Need help with jax?

Click the “chat” button below for chat support from the developer who created it, or find similar developers for support.

Composable transformations of Python+NumPy programs: differentiate, vectorize, JIT to GPU/TPU, and more

10.3K Stars 881 Forks Other 6.0K Commits 691 Opened issues

Readme

**Quickstart**
| **Transformations**
| **Install guide**
| **Neural net libraries**
| **Change logs**
| **Reference docs**
| **Code search**

**News:** JAX tops largest-scale MLPerf Training 0.7 benchmarks!

JAX is Autograd and XLA, brought together for high-performance machine learning research.

With its updated version of Autograd, JAX can automatically differentiate native Python and NumPy functions. It can differentiate through loops, branches, recursion, and closures, and it can take derivatives of derivatives of derivatives. It supports reverse-mode differentiation (a.k.a. backpropagation) via

gradas well as forward-mode differentiation, and the two can be composed arbitrarily to any order.

What’s new is that JAX uses XLA to compile and run your NumPy programs on GPUs and TPUs. Compilation happens under the hood by default, with library calls getting just-in-time compiled and executed. But JAX also lets you just-in-time compile your own Python functions into XLA-optimized kernels using a one-function API,

jit. Compilation and automatic differentiation can be composed arbitrarily, so you can express sophisticated algorithms and get maximal performance without leaving Python. You can even program multiple GPUs or TPU cores at once using

pmap, and differentiate through the whole thing.

Dig a little deeper, and you'll see that JAX is really an extensible system for composable function transformations. Both

gradand

jitare instances of such transformations. Others are

vmapfor automatic vectorization and

pmapfor single-program multiple-data (SPMD) parallel programming of multiple accelerators, with more to come.

This is a research project, not an official Google product. Expect bugs and sharp edges. Please help by trying it out, reporting bugs, and letting us know what you think!

import jax.numpy as jnp from jax import grad, jit, vmapdef predict(params, inputs): for W, b in params: outputs = jnp.dot(inputs, W) + b inputs = jnp.tanh(outputs) return outputs

def logprob_fun(params, inputs, targets): preds = predict(params, inputs) return jnp.sum((preds - targets)**2)

grad_fun = jit(grad(logprob_fun)) # compiled gradient evaluation function perex_grads = jit(vmap(grad_fun, in_axes=(None, 0, 0))) # fast per-example grads

- Quickstart: Colab in the Cloud
- Transformations
- Current gotchas
- Installation
- Neural net libraries
- Citing JAX
- Reference documentation

Jump right in using a notebook in your browser, connected to a Google Cloud GPU. Here are some starter notebooks: - The basics: NumPy on accelerators,

gradfor differentiation,

jitfor compilation, and

vmapfor vectorization - Training a Simple Neural Network, with TensorFlow Dataset Data Loading

**JAX now runs on Cloud TPUs.** To try out the preview, see the Cloud TPU
Colabs.

For a deeper dive into JAX: - The Autodiff Cookbook, Part 1: easy and powerful automatic differentiation in JAX - Common gotchas and sharp edges - See the full list of notebooks.

You can also take a look at the mini-libraries in

jax.experimental, like

staxfor building neural networks and

optimizersfor first-order stochastic optimization, or the examples.

At its core, JAX is an extensible system for transforming numerical functions. Here are four of primary interest:

grad,

jit,

vmap, and

pmap.

grad

JAX has roughly the same API as Autograd. The most popular function is

gradfor reverse-mode gradients:

from jax import grad import jax.numpy as jnpdef tanh(x): # Define a function y = jnp.exp(-2.0 * x) return (1.0 - y) / (1.0 + y)

grad_tanh = grad(tanh) # Obtain its gradient function print(grad_tanh(1.0)) # Evaluate it at x = 1.0

## prints 0.4199743

You can differentiate to any order with

grad.

print(grad(grad(grad(tanh)))(1.0)) # prints 0.62162673

For more advanced autodiff, you can use

jax.vjpfor reverse-mode vector-Jacobian products and

jax.jvpfor forward-mode Jacobian-vector products. The two can be composed arbitrarily with one another, and with other JAX transformations. Here's one way to compose those to make a function that efficiently computes full Hessian matrices:

from jax import jit, jacfwd, jacrevdef hessian(fun): return jit(jacfwd(jacrev(fun)))

As with Autograd, you're free to use differentiation with Python control structures:

def abs_val(x): if x > 0: return x else: return -xabs_val_grad = grad(abs_val) print(abs_val_grad(1.0)) # prints 1.0 print(abs_val_grad(-1.0)) # prints -1.0 (abs_val is re-evaluated)

See the reference docs on automatic differentiation and the JAX Autodiff Cookbook for more.

jit

You can use XLA to compile your functions end-to-end with

jit, used either as an

@jitdecorator or as a higher-order function.

import jax.numpy as jnp from jax import jitdef slow_f(x):

## Element-wise ops see a large benefit from fusion

return x * x + x * 2.0

x = jnp.ones((5000, 5000)) fast_f = jit(slow_f) %timeit -n10 -r3 fast_f(x) # ~ 4.5 ms / loop on Titan X %timeit -n10 -r3 slow_f(x) # ~ 14.5 ms / loop (also on GPU via JAX)

You can mix

jitand

gradand any other JAX transformation however you like.

Using

jitputs constraints on the kind of Python control flow the function can use; see the Gotchas Notebook for more.

vmap

vmapis the vectorizing map. It has the familiar semantics of mapping a function along array axes, but instead of keeping the loop on the outside, it pushes the loop down into a function’s primitive operations for better performance.

Using

vmapcan save you from having to carry around batch dimensions in your code. For example, consider this simple

def predict(params, input_vec): assert input_vec.ndim == 1 for W, b in params: output_vec = jnp.dot(W, input_vec) + b # `input_vec` on the right-hand side! input_vec = jnp.tanh(output_vec) return output_vec

We often instead write

jnp.dot(inputs, W)to allow for a batch dimension on the left side of

inputs, but we’ve written this particular prediction function to apply only to single input vectors. If we wanted to apply this function to a batch of inputs at once, semantically we could just write

from functools import partial predictions = jnp.stack(list(map(partial(predict, params), input_batch)))

But pushing one example through the network at a time would be slow! It’s better to vectorize the computation, so that at every layer we’re doing matrix-matrix multiplies rather than matrix-vector multiplies.

The

vmapfunction does that transformation for us. That is, if we write

from jax import vmap predictions = vmap(partial(predict, params))(input_batch) # or, alternatively predictions = vmap(predict, in_axes=(None, 0))(params, input_batch)

then the

vmapfunction will push the outer loop inside the function, and our machine will end up executing matrix-matrix multiplications exactly as if we’d done the batching by hand.

It’s easy enough to manually batch a simple neural network without

vmap, but in other cases manual vectorization can be impractical or impossible. Take the problem of efficiently computing per-example gradients: that is, for a fixed set of parameters, we want to compute the gradient of our loss function evaluated separately at each example in a batch. With

vmap, it’s easy:

per_example_gradients = vmap(partial(grad(loss), params))(inputs, targets)

Of course,

vmapcan be arbitrarily composed with

jit,

grad, and any other JAX transformation! We use

vmapwith both forward- and reverse-mode automatic differentiation for fast Jacobian and Hessian matrix calculations in

jax.jacfwd,

jax.jacrev, and

jax.hessian.

pmap

For parallel programming of multiple accelerators, like multiple GPUs, use

pmap. With

pmapyou write single-program multiple-data (SPMD) programs, including fast parallel collective communication operations. Applying

pmapwill mean that the function you write is compiled by XLA (similarly to

jit), then replicated and executed in parallel across devices.

Here's an example on an 8-GPU machine:

from jax import random, pmap import jax.numpy as jnp## Create 8 random 5000 x 6000 matrices, one per GPU

keys = random.split(random.PRNGKey(0), 8) mats = pmap(lambda key: random.normal(key, (5000, 6000)))(keys)

## Run a local matmul on each device in parallel (no data transfer)

result = pmap(lambda x: jnp.dot(x, x.T))(mats) # result.shape is (8, 5000, 5000)

## Compute the mean on each device in parallel and print the result

print(pmap(jnp.mean)(result))

## prints [1.1566595 1.1805978 ... 1.2321935 1.2015157]

In addition to expressing pure maps, you can use fast collective communication operations between devices:

from functools import partial from jax import lax@partial(pmap, axis_name='i') def normalize(x): return x / lax.psum(x, 'i')

print(normalize(jnp.arange(4.)))

## prints [0. 0.16666667 0.33333334 0.5 ]

You can even nest

pmapfunctions for more sophisticated communication patterns.

It all composes, so you're free to differentiate through parallel computations:

from jax import grad@pmap def f(x): y = jnp.sin(x) @pmap def g(z): return jnp.cos(z) * jnp.tan(y.sum()) * jnp.tanh(x).sum() return grad(lambda w: jnp.sum(g(w)))(x)

print(f(x))

## [[ 0. , -0.7170853 ],

## [-3.1085174 , -0.4824318 ],

## [10.366636 , 13.135289 ],

## [ 0.22163185, -0.52112055]]

print(grad(lambda x: jnp.sum(f(x)))(x))

## [[ -3.2369726, -1.6356447],

## [ 4.7572474, 11.606951 ],

## [-98.524414 , 42.76499 ],

## [ -1.6007166, -1.2568436]]

When reverse-mode differentiating a

pmapfunction (e.g. with

grad), the backward pass of the computation is parallelized just like the forward pass.

See the SPMD Cookbook and the SPMD MNIST classifier from scratch example for more.

For a more thorough survey of current gotchas, with examples and explanations, we highly recommend reading the Gotchas Notebook. Some standouts:

- JAX transformations only work on pure functions, which don't have side-effects and respect referential transparency (i.e. object identity testing with
is

isn't preserved). If you use a JAX transformation on an impure Python function, you might see an error likeException: Can't lift Traced...

orException: Different traces at same level

. -
In-place mutating updates of
arrays, like
x[i] += y

, aren't supported, but there are functional alternatives. Under ajit

, those functional alternatives will reuse buffers in-place automatically. - Random numbers are different, but for good reasons.
- If you're looking for convolution
operators,
they're in the
jax.lax

package. - JAX enforces single-precision (32-bit, e.g.
float32

) values by default, and to enable double-precision (64-bit, e.g.float64

) one needs to set thejax_enable_x64

variable at startup (or set the environment variableJAX_ENABLE_X64=True

). - Some of NumPy's dtype promotion semantics involving a mix of Python scalars
and NumPy types aren't preserved, namely
np.add(1, np.array([2], np.float32)).dtype

isfloat64

rather thanfloat32

. - Some transformations, like
jit

, constrain how you can use Python control flow. You'll always get loud errors if something goes wrong. You might have to usejit

'sstatic_argnums

parameter, structured control flow primitives likelax.scan

, or just usejit

on smaller subfunctions.

JAX is written in pure Python, but it depends on XLA, which needs to be installed as the

jaxlibpackage. Use the following instructions to install a binary package with

pip, or to build JAX from source.

We support installing or building

jaxlibon Linux (Ubuntu 16.04 or later) and macOS (10.12 or later) platforms. Windows users can use JAX on CPU via the Windows Subsystem for Linux. We're not currently working on native Windows support, but contributions are welcome (see #438).

To install a CPU-only version, which might be useful for doing local development on a laptop, you can run

pip install --upgrade pip pip install --upgrade jax jaxlib # CPU-only version

On Linux, it is often necessary to first update

pipto a version that supports

manylinux2010wheels.

If you want to install JAX with both CPU and GPU support, using existing CUDA and CUDNN7 installations on your machine (for example, preinstalled on your cloud VM), you can run

pip install --upgrade pip pip install --upgrade jax jaxlib==0.1.57+cuda110 -f https://storage.googleapis.com/jax-releases/jax_releases.html

The jaxlib version must correspond to the version of the existing CUDA installation you want to use, with

cuda110for CUDA 11.0,

cuda102for CUDA 10.2, and

cuda101for CUDA 10.1. You can find your CUDA version with: install path:

nvcc --version

Note that some GPU functionality expects the CUDA installation to be at

/usr/local/cuda-X.X, where X.X should be replaced with the CUDA version number (e.g.

cuda-10.2). If CUDA is installed elsewhere on your system, you can either create a symlink:

sudo ln -s /path/to/cuda /usr/local/cuda-X.X

Or set the following environment variable before importing JAX:

XLA_FLAGS=--xla_gpu_cuda_data_dir=/path/to/cuda

Please let us know on the issue tracker if you run into any errors or problems with the prebuilt wheels.

Multiple Google research groups develop and share libraries for training neural networks in JAX. If you want a fully featured library for neural network training with examples and how-to guides, try Flax. Another option is Trax, a combinator-based framework focused on ease-of-use and end-to-end single-command examples, especially for sequence models and reinforcement learning. Finally, Objax is a minimalist object-oriented framework with a PyTorch-like interface.

DeepMind has open-sourced an ecosystem of libraries around JAX including Haiku for neural network modules, Optax for gradient processing and optimization, RLax for RL algorithms, and chex for reliable code and testing.

To cite this repository:

@software{jax2018github, author = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and Skye Wanderman-Milne}, title = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs}, url = {http://github.com/google/jax}, version = {0.2.5}, year = {2018}, }

In the above bibtex entry, names are in alphabetical order, the version number is intended to be that from jax/version.py, and the year corresponds to the project's open-source release.

A nascent version of JAX, supporting only automatic differentiation and compilation to XLA, was described in a paper that appeared at SysML 2018. We're currently working on covering JAX's ideas and capabilities in a more comprehensive and up-to-date paper.

For details about the JAX API, see the reference documentation.

For getting started as a JAX developer, see the developer documentation.