jax

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 return x * x + x * 2.0 x = jnp.ones((5000, 5000)) fast_f = jax.jit(slow_f) %timeit -n10 -r3 fast_f(x) %timeit -n10 -r3 slow_f(x) Using jax.jit constrains the kind of Python control flow the function can use; see the tutorial on Control Flow and Logical Operators with JIT for more. Auto-vectorization with vmap vmap maps a function along array axes. But instead of just looping over function applications, it pushes the loop down onto the function’s primitive operations, e.g. turning matrix-vector multiplies into matrix-matrix multiplies for better performance. Using vmap can save you from having to carry around batch dimensions in your code: import jax import jax.numpy as jnp def l1_distance(x, y): assert x.ndim == y.ndim == 1 # only works on 1D inputs return jnp.sum(jnp.abs(x - y)) def pairwise_distances(dist1D, xs): return jax.vmap(jax.vmap(dist1D, (0, None)), (None, 0))(xs, xs) xs = jax.random.normal(jax.random.key(0), (100, 3)) dists = pairwise_distances(l1_distance, xs) dists.shape # (100, 100) By composing jax.vmap with jax.grad and jax.jit, we can get efficient Jacobian matrices, or per-example gradients: per_example_grads = jax.jit(jax.vmap(jax.grad(loss), in_axes=(None, 0, 0))) Scaling To scale your computations across thousands of devices, you can use any composition of these: Compiler-based automatic parallelization where you program as if using a single global machine, and the compiler chooses how to shard data and partition computation (with some user-provided constraints); Explicit sharding and automatic partitioning where you still have a global view but data shardings are explicit in JAX types, inspectable using jax.typeof; Manual per-device programming where you have a per-device view of data and computation, and can communicate with explicit collectives. Mode View? Explicit sharding? Explicit Collectives? Auto Global ❌ ❌ Explicit Global ✅ ❌ Manual Per-device ✅ ✅ from jax.sharding import set_mesh, AxisType, PartitionSpec as P mesh = jax.make_mesh((8,), ('data',), axis_types=(AxisType.Explicit,)) set_mesh(mesh) # parameters are sharded for FSDP: for W, b in params: print(f'{jax.typeof(W)}') # f32[512@data,512] print(f'{jax.typeof(b)}') # f32[512] # shard data for batch parallelism: inputs, targets = jax.device_put((inputs, targets), P('data')) # evaluate gradients, automatically parallelized! gradfun = jax.jit(jax.grad(loss)) param_grads = gradfun(params, (inputs, targets)) See the tutorial and advanced guides for more. Gotchas and sharp bits See the Gotchas Notebook. Installation Supported platforms Linux x86_64 Linux aarch64 Mac aarch64 Windows x86_64 Windows WSL2 x86_64 CPU yes yes yes yes yes NVIDIA GPU yes yes n/a no experimental Google TPU yes n/a n/a n/a n/a AMD GPU yes no n/a no experimental Apple GPU n/a no experimental n/a n/a Intel GPU experimental n/a n/a no no Instructions Platform Instructions CPU pip install -U jax NVIDIA GPU pip install -U "jax[cuda13]" Google TPU pip install -U "jax[tpu]" AMD GP