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.get_variable, 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.) with tfe.GradientTape() as g: g.watch(x) y = x * x grad = g.gradient(y, [x]) .html# Will compute to 6.0
GradientTapes can be nested to compute higher-order derivatives. For example,
x = tf.constant(3.0) with tfe.GradientTape() as g: with tfe.GradientTape() as gg: gg.watch(x) y = x * x dy_dx = gg.gradient(y, [x]) .html# Will compute to 6.0 d2y_dx2 = g.gradient(dy_dx, [x]) .html# Will compute to 2.0
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 tfe.GradientTape(persistent=True) as g: g.watch(x) y = x * x z = y * y dy_dx = g.gradient(z, [x]) .html# 6.0 dz_dx = g.gradient(y, [x]) .html# 108.0 (4*x^3 at x = 3) del g .html# Drop the reference to the tape .html#.html# Methods <h3 id="__init__"><code>__init__</code></h3> ``` python __init__(persistent=False)
Creates a new GradientTape.
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.
__exit__( typ, value, traceback )
gradient( target, sources, output_gradients=None )
Computes the gradient using operations recorded in context of this tape.
target: Tensor to be differentiated.
sources: a list or nested structure of Tensors or Variables.
targetwill be differentiated against elements in
output_gradients: a list of gradients, one for each element of target. Defaults to None.
a list or nested structure of Tensors (or IndexedSlices, or None),
one for each element in
sources. Returned structure is the same as
the structure of
RuntimeError: if called inside the context of the tape, or if called more than once on a non-persistent tape.
tensor is being traced by this tape.
tensor: a Tensor or list of Tensors.