UX Limitations

functorch, like JAX, has restrictions around what can be transformed. In general, JAX’s limitations are that transforms only work with pure functions: that is, functions where the output is completely determined by the input and that do not involve side effects (like mutation).

We have a similar guarantee: our transforms work well with pure functions. However, we do support certain in-place operations. On one hand, writing code compatible with functorch transforms may involve changing how you write PyTorch code, on the other hand, you may find that our transforms let you express things that were previously difficult to express in PyTorch.

General limitations

All functorch transforms share a limitation in that a function should not assign to global variables. Instead, all outputs to a function must be returned from the function. This restriction comes from how functorch is implemented: each transform wraps Tensor inputs in special functorch Tensor subclasses that facilitate the transform.

So, instead of the following:

import torch
from functorch import grad

# Don't do this
intermediate = None

def f(x):
  global intermediate
  intermediate = x.sin()
  z = intermediate.sin()
  return z

x = torch.randn([])
grad_x = grad(f)(x)

Please rewrite f to return intermediate:

def f(x):
  intermediate = x.sin()
  z = intermediate.sin()
  return z, intermediate

grad_x, intermediate = grad(f, has_aux=True)(x)

torch.autograd APIs

If you are trying to use a torch.autograd API like torch.autograd.grad or torch.autograd.backward inside of a function being transformed by vmap() or one of functorch’s AD transforms (vjp(), jvp(), jacrev(), jacfwd()), the transform may not be able to transform over it. If it is unable to do so, you’ll receive an error message.

This is a fundamental design limitation in how PyTorch’s AD support is implemented and the reason why we designed the functorch library. Please instead use the functorch equivalents of the torch.autograd APIs: - torch.autograd.grad, Tensor.backward -> functorch.vjp or functorch.grad - torch.autograd.functional.jvp -> functorch.jvp - torch.autograd.functional.jacobian -> functorch.jacrev or functorch.jacfwd - torch.autograd.functional.hessian -> functorch.hessian

vmap limitations


vmap() is our most restrictive transform. The grad-related transforms (grad(), vjp(), jvp()) do not have these limitations. jacfwd() (and hessian(), which is implemented with jacfwd()) is a composition of vmap() and jvp() so it also has these limitations.

vmap(func) is a transform that returns a function that maps func over some new dimension of each input Tensor. The mental model for vmap is that it is like running a for-loop: for pure functions (i.e. in the absence of side effects), vmap(f)(x) is equivalent to:

torch.stack([f(x_i) for x_i in x.unbind(0)])

Mutation: Arbitrary mutation of Python data structures

In the presence of side effects, vmap() no longer acts like it is running a for-loop. For example, the following function:

def f(x, list):
  return x.sum(0)

x = torch.randn(3, 1)
lst = [0, 1, 2, 3]

result = vmap(f, in_dims=(0, None))(x, lst)

will print “hello!” once and pop only one element from lst.

vmap() executes f a single time, so all side effects only happen once.

This is a consequence of how vmap is implemented. functorch has a special, internal BatchedTensor class. vmap(f)(*inputs) takes all Tensor inputs, turns them into BatchedTensors, and calls f(*batched_tensor_inputs). BatchedTensor overrides the PyTorch API to produce batched (i.e. vectorized) behavior for each PyTorch operator.

Mutation: in-place PyTorch Operations

vmap() will raise an error if it encounters an unsupported PyTorch in-place operation and it will succeed otherwise. Unsupported operations are those that would cause a Tensor with more elements to be written to a Tensor with fewer elements. Here’s an example of how this can occur:

def f(x, y):
  return x

x = torch.randn(1)
y = torch.randn(3)

# Raises an error because `y` has fewer elements than `x`.
vmap(f, in_dims=(None, 0))(x, y)

x is a Tensor with one element, y is a Tensor with three elements. x + y has three elements (due to broadcasting), but attempting to write three elements back into x, which only has one element, raises an error due to attempting to write three elements into a Tensor with a single element.

There is no problem if the Tensor being written to has the same number of elements (or more):

def f(x, y):
  return x

x = torch.randn(3)
y = torch.randn(3)
expected = x + y

# Does not raise an error because x and y have the same number of elements.
vmap(f, in_dims=(0, 0))(x, y)
assert torch.allclose(x, expected)

Mutation: out= PyTorch Operations

vmap() doesn’t support the out= keyword argument in PyTorch operations. It will error out gracefully if it encounters that in your code.

This is not a fundamental limitation; we could theoretically support this in the future but we have chosen not to for now.

Data-dependent Python control flow

We don’t yet support vmap over data-dependent control flow. Data-dependent control flow is when the condition of an if-statement, while-loop, or for-loop is a Tensor that is being vmap’ed over. For example, the following will raise an error message:

def relu(x):
  if x > 0:
    return x
  return 0

x = torch.randn(3)

However, any control flow that is not dependent on the values in vmap’ed tensors will work:

def custom_dot(x):
  if x.dim() == 1:
    return, x)
  return (x * x).sum()

x = torch.randn(3)

JAX supports transforming over data-dependent control flow using special control flow operators (e.g. jax.lax.cond, jax.lax.while_loop). We’re investigating adding equivalents of those to functorch (open an issue on GitHub to voice your support!).

Data-dependent operations (.item())

We do not (and will not) support vmap over a user-defined function that calls .item() on a Tensor. For example, the following will raise an error message:

def f(x):
  return x.item()

x = torch.randn(3)

Please try to rewrite your code to not use .item() calls.

You may also encounter an error message about using .item() but you might not have used it. In those cases, it is possible that PyTorch internally is calling .item() – please file an issue on GitHub and we’ll fix PyTorch internals.

Dynamic shape operations (nonzero and friends)

vmap(f) requires that f applied to every “example” in your input returns a Tensor with the same shape. Operations such as torch.nonzero, torch.is_nonzero are not supported and will error as a result.

To see why, consider the following example:

xs = torch.tensor([[0, 1, 2], [0, 0, 3]])

torch.nonzero(xs[0]) returns a Tensor of shape 2; but torch.nonzero(xs[1]) returns a Tensor of shape 1. We are unable to construct a single Tensor as an output; the output would need to be a ragged Tensor (and PyTorch does not yet have the concept of a ragged Tensor).


The user’s intention when calling a random operation can be unclear. Specifically, some users may want the random behavior to be the same across batches while others may want it to differ across batches. To address this, vmap takes a randomness flag.

The flag can only be passed to vmap and can take on 3 values, “error,” “different,” or “same,” defaulting to error. Under “error” mode, any call to a random function will produce an error asking the user to use one of the other two flags based on their use case.

Under “different” randomness, elements in a batch produce different random values. For instance,

def add_noise(x):
  y = torch.randn(())  # y will be different across the batch
  return x + y

x = torch.ones(3)
result = vmap(add_noise, randomness="different")(x)  # we get 3 different values

Under “same” randomness, elements in a batch produce same random values. For instance,

def add_noise(x):
  y = torch.randn(())  # y will be the same across the batch
  return x + y

x = torch.ones(3)
result = vmap(add_noise, randomness="same")(x)  # we get the same value, repeated 3 times


Our system only determine the randomness behavior of PyTorch operators and cannot control the behavior of other libraries, like numpy. This is similar to JAX’s limitations with their solutions


Multiple vmap calls using either type of supported randomness will not produce the same results. Like with standard PyTorch, a user can get randomness reproducibility through either using torch.manual_seed() outside of vmap or by using generators.


Finally, our randomness differs from JAX because we aren’t using a stateless PRNG, in part because PyTorch doesn’t have full support for a stateless PRNG. Instead, we’ve introduced a flag system to allow for the most common forms of randomness that we see. If your use case does not fit these forms of randomness, please file an issue.


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