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Record operations for automatic differentiation.
tf.GradientTape(
persistent=False, watch_accessed_variables=True
)
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 higherorder 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:
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.
Methods
batch_jacobian
batch_jacobian(
target,
source,
unconnected_gradients=tf.UnconnectedGradients.NONE
,
parallel_iterations=None,
experimental_use_pfor=True
)
Computes and stacks perexample jacobians.
See wikipedia article 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.
Example usage:
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
perexample jacobians.

Raises  

RuntimeError

If called on a used, nonpersistent tape. 
RuntimeError

If called on a nonpersistent 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.

gradient
gradient(
target,
sources,
output_gradients=None,
unconnected_gradients=tf.UnconnectedGradients.NONE
)
Computes the gradient using operations recorded in context of this tape.
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, nonpersistent 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. 
jacobian
jacobian(
target,
sources,
unconnected_gradients=tf.UnconnectedGradients.NONE
,
parallel_iterations=None,
experimental_use_pfor=True
)
Computes the jacobian using operations recorded in context of this tape.
Seewikipedia article for the definition of a Jacobian.
Example usage:
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, nonpersistent tape. 
RuntimeError

If called on a nonpersistent tape with eager execution enabled and without enabling experimental_use_pfor. 
ValueError

If vectorization of jacobian computation fails. 
reset
reset()
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()
stop_recording
@tf_contextlib.contextmanager
stop_recording()
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. 
watch
watch(
tensor
)
Ensures that tensor
is being traced by this tape.
Args  

tensor

a Tensor/Variable or list of Tensors/Variables. 
Raises  

ValueError

if it encounters something that is not a tensor. 
watched_variables
watched_variables()
Returns variables watched by this tape in order of construction.
__enter__
__enter__()
Enters a context inside which operations are recorded on this tape.
__exit__
__exit__(
typ, value, traceback
)
Exits the recording context, no further operations are traced.