Transformable numerical computing at scale

Transformations | Scaling | Install guide | Change logs | Reference docs

What is JAX?

JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning.

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

JAX uses XLA to compile and scale your NumPy programs on TPUs, GPUs, and other hardware accelerators. You can compile your own pure functions with jax.jit. Compilation and automatic differentiation can be composed arbitrarily.

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

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

import jax
import jax.numpy as jnp

def predict(params, inputs):
  for W, b in params:
    outputs = jnp.dot(inputs, W) + b
    inputs = jnp.tanh(outputs)  # inputs to the next layer
  return outputs                # no activation on last layer

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

grad_loss = jax.jit(jax.grad(loss))  # compiled gradient evaluation function
perex_grads = jax.jit(jax.vmap(grad_loss, in_axes=(None, 0, 0)))  # fast per-example grads

Contents

• Transformations
• Scaling
• Current gotchas
• Installation
• Citing JAX
• Reference documentation

Transformations

At its core, JAX is an extensible system for transforming numerical functions. Here are three: jax.grad, jax.jit, and jax.vmap.

Automatic differentiation with grad

Use jax.grad to efficiently compute reverse-mode gradients:

import jax
import jax.numpy as jnp

def tanh(x):
  y = jnp.exp(-2.0 * x)
  return (1.0 - y) / (1.0 + y)

grad_tanh = jax.grad(tanh)
print(grad_tanh(1.0))
# prints 0.4199743

You can differentiate to any order with grad:

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

You're free to use differentiation with Python control flow:

def abs_val(x):
  if x > 0:
    return x
  else:
    return -x

abs_val_grad = jax.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 JAX Autodiff Cookbook and the reference docs on automatic differentiation for more.

Compilation with jit

Use XLA to compile your functions end-to-end with jit, used either as an @jit decorator or as a higher-order function.

import jax
import jax.numpy as jnp

def slow_f(x):
  # Element-wise ops see a large benefit from fusion
  re