pytorch/docs/source/func.whirlwind_tour.md

torch.func Whirlwind Tour

What is torch.func?

.. currentmodule:: torch.func

torch.func, previously known as functorch, is a library for JAX-like composable function transforms in PyTorch.

• A "function transform" is a higher-order function that accepts a numerical function and returns a new function that computes a different quantity.
• torch.func has auto-differentiation transforms (grad(f) returns a function that computes the gradient of f), a vectorization/batching transform (vmap(f) returns a function that computes f over batches of inputs), and others.
• These function transforms can compose with each other arbitrarily. For example, composing vmap(grad(f)) computes a quantity called per-sample-gradients that stock PyTorch cannot efficiently compute today.

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 {func}vmap, {func}grad, {func}vjp, and {func}jvp transforms allows us to express the above without designing a separate subsystem for each.

What are the transforms?

{func}grad (gradient computation)

grad(func) is our gradient computation transform. It returns a new function that computes the gradients of func. It assumes func returns a single-element Tensor and by default it computes the gradients of the output of func w.r.t. to the first input.

import torch
from torch.func 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())

{func}vmap (auto-vectorization)

Note: {func}vmap imposes restrictions on the code that it can be used on. For more details, please see {ref}ux-limitations.

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 torch.func 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
    return feature_vec.dot(weights).relu()

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

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

from torch.func import vmap
batch_size, feature_size = 3, 5

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

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)

{func}vjp (vector-Jacobian product)

The {func}vjp transform applies func to inputs and returns a new function that computes the vector-Jacobian product (vjp) given some cotangents Tensors.

from torch.func import vjp

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

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

{func}jvp (Jacobian-vector product)

The {func}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 torch.func import jvp
x = torch.randn(5)
y = torch.randn(5)
f = lambda x, y: (x * y)
_, out_tangent = jvp(f, (x, y), (torch.ones(5), torch.ones(5)))
assert torch.allclose(out_tangent, x + y)

{func}jacrev, {func}jacfwd, and {func}hessian

The {func}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 torch.func import jacrev
x = torch.randn(5)
jacobian = jacrev(torch.sin)(x)
expected = torch.diag(torch.cos(x))
assert torch.allclose(jacobian, expected)

{func}jacrev can be composed with {func}vmap to produce batched jacobians:

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

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

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

Composing {func}jacrev with itself or {func}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)

{func}hessian is a convenience function that combines jacfwd and jacrev:

from torch.func import hessian

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

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