Compute the Jacobian of a given function.
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 consider using torch.func.jacrev() or torch.func.jacfwd() instead if you are looking for something less experimental and more performant. When computing the jacobian, usually we invoke autograd.grad once per row of the jacobian. If this flag is True, we perform only a single autograd.grad call with batched_grad=True which uses the vmap prototype feature. Though this should lead to performance improvements in many cases, because this feature is still experimental, there may be performance cliffs. See torch.autograd.grad()’s batched_grad parameter for more information.
strategy (str, optional) – Set to "forward-mode" or "reverse-mode" to determine whether the Jacobian will be computed with forward or reverse mode AD. Currently, "forward-mode" requires vectorized=True. Defaults to "reverse-mode". If func has more outputs than inputs, "forward-mode" tends to be more performant. Otherwise, prefer to use "reverse-mode".
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. If strategy is forward-mode, the dtype will be that of the output; otherwise, the input.
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.]]))
>>> def linear_model(x): ... W = torch.tensor([[2.0, -1.0], [0.0, 1.0]]) ... b = torch.tensor([1.0, 0.5]) ... return x @ W.T + b
>>> x = torch.randn(4, 2, requires_grad=True) >>> jac = jacobian(linear_model, x, vectorize=True) >>> jac.shape torch.Size([4, 2, 4, 2])
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