functorch.jacfwd

functorch.jacfwd(func, argnums=0, has_aux=False)

Computes the Jacobian of func with respect to the arg(s) at index argnum using forward-mode autodiff

Parameters

• func (function) – A Python function that takes one or more arguments, one of which must be a Tensor, and returns one or more Tensors

• argnums (int or Tuple[int]) – Optional, integer or tuple of integers, saying which arguments to get the Jacobian with respect to. Default: 0.

• has_aux (bool) – Flag indicating that func returns a (output, aux) tuple where the first element is the output of the function to be differentiated and the second element is auxiliary objects that will not be differentiated. Default: False.

Returns

Returns a function that takes in the same inputs as func and returns the Jacobian of func with respect to the arg(s) at argnums. If has_aux is True, then the returned function instead returns a (jacobian, aux) tuple where jacobian is the Jacobian and aux is auxiliary objects returned by func.

Warning

PyTorch’s forward-mode AD coverage on operators is not very good at the moment. You may see this API error out with “forward-mode AD not implemented for operator X”. If so, please file us a bug report and we will prioritize it.

A basic usage with a pointwise, unary operation will give a diagonal array as the Jacobian

>>> from functorch import jacfwd
>>> x = torch.randn(5)
>>> jacobian = jacfwd(torch.sin)(x)
>>> expected = torch.diag(torch.cos(x))
>>> assert torch.allclose(jacobian, expected)

jacfwd() can be composed with vmap to produce batched Jacobians:

>>> from functorch import jacfwd, vmap
>>> x = torch.randn(64, 5)
>>> jacobian = vmap(jacfwd(torch.sin))(x)
>>> assert jacobian.shape == (64, 5, 5)

If you would like to compute the output of the function as well as the jacobian of the function, use the has_aux flag to return the output as an auxiliary object:

>>> from functorch import jacfwd
>>> x = torch.randn(5)
>>>
>>> def f(x):
>>>   return x.sin()
>>>
>>> def g(x):
>>>   result = f(x)
>>>   return result, result
>>>
>>> jacobian_f, f_x = jacfwd(g, has_aux=True)(x)
>>> assert torch.allclose(f_x, f(x))

Additionally, jacrev() can be composed with itself or jacrev() to produce Hessians

>>> from functorch import jacfwd, jacrev
>>> def f(x):
>>>   return x.sin().sum()
>>>
>>> x = torch.randn(5)
>>> hessian = jacfwd(jacrev(f))(x)
>>> assert torch.allclose(hessian, torch.diag(-x.sin()))

By default, jacfwd() computes the Jacobian with respect to the first input. However, it can compute the Jacboian with respect to a different argument by using argnums:

>>> from functorch import jacfwd
>>> def f(x, y):
>>>   return x + y ** 2
>>>
>>> x, y = torch.randn(5), torch.randn(5)
>>> jacobian = jacfwd(f, argnums=1)(x, y)
>>> expected = torch.diag(2 * y)
>>> assert torch.allclose(jacobian, expected)

Additionally, passing a tuple to argnums will compute the Jacobian with respect to multiple arguments

>>> from functorch import jacfwd
>>> def f(x, y):
>>>   return x + y ** 2
>>>
>>> x, y = torch.randn(5), torch.randn(5)
>>> jacobian = jacfwd(f, argnums=(0, 1))(x, y)
>>> expectedX = torch.diag(torch.ones_like(x))
>>> expectedY = torch.diag(2 * y)
>>> assert torch.allclose(jacobian[0], expectedX)
>>> assert torch.allclose(jacobian[1], expectedY)