JAX (software)

JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning. It is developed by Google with contributions from Nvidia and other community contributors.

It is described as bringing together a modified version o
autograd
(automatic obtaining of the gradient function through differentiation of a function) and OpenXLA's XLA (Accelerated Linear Algebra). It is designed to follow the structure and workflow of NumPy as closely as possible and works with various existing frameworks such as TensorFlow and PyTorch. The primary features of JAX are:

# Providing a unified NumPy-like interface to computations that run on CPU, GPU, or TPU, in local or distributed settings.
# Built-in Just-In-Time (JIT) compilation via Open XLA, an open-source machine learning compiler ecosystem.
# Efficient evaluation of gradients via its automatic differentiation transformations.
# Automatically vectorized to efficiently map them over arrays representing batches of inputs.

grad

The below code demonstrates the grad function's automatic differentiation.

# imports
from jax import grad
import jax.numpy as jnp

# define the logistic function
def logistic(x):
return jnp.exp(x) / (jnp.exp(x) + 1)

# obtain the gradient function of the logistic function
grad_logistic = grad(logistic)

# evaluate the gradient of the logistic function at x = 1
grad_log_out = grad_logistic(1.0)
print(grad_log_out)

The final line should outputː

0.19661194

jit

The below code demonstrates the jit function's optimization through fusion.

# imports
from jax import jit
import jax.numpy as jnp

# define the cube function
def cube(x):
return x * x * x

# generate data
x = jnp.ones((10000, 10000))

# create the jit version of the cube function
jit_cube = jit(cube)

# apply the cube and jit_cube functions to the same data for speed comparison
cube(x)
jit_cube(x)

The computation time for (line #17) should be noticeably shorter than that for (line #16). Increasing the values on line #7, will further exacerbate the difference.

vmap

The below code demonstrates the vmap function's vectorization.

# imports
from jax import vmap partial
import jax.numpy as jnp

# define function
def grads(self, inputs):
in_grad_partial = jax.partial(self._net_grads, self._net_params)
grad_vmap = jax.vmap(in_grad_partial)
rich_grads = grad_vmap(inputs)
flat_grads = np.asarray(self._flatten_batch(rich_grads))
assert flat_grads.ndim

2 and flat_grads.shape

inputs.shape return flat_grads

The GIF on the right of this section illustrates the notion of vectorized addition.

pmap

The below code demonstrates the pmap function's parallelization for matrix multiplication.

# import pmap and random from JAX; import JAX NumPy
from jax import pmap, random
import jax.numpy as jnp

# generate 2 random matrices of dimensions 5000 x 6000, one per device
random_keys = random.split(random.PRNGKey(0), 2)
matrices = pmap(lambda key: random.normal(key, (5000, 6000)))(random_keys)

# without data transfer, in parallel, perform a local matrix multiplication on each CPU/GPU
outputs = pmap(lambda x: jnp.dot(x, x.T))(matrices)

# without data transfer, in parallel, obtain the mean for both matrices on each CPU/GPU separately
means = pmap(jnp.mean)(outputs)
print(means)

The final line should print the valuesː

.1566595 1.1805978

See also

* NumPy
* TensorFlow
* PyTorch
* CUDA
* Accelerated Linear Algebra

External links

* Documentationː
* Colab (Jupyter/iPython) Quickstart Guideː
* TensorFlow's XLAː (Accelerated Linear Algebra)
* YouTube TensorFlow Channel "Intro to JAX: Accelerating Machine Learning research":
* Original paperː

References

{{differentiable computing

Machine learning
Google
Articles with example Python (programming language) code