Constructs symbolic derivatives of sum of ys
w.r.t. x in xs
.
tf.compat.v1.gradients( ys, xs, grad_ys=None, name='gradients', colocate_gradients_with_ops=False, gate_gradients=False, aggregation_method=None, stop_gradients=None, unconnected_gradients=tf.UnconnectedGradients.NONE )
ys
and xs
are each a Tensor
or a list of tensors. grad_ys
is a list of Tensor
, holding the gradients received by the ys
. The list must be the same length as ys
.
gradients()
adds ops to the graph to output the derivatives of ys
with respect to xs
. It returns a list of Tensor
of length len(xs)
where each tensor is the sum(dy/dx)
for y in ys
and for x in xs
.
grad_ys
is a list of tensors of the same length as ys
that holds the initial gradients for each y in ys
. When grad_ys
is None, we fill in a tensor of '1's of the shape of y for each y in ys
. A user can provide their own initial grad_ys
to compute the derivatives using a different initial gradient for each y (e.g., if one wanted to weight the gradient differently for each value in each y).
stop_gradients
is a Tensor
or a list of tensors to be considered constant with respect to all xs
. These tensors will not be backpropagated through, as though they had been explicitly disconnected using stop_gradient
. Among other things, this allows computation of partial derivatives as opposed to total derivatives. For example:
a = tf.constant(0.) b = 2 * a g = tf.gradients(a + b, [a, b], stop_gradients=[a, b])
Here the partial derivatives g
evaluate to [1.0, 1.0]
, compared to the total derivatives tf.gradients(a + b, [a, b])
, which take into account the influence of a
on b
and evaluate to [3.0, 1.0]
. Note that the above is equivalent to:
a = tf.stop_gradient(tf.constant(0.)) b = tf.stop_gradient(2 * a) g = tf.gradients(a + b, [a, b])
stop_gradients
provides a way of stopping gradient after the graph has already been constructed, as compared to tf.stop_gradient
which is used during graph construction. When the two approaches are combined, backpropagation stops at both tf.stop_gradient
nodes and nodes in stop_gradients
, whichever is encountered first.
All integer tensors are considered constant with respect to all xs
, as if they were included in stop_gradients
.
unconnected_gradients
determines the value returned for each x in xs if it is unconnected in the graph to ys. By default this is None to safeguard against errors. Mathematically these gradients are zero which can be requested using the 'zero'
option. tf.UnconnectedGradients
provides the following options and behaviors:
a = tf.ones([1, 2]) b = tf.ones([3, 1]) g1 = tf.gradients([b], [a], unconnected_gradients='none') sess.run(g1) # [None] g2 = tf.gradients([b], [a], unconnected_gradients='zero') sess.run(g2) # [array([[0., 0.]], dtype=float32)]
Let us take one practical example which comes during the back propogation phase. This function is used to evaluate the derivatives of the cost function with respect to Weights Ws
and Biases bs
. Below sample implementation provides the exaplantion of what it is actually used for :
Ws = tf.constant(0.) bs = 2 * Ws cost = Ws + bs # This is just an example. So, please ignore the formulas. g = tf.gradients(cost, [Ws, bs]) dCost_dW, dCost_db = g
Args | |
---|---|
ys | A Tensor or list of tensors to be differentiated. |
xs | A Tensor or list of tensors to be used for differentiation. |
grad_ys | Optional. A Tensor or list of tensors the same size as ys and holding the gradients computed for each y in ys . |
name | Optional name to use for grouping all the gradient ops together. defaults to 'gradients'. |
colocate_gradients_with_ops | If True, try colocating gradients with the corresponding op. |
gate_gradients | If True, add a tuple around the gradients returned for an operations. This avoids some race conditions. |
aggregation_method | Specifies the method used to combine gradient terms. Accepted values are constants defined in the class AggregationMethod . |
stop_gradients | Optional. A Tensor or list of tensors not to differentiate through. |
unconnected_gradients | Optional. Specifies the gradient value returned when the given input tensors are unconnected. Accepted values are constants defined in the class tf.UnconnectedGradients and the default value is none . |
Returns | |
---|---|
A list of Tensor of length len(xs) where each tensor is the sum(dy/dx) for y in ys and for x in xs . |
Raises | |
---|---|
LookupError | if one of the operations between x and y does not have a registered gradient function. |
ValueError | if the arguments are invalid. |
RuntimeError | if called in Eager mode. |
© 2020 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/versions/r2.3/api_docs/python/tf/compat/v1/gradients