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# functorch.vjp¶

functorch.vjp(func, *primals, has_aux=False)[source]

Standing for the vector-Jacobian product, returns a tuple containing the results of func applied to primals and a function that, when given cotangents, computes the reverse-mode Jacobian of func with respect to primals times cotangents.

Parameters
• func (Callable) – A Python function that takes one or more arguments. Must return one or more Tensors.

• primals (Tensors) – Positional arguments to func that must all be Tensors. The returned function will also be computing the derivative with respect to these arguments

• 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 other auxiliary objects that will not be differentiated. Default: False.

Returns

Returns a (output, vjp_fn) tuple containing the output of func applied to primals and a function that computes the vjp of func with respect to all primals using the cotangents passed to the returned function. If has_aux is True, then instead returns a (output, vjp_fn, aux) tuple. The returned vjp_fn function will return a tuple of each VJP.

When used in simple cases, vjp() behaves the same as grad()

>>> x = torch.randn([5])
>>> f = lambda x: x.sin().sum()
>>> (_, vjpfunc) = torch.func.vjp(f, x)


However, vjp() can support functions with multiple outputs by passing in the cotangents for each of the outputs

>>> x = torch.randn([5])
>>> f = lambda x: (x.sin(), x.cos())
>>> (_, vjpfunc) = torch.func.vjp(f, x)
>>> vjps = vjpfunc((torch.ones([5]), torch.ones([5])))
>>> assert torch.allclose(vjps[0], x.cos() + -x.sin())


vjp() can even support outputs being Python structs

>>> x = torch.randn([5])
>>> f = lambda x: {'first': x.sin(), 'second': x.cos()}
>>> (_, vjpfunc) = torch.func.vjp(f, x)
>>> cotangents = {'first': torch.ones([5]), 'second': torch.ones([5])}
>>> vjps = vjpfunc(cotangents)
>>> assert torch.allclose(vjps[0], x.cos() + -x.sin())


The function returned by vjp() will compute the partials with respect to each of the primals

>>> x, y = torch.randn([5, 4]), torch.randn([4, 5])
>>> (_, vjpfunc) = torch.func.vjp(torch.matmul, x, y)
>>> cotangents = torch.randn([5, 5])
>>> vjps = vjpfunc(cotangents)
>>> assert len(vjps) == 2
>>> assert torch.allclose(vjps[0], torch.matmul(cotangents, y.transpose(0, 1)))
>>> assert torch.allclose(vjps[1], torch.matmul(x.transpose(0, 1), cotangents))


primals are the positional arguments for f. All kwargs use their default value

>>> x = torch.randn([5])
>>> def f(x, scale=4.):
>>>   return x * scale
>>>
>>> (_, vjpfunc) = torch.func.vjp(f, x)
>>> vjps = vjpfunc(torch.ones_like(x))
>>> assert torch.allclose(vjps[0], torch.full(x.shape, 4.))


Note

Using PyTorch torch.no_grad together with vjp. Case 1: Using torch.no_grad inside a function:

>>> def f(x):
>>>         c = x ** 2
>>>     return x - c


In this case, vjp(f)(x) will respect the inner torch.no_grad.

Case 2: Using vjp inside torch.no_grad context manager:

>>> # xdoctest: +SKIP(failing)
>>>     vjp(f)(x)


In this case, vjp will respect the inner torch.no_grad, but not the outer one. This is because vjp is a “function transform”: its result should not depend on the result of a context manager outside of f.

Warning

We’ve integrated functorch into PyTorch. As the final step of the integration, functorch.vjp is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use torch.func.vjp instead; see the PyTorch 2.0 release notes and/or the torch.func migration guide for more details https://pytorch.org/docs/main/func.migrating.html

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