torch.autograd.functional.jacobian

torch.autograd.functional.jacobian(func, inputs, create_graph=False, strict=False, vectorize=False)

Function that computes the Jacobian of a given function.

Parameters

• func (function) – a Python function that takes Tensor inputs and returns a tuple of Tensors or a Tensor.

• inputs (tuple of Tensors or Tensor) – inputs to the function func.

• create_graph (bool, optional) – If True, the Jacobian will be computed in a differentiable manner. Note that when strict is False, the result can not require gradients or be disconnected from the inputs. Defaults to False.

• strict (bool, optional) – If True, an error will be raised when we detect that there exists an input such that all the outputs are independent of it. If False, we return a Tensor of zeros as the jacobian for said inputs, which is the expected mathematical value. Defaults to False.

• vectorize (bool, optional) – This feature is experimental, please use at your own risk. When computing the jacobian, usually we invoke autograd.grad once per row of the jacobian. If this flag is True, we use the vmap prototype feature as the backend to vectorize calls to autograd.grad so we only invoke it once instead of once per row. This should lead to performance improvements in many use cases, however, due to this feature being incomplete, there may be performance cliffs. Please use torch._C._debug_only_display_vmap_fallback_warnings(True) to show any performance warnings and file us issues if warnings exist for your use case. Defaults to False.

Returns

if there is a single input and output, this will be a single Tensor containing the Jacobian for the linearized inputs and output. If one of the two is a tuple, then the Jacobian will be a tuple of Tensors. If both of them are tuples, then the Jacobian will be a tuple of tuple of Tensors where Jacobian[i][j] will contain the Jacobian of the ith output and jth input and will have as size the concatenation of the sizes of the corresponding output and the corresponding input and will have same dtype and device as the corresponding input.

Return type

Jacobian (Tensor or nested tuple of Tensors)

Example

>>> def exp_reducer(x):
...   return x.exp().sum(dim=1)
>>> inputs = torch.rand(2, 2)
>>> jacobian(exp_reducer, inputs)
tensor([[[1.4917, 2.4352],
         [0.0000, 0.0000]],
        [[0.0000, 0.0000],
         [2.4369, 2.3799]]])

>>> jacobian(exp_reducer, inputs, create_graph=True)
tensor([[[1.4917, 2.4352],
         [0.0000, 0.0000]],
        [[0.0000, 0.0000],
         [2.4369, 2.3799]]], grad_fn=<ViewBackward>)

>>> def exp_adder(x, y):
...   return 2 * x.exp() + 3 * y
>>> inputs = (torch.rand(2), torch.rand(2))
>>> jacobian(exp_adder, inputs)
(tensor([[2.8052, 0.0000],
        [0.0000, 3.3963]]),
 tensor([[3., 0.],
         [0., 3.]]))