# W3cubDocs

/TensorFlow 2.4

Constructs symbolic derivatives of sum of `ys` w.r.t. x in `xs`.

`tf.gradients` is only valid in a graph context. In particular, it is valid in the context of a `tf.function` wrapper, where code is executing as a graph.

`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:

```@tf.function
def example():
a = tf.constant(0.)
b = 2 * a
example()
[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>,
<tf.Tensor: shape=(), dtype=float32, numpy=1.0>]
```

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:

```@tf.function
def example():
return tf.gradients(a + b, [a, b])
example()
[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>,
<tf.Tensor: shape=(), dtype=float32, numpy=1.0>]
```

`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:

```@tf.function
def example(use_zero):
a = tf.ones([1, 2])
b = tf.ones([3, 1])
if use_zero:
else:
example(False)
[None]
example(True)
[<tf.Tensor: shape=(1, 2), dtype=float32, numpy=array([[0., 0.]], ...)>]
```

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 :

```@tf.function
def example():
Ws = tf.constant(0.)
bs = 2 * Ws
cost = Ws + bs  # This is just an example. Please ignore the formulas.
dCost_dW, dCost_db = g
return dCost_dW, dCost_db
example()
(<tf.Tensor: shape=(), dtype=float32, numpy=3.0>,
<tf.Tensor: shape=(), dtype=float32, numpy=1.0>)
```
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'.
`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.