Whirlwind Tour

functorch is JAX-like composable function transforms for PyTorch. In this whirlwind tour, we’ll introduce all the functorch transforms.

Why composable function transforms?

There are a number of use cases that are tricky to do in PyTorch today:

  • computing per-sample-gradients (or other per-sample quantities)

  • running ensembles of models on a single machine

  • efficiently batching together tasks in the inner-loop of MAML

  • efficiently computing Jacobians and Hessians

  • efficiently computing batched Jacobians and Hessians

Composing vmap, grad, vjp, and jvp transforms allows us to express the above without designing a separate subsystem for each. This idea of composable function transforms comes from the JAX framework.

What are the transforms?

Right now, we support the following transforms:

  • grad, vjp, jvp,

  • jacrev, jacfwd, hessian

  • vmap

Furthermore, we have some utilities for working with PyTorch modules.

  • make_functional(model)

  • make_functional_with_buffers(model)


Note: vmap imposes restrictions on the code that it can be used on. For more details, please read its docstring.

vmap(func)(*inputs) is a transform that adds a dimension to all Tensor operations in func. vmap(func) returns a new function that maps func over some dimension (default: 0) of each Tensor in inputs.

vmap is useful for hiding batch dimensions: one can write a function func that runs on examples and then lift it to a function that can take batches of examples with vmap(func), leading to a simpler modeling experience:

import torch
from functorch import vmap
batch_size, feature_size = 3, 5
weights = torch.randn(feature_size, requires_grad=True)

def model(feature_vec):
    # Very simple linear model with activation
    assert feature_vec.dim() == 1

examples = torch.randn(batch_size, feature_size)
result = vmap(model)(examples)


grad(func)(*inputs) assumes func returns a single-element Tensor. By default, it computes the gradients of the output of func w.r.t. to inputs[0].

from functorch import grad
x = torch.randn([])
cos_x = grad(lambda x: torch.sin(x))(x)
assert torch.allclose(cos_x, x.cos())

# Second-order gradients
neg_sin_x = grad(grad(lambda x: torch.sin(x)))(x)
assert torch.allclose(neg_sin_x, -x.sin())

When composed with vmap, grad can be used to compute per-sample-gradients:

from functorch import vmap
batch_size, feature_size = 3, 5

def model(weights,feature_vec):
    # Very simple linear model with activation
    assert feature_vec.dim() == 1

def compute_loss(weights, example, target):
    y = model(weights, example)
    return ((y - target) ** 2).mean()  # MSELoss

weights = torch.randn(feature_size, requires_grad=True)
examples = torch.randn(batch_size, feature_size)
targets = torch.randn(batch_size)
inputs = (weights,examples, targets)
grad_weight_per_example = vmap(grad(compute_loss), in_dims=(None, 0, 0))(*inputs)


The vjp transform applies func to inputs and returns a new function that computes vjps given some cotangents Tensors.

from functorch import vjp

inputs = torch.randn(3)
func = torch.sin
cotangents = (torch.randn(3),)

outputs, vjp_fn = vjp(func, inputs); vjps = vjp_fn(*cotangents)


The jvp transforms computes Jacobian-vector-products and is also known as “forward-mode AD”. It is not a higher-order function unlike most other transforms, but it returns the outputs of func(inputs) as well as the jvps.

from functorch import jvp
x = torch.randn(5)
y = torch.randn(5)
f = lambda x, y: (x * y)
_, output = jvp(f, (x, y), (torch.ones(5), torch.ones(5)))
assert torch.allclose(output, x + y)

jacrev, jacfwd, and hessian

The jacrev transform returns a new function that takes in x and returns the Jacobian of the function with respect to x using reverse-mode AD.

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

Use jacrev to compute the jacobian. This can be composed with vmap to produce batched jacobians:

x = torch.randn(64, 5)
jacobian = vmap(jacrev(torch.sin))(x)
assert jacobian.shape == (64, 5, 5)

jacfwd is a drop-in replacement for jacrev that computes Jacobians using forward-mode AD:

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

Composing jacrev with itself or jacfwd can produce hessians:

def f(x):
  return x.sin().sum()

x = torch.randn(5)
hessian0 = jacrev(jacrev(f))(x)
hessian1 = jacfwd(jacrev(f))(x)

The hessian is a convenience function that combines jacfwd and jacrev:

from functorch import hessian

def f(x):
  return x.sin().sum()

x = torch.randn(5)
hess = hessian(f)(x)


Check out our other tutorials (in the left bar) for more detailed explanations of how to apply functorch transforms for various use cases. functorch is very much a work in progress and we’d love to hear how you’re using it – we encourage you to start a conversation at our issues tracker to discuss your use case.