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Function that computes the dot product between a vector v and the Jacobian of the given function at the point given by the inputs.

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.

• v (tuple of Tensors or Tensor) – The vector for which the vector Jacobian product is computed. Must be the same size as the output of func. This argument is optional when the output of func contains a single element and (if it is not provided) will be set as a Tensor containing a single 1.

• create_graph (bool, optional) – If True, both the output and result will be computed in a differentiable way. 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 vjp for said inputs, which is the expected mathematical value. Defaults to False.

Returns:

tuple with:

func_output (tuple of Tensors or Tensor): output of func(inputs)

vjp (tuple of Tensors or Tensor): result of the dot product with the same shape as the inputs.

Return type:

output (tuple)

Example

>>> def exp_reducer(x):
...     return x.exp().sum(dim=1)
>>> inputs = torch.rand(4, 4)
>>> v = torch.ones(4)
>>> vjp(exp_reducer, inputs, v)
(tensor([5.7817, 7.2458, 5.7830, 6.7782]),
tensor([[1.4458, 1.3962, 1.3042, 1.6354],
[2.1288, 1.0652, 1.5483, 2.5035],
[2.2046, 1.1292, 1.1432, 1.3059],
[1.3225, 1.6652, 1.7753, 2.0152]]))

>>> vjp(exp_reducer, inputs, v, create_graph=True)
tensor([[1.4458, 1.3962, 1.3042, 1.6354],
[2.1288, 1.0652, 1.5483, 2.5035],
[2.2046, 1.1292, 1.1432, 1.3059],

>>> def adder(x, y):
...     return 2 * x + 3 * y
>>> inputs = (torch.rand(2), torch.rand(2))
>>> v = torch.ones(2)
(tensor([2.4225, 2.3340]),
(tensor([2., 2.]), tensor([3., 3.]))) ## Docs

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