# Copyright 2017 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Code for backpropagation using the tape utilities."""
# TODO(b/159343581): Properly support CompositeTensor in all functions in this
# file.
import functools
import operator
import sys
import six
from tensorflow.python import pywrap_tfe
from tensorflow.python.eager import backprop_util
from tensorflow.python.eager import context
from tensorflow.python.eager import execute
from tensorflow.python.eager import imperative_grad
from tensorflow.python.eager import tape
from tensorflow.python.framework import composite_tensor_gradient
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import indexed_slices
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_shape
from tensorflow.python.framework import tensor_util
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import check_ops
from tensorflow.python.ops import control_flow_util
from tensorflow.python.ops import default_gradient
from tensorflow.python.ops import gen_array_ops
from tensorflow.python.ops import gen_math_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import resource_variable_ops
from tensorflow.python.ops.unconnected_gradients import UnconnectedGradients
from tensorflow.python.platform import tf_logging as logging
from tensorflow.python.util import _pywrap_utils
from tensorflow.python.util import nest
from tensorflow.python.util import tf_contextlib
from tensorflow.python.util import tf_inspect
from tensorflow.python.util.lazy_loader import LazyLoader
from tensorflow.python.util.tf_export import tf_export
# Note that we need to lazy load the following two modules to avoid creating
# circular dependencies.
# TODO(b/119775953): fix the circular dependencies.
pfor_ops = LazyLoader(
"pfor_ops", globals(),
"tensorflow.python.ops.parallel_for.control_flow_ops")
function = LazyLoader("function", globals(),
"tensorflow.python.eager.function")
_op_attr_type_cache = {}
def op_attr_type(op_type, attr_name):
try:
return _op_attr_type_cache[(op_type, attr_name)]
except KeyError:
context.ensure_initialized()
h = context.context()._handle # pylint: disable=protected-access
attr_type = pywrap_tfe.TFE_OpNameGetAttrType(h, op_type, attr_name)
_op_attr_type_cache[(op_type, attr_name)] = attr_type
return attr_type
def make_attr(attr_type, value):
# pybind11 enums do not return the raw value like SWIG enums do. They are
# useful when comparing amongst each other but not direct integers as we are
# doing in most tests.
# https://pybind11.readthedocs.io/en/stable/classes.html#enumerations-and-internal-types
# TODO(amitpatankar): After all SWIG transitions, convert the enum comparisons
# from integer value to class.
if attr_type == int(pywrap_tfe.TF_ATTR_TYPE):
return dtypes.as_dtype(value)
if attr_type == [int(pywrap_tfe.TF_ATTR_TYPE)]:
return [dtypes.as_dtype(v) for v in value]
if attr_type == int(pywrap_tfe.TF_ATTR_SHAPE):
return tensor_shape.as_shape(value).as_proto()
if attr_type == [int(pywrap_tfe.TF_ATTR_SHAPE)]:
return [tensor_shape.as_shape(v).as_proto() for v in value]
if isinstance(value, str):
return value.encode()
return value
class _MockOp(object):
"""Pretends to be a tf.Operation for the gradient functions."""
def __init__(self, attrs, inputs, outputs, typ, skip_input_indices):
self.attrs = attrs
self.inputs = inputs
self.outputs = outputs
self.type = typ
self.skip_input_indices = skip_input_indices
def get_attr(self, attr):
typ = op_attr_type(self.type, attr)
for i in range(0, len(self.attrs), 2):
if self.attrs[i] == attr:
return make_attr(typ, self.attrs[i + 1])
raise KeyError(attr)
def _get_control_flow_context(self):
raise NotImplementedError(
"tf.GradientTape.gradients() does not support graph control flow "
"operations like tf.cond or tf.while at this time. Use tf.gradients() "
"instead. If you need this feature, please file a feature request at "
"https://github.com/tensorflow/tensorflow/issues/new"
)
def _gradient_function(op_name, attr_tuple, num_inputs, inputs, outputs,
out_grads, skip_input_indices, forward_pass_name_scope):
"""Calls the gradient function of the op.
Args:
op_name: the name of the op to be differentiated.
attr_tuple: the attrs, as a tuple.
num_inputs: the number of inputs to the op.
inputs: inputs to the original operation.
outputs: outputs to the original operation.
out_grads: gradients of the operation wrt its outputs.
skip_input_indices: a tuple that is passed to the gradient function,
indicating which inputs to skip calculating the gradient for
forward_pass_name_scope: the namescope of the op in the forward pass.
Returns:
The gradients with respect to the inputs of the function, as a list.
"""
mock_op = _MockOp(attr_tuple, inputs, outputs, op_name, skip_input_indices)
grad_fn = ops._gradient_registry.lookup(op_name) # pylint: disable=protected-access
if grad_fn is None:
return [None] * num_inputs
# This does not work with v1 TensorArrays.
if ops.executing_eagerly_outside_functions(
) or control_flow_util.EnableControlFlowV2(ops.get_default_graph()):
gradient_name_scope = "gradient_tape/"
if forward_pass_name_scope:
gradient_name_scope += forward_pass_name_scope + "/"
with ops.name_scope(gradient_name_scope):
return grad_fn(mock_op, *out_grads)
else:
return grad_fn(mock_op, *out_grads)
pywrap_tfe.TFE_Py_RegisterGradientFunction(_gradient_function)
def _must_record_gradient():
return not pywrap_tfe.TFE_Py_TapeSetIsEmpty()
@tf_export("__internal__.record_gradient", v1=[])
def record_gradient(op_name, inputs, attrs, outputs):
"""Explicitly record the gradient for a given op.
Args:
op_name: The op name as listed in the `OpDef` for the op.
inputs: A list of tensor inputs to the op.
attrs: The op attributes as a flattened list of alternating attribute names
and attribute values.
outputs: A list of tensor outputs from the op.
"""
pywrap_tfe.TFE_Py_RecordGradient(op_name, inputs, attrs, outputs,
ops.get_name_scope())
execute.must_record_gradient = _must_record_gradient
execute.record_gradient = record_gradient
def implicit_val_and_grad(f):
"""Returns a function which differentiates f with respect to variables.
The wrapped function returns the value and the gradient of f when called with
the same arguments. The gradient is with respect to all trainable TFE
variables accessed by `f`.
This function is useful when the exact set of variables to differentiate with
is not known ahead of time.
Example:
```python
dense_layer = tf.compat.v1.layers.Dense(1)
def loss(x, y):
return tf.reduce_sum(tf.square(dense_layer(x) - y))
# Obtain the gradient function.
val_grad_fn = tfe.implicit_value_and_gradients(loss)
# Invoke the gradient function with concrete values of x and y.
x = tf.constant([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
y = tf.constant([[10.0], [20.0]])
value, grads_and_vars = val_grad_fn(x, y)
print('Value of loss: %s' % value)
# Apply the gradients to Variables.
optimizer = tf.compat.v1.train.GradientDescentOptimizer(0.1)
optimizer.apply_gradients(grads_and_vars)
```
Args:
f: function to be differentiated. If `f` returns a scalar, this scalar will
be differentiated. If `f` returns a tensor or list of tensors, by default
a scalar will be computed by adding all their values to produce a single
scalar.
Returns:
A function which, when called, returns a tuple pair.
Its first element is the value to which the function evaluates.
Its second element is list of (gradient, variable) pairs.
Raises:
ValueError: if `f` returns None.
"""
# TODO(cais): Remove calls to tf.constant() once the gradients functions
# accept lists and np.ndarrays.
def grad_fn(*args, **kwds):
"""Computes the gradient of the wrapped function."""
this_tape = tape.push_new_tape()
try:
end_node = f(*args, **kwds)
if end_node is None:
raise ValueError("Cannot differentiate a function that returns None; "
"did you forget to return a value from {}?".format(
f.__name__))
finally:
tape.pop_tape(this_tape)
# Note: variables are returned in construction order. This ensures unique
# order across executions.
variables = this_tape.watched_variables()
if not variables:
raise ValueError("No trainable variables were accessed while the "
"function was being computed.")
sources = [v.handle for v in variables]
for s in sources:
if getattr(s, "is_packed", False):
raise ValueError(
"GradientTape.gradient is not supported on packed EagerTensors yet."
)
grad = imperative_grad.imperative_grad(this_tape, nest.flatten(end_node),
sources)
return end_node, list(zip(grad, variables))
return grad_fn
def implicit_grad(f):
"""Returns a function which differentiates f with respect to variables.
The wrapped function returns the gradient of f when called with the same
arguments. The gradient is with respect to all trainable TFE variables
accessed by `f`.
This function is useful when the exact set of variables to differentiate with
is not known ahead of time.
Example:
```python
dense_layer = tf.compat.v1.layers.Dense(1)
def loss(x, y):
return tf.reduce_sum(tf.square(dense_layer(x) - y))
# Obtain the gradient function.
grad_fn = tfe.implicit_gradients(loss)
# Invoke the gradient function with concrete values of x and y.
x = tf.constant([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
y = tf.constant([[10.0], [20.0]])
grads_and_vars = grad_fn(x, y)
# Apply the gradients to Variables.
optimizer = tf.compat.v1.train.GradientDescentOptimizer(0.1)
optimizer.apply_gradients(grads_and_vars)
```
Args:
f: function to be differentiated. If `f` returns a scalar, this scalar will
be differentiated. If `f` returns a tensor or list of tensors, by default
a scalar will be computed by adding all their values to produce a single
scalar.
Returns:
A function which, when called, returns a list of (gradient, variable) pairs.
"""
# TODO(cais): Remove calls to tf.constant() once the gradients functions
# accept lists and np.ndarrays.
def grad_fn(*args, **kwds):
"""Computes the gradient of the wrapped function."""
return implicit_val_and_grad(f)(*args, **kwds)[1]
return grad_fn
def _get_arg_spec(f, params, param_args):
"""The positions of the parameters of f to be differentiated in param_args."""
try:
args = tf_inspect.getfullargspec(f).args
except TypeError as e:
# TypeError can happen when f is a callable object.
if params is None:
return range(len(param_args))
elif all(isinstance(x, int) for x in params):
return params
raise ValueError("Either callable provided is not a function or could not "
"inspect its arguments by name: %s. Original error: %s"
% (f, e))
if params is None:
if not args:
return range(len(param_args))
if args[0] == "self":
return range(len(args) - 1)
else:
return range(len(args))
elif all(isinstance(x, six.string_types) for x in params):
return [args.index(n) for n in params]
elif all(isinstance(x, int) for x in params):
return params
else:
raise ValueError(
"params must be all strings or all integers; got %s." % params)
def gradients_function(f, params=None):
"""Returns a function which differentiates f with respect to params.
Example:
```python
# f(x, y) = (x ^ 3) * y - x * (y ^ 2)
# Therefore, the 1st order derivatives are:
# df / dx = 3 * (x ^ 2) * y - y ^ 2
# df / dy = x ^ 3 - 2 * x * y
# The 2nd order derivatives with respect to x is:
# d^2 f / (dx)^2 = 6 * x * y
def f(x, y):
return x * x * x * y - x * y * y
# Obtain a function that returns 1st order gradients.
grad_fn = tfe.gradients_function(f)
x = 2.0
y = 3.0
# Invoke the 1st order gradient function.
x_grad, y_grad = grad_fn(x, y)
assert x_grad.numpy() == 3 * (2 ** 2) * 3 - 3 ** 2
assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
# Obtain a function that returns the 2nd order gradient with respect to x.
gradgrad_fn = tfe.gradients_function(lambda x, y: grad_fn(x, y)[0])
# Invoke the 2nd order gradient function.
x_gradgrad = gradgrad_fn(x, y)[0]
assert x_gradgrad.numpy() == 6 * 2 * 3
# To obtain a callable that returns the gradient(s) of `f` with respect to a
# subset of its inputs, use the `params` keyword argument with
# `gradients_function()`.
ygrad_fn = tfe.gradients_function(f, params=[1])
(y_grad,) = ygrad_fn(x, y)
assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
```
Note that only tensors with real or complex dtypes are differentiable.
Args:
f: function to be differentiated. If `f` returns a scalar, this scalar will
be differentiated. If `f` returns a tensor or list of tensors, by default
a scalar will be computed by adding all their values to produce a single
scalar. If desired, the tensors can be elementwise multiplied by the
tensors passed as the `dy` keyword argument to the returned gradient
function.
params: list of parameter names of f or list of integers indexing the
parameters with respect to which we'll differentiate. Passing None
differentiates with respect to all parameters.
Returns:
function which, when called, returns the value of f and the gradient
of `f` with respect to all of `params`. The function takes an extra optional
keyword argument `dy`. Setting it allows computation of vector jacobian
products for vectors other than the vector of ones.
Raises:
ValueError: if the params are not all strings or all integers.
"""
def decorated(*args, **kwds):
"""Computes the gradient of the decorated function."""
_, grad = val_and_grad_function(f, params=params)(*args, **kwds)
return grad
return decorated
def _ensure_unique_tensor_objects(parameter_positions, args):
"""Make each of the parameter_positions in args a unique ops.Tensor object.
Ensure that each parameter is treated independently.
For example:
def f(x, y): return x * y
g = gradients_function(f)
one = tf.constant(1.)
g(one, one) should return [1., 1.]
(even though the two arguments are the same Tensor object).
Args:
parameter_positions: List of indices into args defining the arguments to
differentiate against.
args: A list of arguments to the function to be differentiated.
Returns:
args, possibly edited in-place.
"""
s = set()
for (i, t) in enumerate(args):
if i in parameter_positions:
tid = ops.tensor_id(t)
if tid in s:
args[i] = gen_array_ops.identity(args[i])
else:
s.add(tid)
return args
def val_and_grad_function(f, params=None):
"""Returns a function that computes f and its derivative w.r.t. params.
Example:
```python
# f(x, y) = (x ^ 3) * y - x * (y ^ 2)
# Therefore, the 1st order derivatives are:
# df / dx = 3 * (x ^ 2) * y - y ^ 2
# df / dy = x ^ 3 - 2 * x * y
def f(x, y):
return x * x * x * y - x * y * y
# Obtain a function that returns the function value and the 1st order
# gradients.
val_grads_fn = tfe.value_and_gradients_function(f)
x = 2.0
y = 3.0
# Invoke the value-and-gradients function.
f_val, (x_grad, y_grad) = val_grads_fn(x, y)
assert f_val.numpy() == (2 ** 3) * 3 - 2 * (3 ** 2)
assert x_grad.numpy() == 3 * (2 ** 2) * 3 - 3 ** 2
assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
# To obtain a callable that returns the value of `f` and the gradient(s) of
# `f` with respect to a subset of its inputs, use the `params` keyword
# argument with `value_and_gradients_function()`.
val_ygrad_fn = tfe.value_and_gradients_function(f, params=[1])
f_val, (y_grad,) = val_ygrad_fn(x, y)
assert f_val.numpy() == (2 ** 3) * 3 - 2 * (3 ** 2)
assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
```
Args:
f: function to be differentiated. If `f` returns a scalar, this scalar will
be differentiated. If `f` returns a tensor or list of tensors, by default
a scalar will be computed by adding all their values to produce a single
scalar. If desired, the tensors can be elementwise multiplied by the
tensors passed as the `dy` keyword argument to the returned gradient
function.
params: list of parameter names of f or list of integers indexing the
parameters with respect to which we'll differentiate. Passing `None`
differentiates with respect to all parameters.
Returns:
function which, when called, returns the value of f and the gradient
of f with respect to all of `params`. The function takes an extra optional
keyword argument "dy". Setting it allows computation of vector jacobian
products for vectors other than the vector of ones.
Raises:
ValueError: if the params are not all strings or all integers.
"""
def decorated(*args, **kwds):
"""Computes the value and gradient of the decorated function."""
dy = kwds.pop("dy", None)
if kwds:
raise ValueError("Functions to be differentiated cannot "
"receive keyword arguments.")
val, vjp = make_vjp(f, params)(*args, **kwds)
return val, vjp(dy=dy)
return decorated
def make_vjp(f, params=None, persistent=True):
"""Returns a function that computes f and its vjp w.r.t.
params.
The term "vjp" here is an abbreviation for vector-jacobian product.
Args:
f: the function to be differentiated.
params: the parameters (numbers or names) to differentiate with respect to.
A value of None will differentiate with respect to all parameters.
persistent: Boolean controlling whether the VJP function can be re-used.
Must be True or False.
Returns:
A function, which when called, returns a tuple (value, vjp), where:
- value is the result of calling f.
- vjp is a function, which takes a vector as an argument and
returns the product of that vector with the Jacobian of f.
Providing no argument to vjp is equivalent to providing a
vector of ones.
For example,
```python
def f(x):
return x * x
wrapped_fn = tfe.make_vjp(f)
result, vjp = wrapped_fn(tf.constant(3.0))
# result is 9.0
vjp() # the vjp function returns 6.0
Raises:
ValueError: if `f` returns None.
"""
def decorated(*args, **kwds):
"""Computes the value and gradient of the decorated function."""
parameter_positions = _get_arg_spec(f, params, args)
assert not kwds, "The gradient function can't take keyword arguments."
this_tape = tape.push_new_tape(persistent=persistent)
try:
sources = []
args = [
ops.convert_to_tensor(arg) if i in parameter_positions else arg
for i, arg in enumerate(args)
]
args = _ensure_unique_tensor_objects(parameter_positions, args)
for i in parameter_positions:
if getattr(args[i], "is_packed", False):
raise ValueError(
"GradientTape.gradient is not supported on packed EagerTensors"
"yet.")
sources.append(args[i])
tape.watch(this_tape, args[i])
result = f(*args)
if result is None:
raise ValueError("Cannot differentiate a function that returns None; "
"did you forget to return a value from {}?".format(
f.__name__))
flat_result = nest.flatten(result)
flat_result = [gen_array_ops.identity(x) for x in flat_result]
result = nest.pack_sequence_as(result, flat_result)
finally:
tape.pop_tape(this_tape)
def vjp(dy=None):
if dy is not None:
dy = [ops.convert_to_tensor(x) for x in nest.flatten(dy)]
return imperative_grad.imperative_grad(
this_tape, nest.flatten(result), sources, output_gradients=dy)
return result, vjp
return decorated
def flatten_nested_indexed_slices(grad):
assert isinstance(grad, indexed_slices.IndexedSlices)
if isinstance(grad.values, ops.Tensor):
return grad
else:
assert isinstance(grad.values, indexed_slices.IndexedSlices)
g = flatten_nested_indexed_slices(grad.values)
return indexed_slices.IndexedSlices(
g.values, array_ops.gather(grad.indices, g.indices), g.dense_shape)
def aggregate_indexed_slices_gradients(grads):
"""Aggregates gradients containing `IndexedSlices`s."""
if len(grads) < 1:
return None
if len(grads) == 1:
return grads[0]
grads = [g for g in grads if g is not None]
# If any gradient is a `Tensor`, sum them up and return a dense tensor
# object.
if any(isinstance(g, ops.Tensor) for g in grads):
return math_ops.add_n(grads)
# The following `_as_indexed_slices_list` casts ids of IndexedSlices into
# int64. It is to make sure the inputs of `concat` all have same the data
# type.
grads = math_ops._as_indexed_slices_list(grads) # pylint: disable=protected-access
grads = [flatten_nested_indexed_slices(x) for x in grads]
# Form IndexedSlices out of the concatenated values and indices.
concat_grad = indexed_slices.IndexedSlices(
array_ops.concat([x.values for x in grads], axis=0),
array_ops.concat([x.indices for x in grads], axis=0),
grads[0].dense_shape)
return concat_grad
def _aggregate_grads(gradients):
"""Aggregate gradients from multiple sources.
Args:
gradients: A list of 'Tensor' or 'IndexedSlices' gradients.
Returns:
If 'gradients' only has 'Tensor', returns an aggregated 'Tensor'.
Otherwise returns an aggregated 'IndexedSlices'.
"""
assert gradients, "No gradients to aggregate"
if len(gradients) == 1:
return gradients[0]
if all(isinstance(g, ops.Tensor) for g in gradients):
return gen_math_ops.add_n(gradients)
else:
assert all(
isinstance(g, (ops.Tensor, indexed_slices.IndexedSlices))
for g in gradients)
return aggregate_indexed_slices_gradients(gradients)
def _num_elements(grad):
"""The number of elements in the `grad` tensor."""
if isinstance(grad, ops.Tensor):
shape_tuple = grad._shape_tuple() # pylint: disable=protected-access
elif isinstance(grad, indexed_slices.IndexedSlices):
shape_tuple = grad.values._shape_tuple() # pylint: disable=protected-access
else:
raise ValueError("`grad` not a Tensor or IndexedSlices.")
if shape_tuple is None or None in shape_tuple:
return 0
return functools.reduce(operator.mul, shape_tuple, 1)
def _fast_fill(value, shape, dtype):
return array_ops.fill(
constant_op.constant(shape, dtype=dtypes.int32),
constant_op.constant(value, dtype=dtype))
def _zeros(shape, dtype):
"""Helper to return (possibly cached) zero tensors in eager mode."""
# Note: variants will use _zeros_like
if dtype == dtypes.string or dtype == dtypes.resource:
return None
ctx = context.context()
if not ctx.executing_eagerly():
return array_ops.zeros(shape, dtype)
device = ctx.device_name
if tensor_util.is_tf_type(shape):
shape_key = shape.ref()
else:
shape_key = shape
cache_key = shape_key, dtype, device
cached = ctx.zeros_cache().get(cache_key)
if cached is None:
if dtypes.as_dtype(dtype).is_bool:
value = False
else:
value = 0
cached = _fast_fill(value, shape, dtype)
ctx.zeros_cache().put(cache_key, cached)
return cached
def _ones(shape, dtype):
as_dtype = dtypes.as_dtype(dtype)
if as_dtype == dtypes.string:
return None
if not context.executing_eagerly():
return array_ops.ones(shape, dtype)
if as_dtype.is_bool:
value = True
else:
value = 1
if shape == (): # pylint: disable=g-explicit-bool-comparison
return constant_op.constant(value, dtype=dtype)
return _fast_fill(value, shape, dtype)
_default_vspace = imperative_grad.VSpace(
num_elements_fn=_num_elements,
aggregate_fn=_aggregate_grads,
zeros_fn=_zeros,
ones_fn=_ones,
zeros_like_fn=default_gradient.zeros_like,
ones_like_fn=default_gradient.ones_like,
graph_shape_fn=gen_array_ops.shape)
pywrap_tfe.TFE_Py_RegisterVSpace(_default_vspace)
def _handle_or_self(x):
"""Unwrap resource variable/ndarray to return tensors."""
if resource_variable_ops.is_resource_variable(x):
return x.handle
return x
[文档]@tf_export("GradientTape", "autodiff.GradientTape", v1=["GradientTape"])
class GradientTape(object):
"""Record operations for automatic differentiation.
Operations are recorded if they are executed within this context manager and
at least one of their inputs is being "watched".
Trainable variables (created by `tf.Variable` or `tf.compat.v1.get_variable`,
where `trainable=True` is default in both cases) are automatically watched.
Tensors can be manually watched by invoking the `watch` method on this context
manager.
For example, consider the function `y = x * x`. The gradient at `x = 3.0` can
be computed as:
>>> x = tf.constant(3.0)
>>> with tf.GradientTape() as g:
... g.watch(x)
... y = x * x
>>> dy_dx = g.gradient(y, x)
>>> print(dy_dx)
tf.Tensor(6.0, shape=(), dtype=float32)
GradientTapes can be nested to compute higher-order derivatives. For example,
>>> x = tf.constant(5.0)
>>> with tf.GradientTape() as g:
... g.watch(x)
... with tf.GradientTape() as gg:
... gg.watch(x)
... y = x * x
... dy_dx = gg.gradient(y, x) # dy_dx = 2 * x
>>> d2y_dx2 = g.gradient(dy_dx, x) # d2y_dx2 = 2
>>> print(dy_dx)
tf.Tensor(10.0, shape=(), dtype=float32)
>>> print(d2y_dx2)
tf.Tensor(2.0, shape=(), dtype=float32)
By default, the resources held by a GradientTape are released as soon as
GradientTape.gradient() method is called. To compute multiple gradients over
the same computation, create a persistent gradient tape. This allows multiple
calls to the gradient() method as resources are released when the tape object
is garbage collected. For example:
>>> x = tf.constant(3.0)
>>> with tf.GradientTape(persistent=True) as g:
... g.watch(x)
... y = x * x
... z = y * y
>>> dz_dx = g.gradient(z, x) # (4*x^3 at x = 3)
>>> print(dz_dx)
tf.Tensor(108.0, shape=(), dtype=float32)
>>> dy_dx = g.gradient(y, x)
>>> print(dy_dx)
tf.Tensor(6.0, shape=(), dtype=float32)
By default GradientTape will automatically watch any trainable variables that
are accessed inside the context. If you want fine grained control over which
variables are watched you can disable automatic tracking by passing
`watch_accessed_variables=False` to the tape constructor:
>>> x = tf.Variable(2.0)
>>> w = tf.Variable(5.0)
>>> with tf.GradientTape(
... watch_accessed_variables=False, persistent=True) as tape:
... tape.watch(x)
... y = x ** 2 # Gradients will be available for `x`.
... z = w ** 3 # No gradients will be available as `w` isn't being watched.
>>> dy_dx = tape.gradient(y, x)
>>> print(dy_dx)
tf.Tensor(4.0, shape=(), dtype=float32)
>>> # No gradients will be available as `w` isn't being watched.
>>> dz_dw = tape.gradient(z, w)
>>> print(dz_dw)
None
Note that when using models you should ensure that your variables exist when
using `watch_accessed_variables=False`. Otherwise it's quite easy to make your
first iteration not have any gradients:
```python
a = tf.keras.layers.Dense(32)
b = tf.keras.layers.Dense(32)
with tf.GradientTape(watch_accessed_variables=False) as tape:
tape.watch(a.variables) # Since `a.build` has not been called at this point
# `a.variables` will return an empty list and the
# tape will not be watching anything.
result = b(a(inputs))
tape.gradient(result, a.variables) # The result of this computation will be
# a list of `None`s since a's variables
# are not being watched.
```
Note that only tensors with real or complex dtypes are differentiable.
"""
def __init__(self, persistent=False, watch_accessed_variables=True):
"""Creates a new GradientTape.
Args:
persistent: Boolean controlling whether a persistent gradient tape
is created. False by default, which means at most one call can
be made to the gradient() method on this object.
watch_accessed_variables: Boolean controlling whether the tape will
automatically `watch` any (trainable) variables accessed while the tape
is active. Defaults to True meaning gradients can be requested from any
result computed in the tape derived from reading a trainable `Variable`.
If False users must explicitly `watch` any `Variable`s they want to
request gradients from.
"""
self._tape = None
self._persistent = persistent
self._watch_accessed_variables = watch_accessed_variables
self._watched_variables = ()
self._recording = False
def __enter__(self):
"""Enters a context inside which operations are recorded on this tape."""
self._push_tape()
return self
def __exit__(self, typ, value, traceback):
"""Exits the recording context, no further operations are traced."""
if self._recording:
self._pop_tape()
def _push_tape(self):
"""Pushes a new tape onto the tape stack."""
if self._recording:
raise ValueError("Tape is still recording, This can happen if you try to "
"re-enter an already-active tape.")
if self._tape is None:
self._tape = tape.push_new_tape(
persistent=self._persistent,
watch_accessed_variables=self._watch_accessed_variables)
else:
tape.push_tape(self._tape)
self._recording = True
def _pop_tape(self):
if not self._recording:
raise ValueError("Tape is not recording.")
tape.pop_tape(self._tape)
self._recording = False
@tf_contextlib.contextmanager
def _ensure_recording(self):
"""Ensures that this tape is recording."""
if not self._recording:
try:
self._push_tape()
yield
finally:
self._pop_tape()
else:
yield
[文档] def watch(self, tensor):
"""Ensures that `tensor` is being traced by this tape.
Args:
tensor: a Tensor or list of Tensors.
Raises:
ValueError: if it encounters something that is not a tensor.
"""
for t in nest.flatten(tensor, expand_composites=True):
if not (_pywrap_utils.IsTensor(t) or _pywrap_utils.IsVariable(t)):
raise ValueError("Passed in object of type {}, not tf.Tensor".format(
type(t)))
if not backprop_util.IsTrainable(t):
logging.log_first_n(
logging.WARN, "The dtype of the watched tensor must be "
"floating (e.g. tf.float32), got %r", 5, t.dtype)
if hasattr(t, "handle"):
# There are many variable-like objects, all of them currently have
# `handle` attribute that points to a tensor. If this changes, internals
# of watch_variable need to change as well.
tape.watch_variable(self._tape, t)
else:
tape.watch(self._tape, t)
[文档] @tf_contextlib.contextmanager
def stop_recording(self):
"""Temporarily stops recording operations on this tape.
Operations executed while this context manager is active will not be
recorded on the tape. This is useful for reducing the memory used by tracing
all computations.
For example:
>>> x = tf.constant(4.0)
>>> with tf.GradientTape() as tape:
... with tape.stop_recording():
... y = x ** 2
>>> dy_dx = tape.gradient(y, x)
>>> print(dy_dx)
None
Yields:
None
Raises:
RuntimeError: if the tape is not currently recording.
"""
if self._tape is None:
raise RuntimeError(
"Trying to stop recording a tape which is not recording.")
self._pop_tape()
try:
yield
finally:
self._push_tape()
[文档] def reset(self):
"""Clears all information stored in this tape.
Equivalent to exiting and reentering the tape context manager with a new
tape. For example, the two following code blocks are equivalent:
```
with tf.GradientTape() as t:
loss = loss_fn()
with tf.GradientTape() as t:
loss += other_loss_fn()
t.gradient(loss, ...) # Only differentiates other_loss_fn, not loss_fn
# The following is equivalent to the above
with tf.GradientTape() as t:
loss = loss_fn()
t.reset()
loss += other_loss_fn()
t.gradient(loss, ...) # Only differentiates other_loss_fn, not loss_fn
```
This is useful if you don't want to exit the context manager for the tape,
or can't because the desired reset point is inside a control flow construct:
```
with tf.GradientTape() as t:
loss = ...
if loss > k:
t.reset()
```
"""
self._pop_tape()
self._tape = None
self._push_tape()
[文档] def watched_variables(self):
"""Returns variables watched by this tape in order of construction."""
if self._tape is not None:
self._watched_variables = self._tape.watched_variables()
return self._watched_variables
[文档] def gradient(self,
target,
sources,
output_gradients=None,
unconnected_gradients=UnconnectedGradients.NONE):
"""Computes the gradient using operations recorded in context of this tape.
Note: Unless you set `persistent=True` a GradientTape can only be used to
compute one set of gradients (or jacobians).
In addition to Tensors, gradient also supports RaggedTensors. For example,
>>> x = tf.ragged.constant([[1.0, 2.0], [3.0]])
>>> with tf.GradientTape() as g:
... g.watch(x)
... y = x * x
>>> g.gradient(y, x)
<tf.RaggedTensor [[2.0, 4.0], [6.0]]>
Args:
target: a list or nested structure of Tensors or Variables or
CompositeTensors to be differentiated.
sources: a list or nested structure of Tensors or Variables or
CompositeTensors. `target` will be differentiated against elements in
`sources`.
output_gradients: a list of gradients, one for each differentiable
element of target. Defaults to None.
unconnected_gradients: a value which can either hold 'none' or 'zero' and
alters the value which will be returned if the target and sources are
unconnected. The possible values and effects are detailed in
'UnconnectedGradients' and it defaults to 'none'.
Returns:
a list or nested structure of Tensors (or IndexedSlices, or None, or
CompositeTensor), one for each element in `sources`. Returned structure
is the same as the structure of `sources`.
Raises:
RuntimeError: If called on a used, non-persistent tape.
RuntimeError: If called inside the context of the tape.
TypeError: If the target is a None object.
ValueError: If the target is a variable or if unconnected gradients is
called with an unknown value.
"""
if self._tape is None:
raise RuntimeError("A non-persistent GradientTape can only be used to "
"compute one set of gradients (or jacobians)")
if self._recording:
if not self._persistent:
self._pop_tape()
else:
logging.log_first_n(
logging.WARN, "Calling GradientTape.gradient on a persistent "
"tape inside its context is significantly less "
"efficient than calling it outside the context (it "
"causes the gradient ops to be recorded on the "
"tape, leading to increased CPU and memory usage). "
"Only call GradientTape.gradient inside the "
"context if you actually want to trace the "
"gradient in order to compute higher order "
"derivatives.", 1)
if target is None:
raise TypeError("Argument `target` should be a list or nested structure"
" of Tensors, Variables or CompositeTensors to be "
"differentiated, but recieved None.")
flat_targets = []
for t in nest.flatten(target):
if not backprop_util.IsTrainable(t):
logging.vlog(
logging.WARN, "The dtype of the target tensor must be "
"floating (e.g. tf.float32) when calling GradientTape.gradient, "
"got %r", t.dtype)
if resource_variable_ops.is_resource_variable(t):
with self:
t = ops.convert_to_tensor(t)
flat_targets.append(t)
flat_targets = composite_tensor_gradient.get_flat_tensors_for_gradients(
flat_targets)
flat_sources = nest.flatten(sources)
for t in flat_sources:
if not backprop_util.IsTrainable(t):
logging.vlog(
logging.WARN, "The dtype of the source tensor must be "
"floating (e.g. tf.float32) when calling GradientTape.gradient, "
"got %r", t.dtype)
if getattr(t, "is_packed", False):
raise ValueError(
"GradientTape.gradient is not supported on packed EagerTensors yet."
)
flat_sources_raw = flat_sources
flat_sources = composite_tensor_gradient.get_flat_tensors_for_gradients(
flat_sources)
flat_sources = [_handle_or_self(x) for x in flat_sources]
if output_gradients is not None:
output_gradients = nest.flatten(output_gradients)
output_gradients = (
composite_tensor_gradient.get_flat_tensors_for_gradients(
output_gradients))
output_gradients = [None if x is None else ops.convert_to_tensor(x)
for x in output_gradients]
flat_grad = imperative_grad.imperative_grad(
self._tape,
flat_targets,
flat_sources,
output_gradients=output_gradients,
sources_raw=flat_sources_raw,
unconnected_gradients=unconnected_gradients)
if not self._persistent:
# Keep track of watched variables before setting tape to None
self._watched_variables = self._tape.watched_variables()
self._tape = None
flat_grad = composite_tensor_gradient.replace_flat_tensors_for_gradients(
flat_sources_raw, flat_grad)
grad = nest.pack_sequence_as(sources, flat_grad)
return grad
[文档] def jacobian(self,
target,
sources,
unconnected_gradients=UnconnectedGradients.NONE,
parallel_iterations=None,
experimental_use_pfor=True):
"""Computes the jacobian using operations recorded in context of this tape.
Note: Unless you set `persistent=True` a GradientTape can only be used to
compute one set of gradients (or jacobians).
Note: By default the jacobian implementation uses parallel for (pfor), which
creates a tf.function under the hood for each jacobian call. For better
performance, and to avoid recompilation and vectorization rewrites on each
call, enclose GradientTape code in @tf.function.
See[wikipedia
article](http://en.wikipedia.org/wiki/jacobian_matrix_and_determinant)
for the definition of a Jacobian.
Example usage:
```python
with tf.GradientTape() as g:
x = tf.constant([1.0, 2.0])
g.watch(x)
y = x * x
jacobian = g.jacobian(y, x)
# jacobian value is [[2., 0.], [0., 4.]]
```
Args:
target: Tensor to be differentiated.
sources: a list or nested structure of Tensors or Variables. `target`
will be differentiated against elements in `sources`.
unconnected_gradients: a value which can either hold 'none' or 'zero' and
alters the value which will be returned if the target and sources are
unconnected. The possible values and effects are detailed in
'UnconnectedGradients' and it defaults to 'none'.
parallel_iterations: A knob to control how many iterations are dispatched
in parallel. This knob can be used to control the total memory usage.
experimental_use_pfor: If true, vectorizes the jacobian computation. Else
falls back to a sequential while_loop. Vectorization can sometimes fail
or lead to excessive memory usage. This option can be used to disable
vectorization in such cases.
Returns:
A list or nested structure of Tensors (or None), one for each element in
`sources`. Returned structure is the same as the structure of `sources`.
Note if any gradient is sparse (IndexedSlices), jacobian function
currently makes it dense and returns a Tensor instead. This may change in
the future.
Raises:
RuntimeError: If called on a used, non-persistent tape.
RuntimeError: If called on a non-persistent tape with eager execution
enabled and without enabling experimental_use_pfor.
ValueError: If vectorization of jacobian computation fails.
"""
if self._tape is None:
raise RuntimeError("A non-persistent GradientTape can only be used to "
"compute one set of gradients (or jacobians)")
flat_sources = nest.flatten(sources)
target_static_shape = target.shape
target_shape = array_ops.shape(target)
# Note that we push and pop the tape here and below. This is needed since we
# need gradients through the enclosed operations.
with self._ensure_recording():
target = array_ops.reshape(target, [-1])
def loop_fn(i):
with self._ensure_recording():
y = array_ops.gather(target, i)
return self.gradient(y, flat_sources,
unconnected_gradients=unconnected_gradients)
try:
target_size = int(target.shape[0])
except TypeError:
target_size = array_ops.shape(target)[0]
if experimental_use_pfor:
try:
output = pfor_ops.pfor(loop_fn, target_size,
parallel_iterations=parallel_iterations)
except ValueError as err:
six.reraise(
ValueError,
ValueError(
str(err) + "\nEncountered an exception while vectorizing the "
"jacobian computation. Vectorization can be disabled by setting"
" experimental_use_pfor to False."),
sys.exc_info()[2])
else:
if context.executing_eagerly() and not self._persistent:
raise RuntimeError(
"GradientTape must be created with persistent=True"
" to compute the jacobian with eager execution enabled and with "
" experimental_use_pfor set to False.")
output = pfor_ops.for_loop(
loop_fn, [target.dtype] * len(flat_sources), target_size,
parallel_iterations=parallel_iterations)
for i, out in enumerate(output):
if out is not None:
new_shape = array_ops.concat(
[target_shape, array_ops.shape(out)[1:]], axis=0)
out = array_ops.reshape(out, new_shape)
if context.executing_eagerly():
out.set_shape(target_static_shape.concatenate(flat_sources[i].shape))
output[i] = out
return nest.pack_sequence_as(sources, output)
[文档] def batch_jacobian(self,
target,
source,
unconnected_gradients=UnconnectedGradients.NONE,
parallel_iterations=None,
experimental_use_pfor=True):
"""Computes and stacks per-example jacobians.
See [wikipedia article](http://en.wikipedia.org/wiki/jacobian_matrix_and_determinant)
for the definition of a Jacobian. This function is essentially an efficient
implementation of the following:
`tf.stack([self.jacobian(y[i], x[i]) for i in range(x.shape[0])])`.
Note that compared to `GradientTape.jacobian` which computes gradient of
each output value w.r.t each input value, this function is useful when
`target[i,...]` is independent of `source[j,...]` for `j != i`. This
assumption allows more efficient computation as compared to
`GradientTape.jacobian`. The output, as well as intermediate activations,
are lower dimensional and avoid a bunch of redundant zeros which would
result in the jacobian computation given the independence assumption.
Note: Unless you set `persistent=True` a GradientTape can only be used to
compute one set of gradients (or jacobians).
Note: By default the batch_jacobian implementation uses parallel for (pfor),
which creates a tf.function under the hood for each batch_jacobian call.
For better performance, and to avoid recompilation and vectorization
rewrites on each call, enclose GradientTape code in @tf.function.
Example usage:
```python
with tf.GradientTape() as g:
x = tf.constant([[1., 2.], [3., 4.]], dtype=tf.float32)
g.watch(x)
y = x * x
batch_jacobian = g.batch_jacobian(y, x)
# batch_jacobian is [[[2, 0], [0, 4]], [[6, 0], [0, 8]]]
```
Args:
target: A tensor with rank 2 or higher and with shape [b, y1, ..., y_n].
`target[i,...]` should only depend on `source[i,...]`.
source: A tensor with rank 2 or higher and with shape [b, x1, ..., x_m].
unconnected_gradients: a value which can either hold 'none' or 'zero' and
alters the value which will be returned if the target and sources are
unconnected. The possible values and effects are detailed in
'UnconnectedGradients' and it defaults to 'none'.
parallel_iterations: A knob to control how many iterations are dispatched
in parallel. This knob can be used to control the total memory usage.
experimental_use_pfor: If true, uses pfor for computing the Jacobian. Else
uses a tf.while_loop.
Returns:
A tensor `t` with shape [b, y_1, ..., y_n, x1, ..., x_m] where `t[i, ...]`
is the jacobian of `target[i, ...]` w.r.t. `source[i, ...]`, i.e. stacked
per-example jacobians.
Raises:
RuntimeError: If called on a used, non-persistent tape.
RuntimeError: If called on a non-persistent tape with eager execution
enabled and without enabling experimental_use_pfor.
ValueError: If vectorization of jacobian computation fails or if first
dimension of `target` and `source` do not match.
"""
if self._tape is None:
raise RuntimeError("A non-persistent GradientTape can only be used to"
"compute one set of gradients (or jacobians)")
target_shape = target.shape
if target_shape.rank is None:
dim = tensor_shape.Dimension(None)
else:
dim = target_shape.dims[0]
if not (target_shape.with_rank_at_least(2) and
source.shape.with_rank_at_least(2) and
dim.is_compatible_with(source.shape[0])):
raise ValueError(
"Need first dimension of target shape (%s) and "
"source shape (%s) to match." % (target.shape, source.shape))
if target_shape.is_fully_defined():
batch_size = int(target_shape[0])
target_row_size = target_shape.num_elements() // batch_size
else:
target_shape = array_ops.shape(target)
batch_size = target_shape[0]
target_row_size = array_ops.size(target) // batch_size
source_shape = array_ops.shape(source)
# Flatten target to 2-D.
# Note that we push and pop the tape here and below. This is needed since we
# need gradients through the enclosed operations.
with self._ensure_recording():
with ops.control_dependencies(
[check_ops.assert_equal(batch_size, source_shape[0])]):
target = array_ops.reshape(target, [batch_size, target_row_size])
run_once = False
def loop_fn(i):
nonlocal run_once
if run_once and not self._persistent:
if parallel_iterations is not None:
raise RuntimeError(
"GradientTape must be created with persistent=True"
" to compute the batch_jacobian with parallel_iterations.")
else:
raise RuntimeError(
"GradientTape must be created with persistent=True"
" to compute the batch_jacobian.")
run_once = True
with self._ensure_recording():
y = array_ops.gather(target, i, axis=1)
return self.gradient(y, source,
unconnected_gradients=unconnected_gradients)
if experimental_use_pfor:
try:
output = pfor_ops.pfor(loop_fn, target_row_size,
parallel_iterations=parallel_iterations)
except ValueError as err:
six.reraise(
ValueError,
ValueError(
str(err) + "\nEncountered an exception while vectorizing the "
"batch_jacobian computation. Vectorization can be disabled by "
"setting experimental_use_pfor to False."),
sys.exc_info()[2])
else:
if context.executing_eagerly() and not self._persistent:
raise RuntimeError(
"GradientTape must be created with persistent=True"
" to compute the batch_jacobian with eager execution enabled and "
" with experimental_use_pfor set to False.")
output = pfor_ops.for_loop(loop_fn, target.dtype, target_row_size,
parallel_iterations=parallel_iterations)
new_shape = array_ops.concat([target_shape, source_shape[1:]], axis=0)
if output is None:
# Note that this block is returning zeros when it could use `None` to
# represent unconnected gradients. This is to maintain compatibility with
# the previous behavior, which ignored `unconnected_gradients`.
output = array_ops.zeros(new_shape, target.dtype)
return output
else:
output = array_ops.reshape(output,
[target_row_size, batch_size, -1])
output = array_ops.transpose(output, [1, 0, 2])
output = array_ops.reshape(output, new_shape)
return output