - slinalg.solve(
hessian_matrix + penalty_const * T.eye(n_parameters),
full_gradient
)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
network_output = self.variables.network_output
prediction_func = self.variables.train_prediction_func
last_error = self.variables.last_error
error_func = self.variables.error_func
mu = self.variables.mu
new_mu = ifelse(
T.lt(last_error, error_func),
mu * self.mu_update_factor,
mu / self.mu_update_factor,
)
mse_for_each_sample = T.mean((network_output - prediction_func)**2,
axis=1)
params = list(iter_parameters(self))
param_vector = parameters2vector(self)
#######################################################################################
n_parameters = count_parameters(self)
self.variables.hessian = theano.shared(value=asfloat(
np.zeros((n_parameters, n_parameters))),
name='hessian_inverse')
parameters = list(iter_parameters(self))
hessian_matrix, full_gradient = find_hessian_and_gradient(
self.variables.error_func, parameters)
#######################################################################################
J = compute_jaccobian(mse_for_each_sample, params)
n_params = J.shape[1]
updated_params = param_vector - T.nlinalg.matrix_inverse(
J.T.dot(J) + new_mu * T.eye(n_params)).dot(
J.T).dot(mse_for_each_sample)
updates = [(mu, new_mu), [(self.variables.hessian, hessian_matrix)]]
parameter_updates = setup_parameter_updates(params, updated_params)
updates.extend(parameter_updates)
return updates
def init_train_updates(self):
inv_hessian = self.variables.inv_hessian
prev_params = self.variables.prev_params
prev_full_gradient = self.variables.prev_full_gradient
params = parameter_values(self.connection)
param_vector = make_single_vector(params)
gradients = tf.gradients(self.variables.error_func, params)
full_gradient = make_single_vector(gradients)
new_inv_hessian = tf.where(
tf.equal(self.variables.epoch, 1), inv_hessian,
self.update_function(inv_H=inv_hessian,
delta_w=param_vector - prev_params,
delta_grad=full_gradient - prev_full_gradient,
epsilon=self.epsilon))
param_delta = -dot(new_inv_hessian, full_gradient)
step = self.find_optimal_step(param_vector, param_delta)
updated_params = param_vector + step * param_delta
updates = setup_parameter_updates(params, updated_params)
# We have to compute these values first, otherwise
# parallelization in tensorflow can mix update order
# and, for example, previous gradient can be equal to
# current gradient value. It happens because tensorflow
# try to execute operations in parallel.
required_variables = [new_inv_hessian, param_vector, full_gradient]
with tf.control_dependencies(required_variables):
updates.extend([
inv_hessian.assign(new_inv_hessian),
prev_params.assign(param_vector),
prev_full_gradient.assign(full_gradient),
])
return updates
def init_train_updates(self):
step = self.variables.step
min_eigval = self.min_eigval
parameters = list(iter_parameters(self))
param_vector = parameters2vector(self)
gradients = T.grad(self.variables.error_func, wrt=parameters)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
second_derivatives = []
for parameter, gradient in zip(parameters, gradients):
second_derivative = T.grad(gradient.sum(), wrt=parameter)
second_derivatives.append(second_derivative.flatten())
hessian_diag = T.concatenate(second_derivatives)
hessian_diag = T.switch(
T.abs_(hessian_diag) < min_eigval,
T.switch(
hessian_diag < 0,
-min_eigval,
min_eigval,
),
hessian_diag
)
# We divide gradient by Hessian diagonal elementwise is the same
# as we just took diagonal Hessian inverse (which is
# reciprocal for each diagonal element) and mutliply
# by gradient. This operation is less clear, but works faster.
updated_parameters = (
param_vector -
step * full_gradient / hessian_diag
)
updates = setup_parameter_updates(parameters, updated_parameters)
return updates
def init_train_updates(self):
step = self.variables.step
epoch = self.variables.epoch
previous_delta = self.variables.prev_delta
previous_gradient = self.variables.prev_gradient
n_parameters = count_parameters(self.connection)
parameters = parameter_values(self.connection)
param_vector = make_single_vector(parameters)
gradients = tf.gradients(self.variables.error_func, parameters)
full_gradient = make_single_vector(gradients)
beta = self.update_function(previous_gradient, full_gradient,
previous_delta, self.epsilon)
parameter_delta = tf.where(tf.equal(tf.mod(epoch, n_parameters),
1), -full_gradient,
-full_gradient + beta * previous_delta)
step = self.find_optimal_step(param_vector, parameter_delta)
updated_parameters = param_vector + step * parameter_delta
updates = setup_parameter_updates(parameters, updated_parameters)
# We have to compute these values first, otherwise
# parallelization in tensorflow can mix update order
# and, for example, previous gradient can be equal to
# current gradient value. It happens because tensorflow
# try to execute operations in parallel.
with tf.control_dependencies([full_gradient, parameter_delta]):
updates.extend([
previous_gradient.assign(full_gradient),
previous_delta.assign(parameter_delta),
])
return updates
def init_train_updates(self):
network_input = self.variables.network_input
network_output = self.variables.network_output
inv_hessian = self.variables.inv_hessian
prev_params = self.variables.prev_params
prev_full_gradient = self.variables.prev_full_gradient
params = parameter_values(self.connection)
param_vector = parameters2vector(self)
gradients = T.grad(self.variables.error_func, wrt=params)
full_gradient = T.concatenate([grad.flatten() for grad in gradients])
new_inv_hessian = ifelse(
T.eq(self.variables.epoch, 1),
inv_hessian,
self.update_function(inv_hessian,
param_vector - prev_params,
full_gradient - prev_full_gradient)
)
param_delta = -new_inv_hessian.dot(full_gradient)
layers_and_parameters = list(iter_parameters(self.layers))
def prediction(step):
updated_params = param_vector + step * param_delta
# This trick allow us to replace shared variables
# with theano variables and get output from the network
start_pos = 0
for layer, attrname, param in layers_and_parameters:
end_pos = start_pos + param.size
updated_param_value = T.reshape(
updated_params[start_pos:end_pos],
param.shape
)
setattr(layer, attrname, updated_param_value)
start_pos = end_pos
output = self.connection.output(network_input)
# We need to replace back parameter to shared variable
for layer, attrname, param in layers_and_parameters:
setattr(layer, attrname, param)
return output
def phi(step):
return self.error(network_output, prediction(step))
def derphi(step):
error_func = self.error(network_output, prediction(step))
return T.grad(error_func, wrt=step)
step = asfloat(line_search(phi, derphi))
updated_params = param_vector + step * param_delta
updates = setup_parameter_updates(params, updated_params)
updates.extend([
(inv_hessian, new_inv_hessian),
(prev_params, param_vector),
(prev_full_gradient, full_gradient),
])
return updates
