Automatic differentiation package  torch.autograd¶
torch.autograd provides classes and functions implementing automatic
differentiation of arbitrary scalar valued functions. It requires minimal
changes to the existing code  you only need to wrap all tensors in
Variable
objects.

torch.autograd.
backward
(variables, grad_variables=None, retain_graph=None, create_graph=None, retain_variables=None)[source]¶ Computes the sum of gradients of given variables w.r.t. graph leaves.
The graph is differentiated using the chain rule. If any of
variables
are nonscalar (i.e. their data has more than one element) and require gradient, the function additionally requires specifyinggrad_variables
. It should be a sequence of matching length, that contains gradient of the differentiated function w.r.t. corresponding variables (None
is an acceptable value for all variables that don’t need gradient tensors).This function accumulates gradients in the leaves  you might need to zero them before calling it.
Parameters:  variables (sequence of Variable) – Variables of which the derivative will be computed.
 grad_variables (sequence of (Tensor, Variable or None)) – Gradients w.r.t.
each element of corresponding variables. Any tensors will be
automatically converted to Variables that are volatile unless
create_graph
is True. None values can be specified for scalar Variables or ones that don’t require grad. If a None value would be acceptable for all grad_variables, then this argument is optional.  retain_graph (bool, optional) – If False, the graph used to compute the grad
will be freed. Note that in nearly all cases setting this option to True
is not needed and often can be worked around in a much more efficient
way. Defaults to the value of
create_graph
.  create_graph (bool, optional) – If true, graph of the derivative will
be constructed, allowing to compute higher order derivative products.
Defaults to False, unless
grad_variables
contains at least one nonvolatile Variable.

torch.autograd.
grad
(outputs, inputs, grad_outputs=None, retain_graph=None, create_graph=None, only_inputs=True)[source]¶ Computes and returns the sum of gradients of outputs w.r.t. the inputs.
grad_outputs
should be a sequence of length matchingoutput
containing the precomputed gradients w.r.t. each of the outputs. If an output doesn’t require_grad, then the gradient can beNone
). Gradients can be given as Tensors when one doesn’t need the graph of the derivative, or as Variables, in which case the graph will be created.If
only_inputs
is True, the function will only return a list of gradients w.r.t the specified inputs. If it’s False, then gradient w.r.t. all remaining leaves will still be computed, and will be accumulated into their.grad
attribute.Parameters:  outputs (sequence of Variable) – outputs of the differentiated function.
 inputs (sequence of Variable) – Inputs w.r.t. which the gradient will be
returned (and not accumulated into
.grad
).  grad_outputs (sequence of Tensor or Variable) – Gradients w.r.t. each output.
Any tensors will be automatically converted to Variables that are
volatile unless
create_graph
is True. None values can be specified for scalar Variables or ones that don’t require grad. If a None value would be acceptable for all grad_variables, then this argument is optional.  retain_graph (bool, optional) – If False, the graph used to compute the grad
will be freed. Note that in nearly all cases setting this option to True
is not needed and often can be worked around in a much more efficient
way. Defaults to the value of
create_graph
.  create_graph (bool, optional) – If True, graph of the derivative will
be constructed, allowing to compute higher order derivative products.
Defaults to False, unless
grad_variables
contains at least one nonvolatile Variable.  only_inputs (bool, optional) – If True, gradient w.r.t. leaves that are
part of the graph, but don’t appear in
inputs
won’t be computed and accumulated. Defaults to True.
Variable¶
API compatibility¶
Variable API is nearly the same as regular Tensor API (with the exception
of a couple inplace methods, that would overwrite inputs required for
gradient computation). In most cases Tensors can be safely replaced with
Variables and the code will remain to work just fine. Because of this,
we’re not documenting all the operations on variables, and you should
refer to torch.Tensor
docs for this purpose.
Inplace operations on Variables¶
Supporting inplace operations in autograd is a hard matter, and we discourage their use in most cases. Autograd’s aggressive buffer freeing and reuse makes it very efficient and there are very few occasions when inplace operations actually lower memory usage by any significant amount. Unless you’re operating under heavy memory pressure, you might never need to use them.
Inplace correctness checks¶
All Variable
s keep track of inplace operations applied to them, and
if the implementation detects that a variable was saved for backward in one of
the functions, but it was modified inplace afterwards, an error will be raised
once backward pass is started. This ensures that if you’re using inplace
functions and not seeing any errors, you can be sure that the computed
gradients are correct.

class
torch.autograd.
Variable
[source]¶ Wraps a tensor and records the operations applied to it.
Variable is a thin wrapper around a Tensor object, that also holds the gradient w.r.t. to it, and a reference to a function that created it. This reference allows retracing the whole chain of operations that created the data. If the Variable has been created by the user, its grad_fn will be
None
and we call such objects leaf Variables.Since autograd only supports scalar valued function differentiation, grad size always matches the data size. Also, grad is normally only allocated for leaf variables, and will be always zero otherwise.
Variables:  data – Wrapped tensor of any type.
 grad – Variable holding the gradient of type and location matching
the
.data
. This attribute is lazily allocated and can’t be reassigned.  requires_grad – Boolean indicating whether the Variable has been created by a subgraph containing any Variable, that requires it. See Excluding subgraphs from backward for more details. Can be changed only on leaf Variables.
 volatile – Boolean indicating that the Variable should be used in inference mode, i.e. don’t save the history. See Excluding subgraphs from backward for more details. Can be changed only on leaf Variables.
 is_leaf – Boolean indicating if the Variable is a graph leaf (i.e if it was created by the user).
 grad_fn – Gradient function graph trace.
Parameters: 
backward
(gradient=None, retain_graph=None, create_graph=None, retain_variables=None)[source]¶ Computes the gradient of current variable w.r.t. graph leaves.
The graph is differentiated using the chain rule. If the variable is nonscalar (i.e. its data has more than one element) and requires gradient, the function additionally requires specifying
gradient
. It should be a tensor of matching type and location, that contains the gradient of the differentiated function w.r.t.self
.This function accumulates gradients in the leaves  you might need to zero them before calling it.
Parameters:  gradient (Tensor, Variable or None) – Gradient w.r.t. the
variable. If it is a tensor, it will be automatically converted
to a Variable that is volatile unless
create_graph
is True. None values can be specified for scalar Variables or ones that don’t require grad. If a None value would be acceptable then this argument is optional.  retain_graph (bool, optional) – If False, the graph used to compute
the grads will be freed. Note that in nearly all cases setting
this option to True is not needed and often can be worked around
in a much more efficient way. Defaults to the value of
create_graph
.  create_graph (bool, optional) – If true, graph of the derivative will
be constructed, allowing to compute higher order derivative
products. Defaults to False, unless
gradient
is a volatile Variable.
 gradient (Tensor, Variable or None) – Gradient w.r.t. the
variable. If it is a tensor, it will be automatically converted
to a Variable that is volatile unless

detach
()[source]¶ Returns a new Variable, detached from the current graph.
Result will never require gradient. If the input is volatile, the output will be volatile too.
Note
Returned Variable uses the same data tensor, as the original one, and inplace modifications on either of them will be seen, and may trigger errors in correctness checks.

register_hook
(hook)[source]¶ Registers a backward hook.
The hook will be called every time a gradient with respect to the variable is computed. The hook should have the following signature:
hook(grad) > Variable or None
The hook should not modify its argument, but it can optionally return a new gradient which will be used in place of
grad
.This function returns a handle with a method
handle.remove()
that removes the hook from the module.Example
>>> v = Variable(torch.Tensor([0, 0, 0]), requires_grad=True) >>> h = v.register_hook(lambda grad: grad * 2) # double the gradient >>> v.backward(torch.Tensor([1, 1, 1])) >>> v.grad.data 2 2 2 [torch.FloatTensor of size 3] >>> h.remove() # removes the hook

reinforce
(reward)[source]¶ Registers a reward obtained as a result of a stochastic process.
Differentiating stochastic nodes requires providing them with reward value. If your graph contains any stochastic operations, you should call this function on their outputs. Otherwise an error will be raised.
Parameters: reward (Tensor) – Tensor with perelement rewards. It has to match the device location and shape of Variable’s data.
Function¶

class
torch.autograd.
Function
[source]¶ Records operation history and defines formulas for differentiating ops.
Every operation performed on
Variable
s creates a new function object, that performs the computation, and records that it happened. The history is retained in the form of a DAG of functions, with edges denoting data dependencies (input < output
). Then, when backward is called, the graph is processed in the topological ordering, by callingbackward()
methods of eachFunction
object, and passing returned gradients on to nextFunction
s.Normally, the only way users interact with functions is by creating subclasses and defining new operations. This is a recommended way of extending torch.autograd.
Since Function logic is a hotspot in most scripts, almost all of it was moved to our C backend, to ensure that the framework overhead is minimal.
Each function is meant to be used only once (in the forward pass).
Variables:  saved_tensors – Tuple of Tensors that were saved in the call to
forward()
.  saved_variables – Tuple of Variables that correspond to the tensors
saved in the call to
forward()
.  needs_input_grad – Tuple of booleans of length
num_inputs
, indicating whether a given input requires gradient. This can be used to optimize buffers saved for backward, and ignoring gradient computation inbackward()
.  num_inputs – Number of inputs given to
forward()
.  num_outputs – Number of tensors returned by
forward()
.  requires_grad – Boolean indicating whether the
backward()
will ever need to be called.

static
backward
(*grad_outputs)[source]¶ Defines a formula for differentiating the operation.
This function is to be overriden by all subclasses.
All arguments are tensors. It has to accept exactly as many arguments, as many outputs did
forward()
return, and it should return as many tensors, as there were inputs toforward()
. Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input.
 saved_tensors – Tuple of Tensors that were saved in the call to