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- What is JAX?
- Quickstart: Colab in the Cloud
- Transformations
- Current gotchas
- Installation
- Neural network libraries
- Citing JAX
- Reference documentation
JAX is Autograd and XLA, brought together for high-performance numerical computing, including large-scale 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 grad as 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 grad and jit are instances of such transformations. Others are vmap for automatic vectorization and pmap for single-program multiple-data (SPMD) parallel programming of multiple accelerators, with more to come.
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, grad for differentiation, jit for compilation, and vmap for 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
Automatic differentiation with grad
JAX has roughly the same API as Autograd. The most popular function is grad for reverse-mode gradients: You can differentiate to any order with grad. For more advanced autodiff, you can use jax.vjp for reverse-mode vector-Jacobian products and jax.jvp for 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: As with Autograd, you're free to use differentiation with Python control structures: See the reference docs on automatic differentiation and the JAX Autodiff Cookbook for more.
Compilation with jit
You can use XLA to compile your functions end-to-end with jit, used either as an @jit decorator or as a higher-order function. You can mix jit and grad and any other JAX transformation however you like. Using jit puts constraints on the kind of Python control flow the function can use; see the Gotchas Notebook for more.
Auto-vectorization with vmap
vmap is 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 vmap can save you from having to carry around batch dimensions in your code. For example, consider this simple unbatched neural network prediction function: We often instead write jnp.dot(activations, W) to allow for a batch dimension on the left side of activations, 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 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 multiplication rather than matrix-vector multiplication. The vmap function does that transformation for us. That is, if we write then the vmap function 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: Of course, vmap can be arbitrarily composed with jit, grad, and any other JAX transformation! We use vmap with both forward- and reverse-mode automatic differentiation for fast Jacobian and Hessian matrix calculations in jax.jacfwd, jax.jacrev, and jax.hessian.
For a more thorough survey of current gotchas, with examples and explanations, we highly recommend reading the Gotchas Notebook. Some standouts:
1.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 like Exception: Can't lift Traced... or Exception: Different traces at same level.
2.In-place mutating updates of arrays, like x[i] += y, aren't supported, but there are functional alternatives. Under a jit, those functional alternatives will reuse buffers in-place automatically.
3.Random numbers are different, but for good reasons.
4.If you're looking for convolution operators, they're in the jax.lax package.
5.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 the jax_enable_x64 variable at startup (or set the environment variable JAX_ENABLE_X64=True). On TPU, JAX uses 32-bit values by default for everything except internal temporary variables in 'matmul-like' operations, such as jax.numpy.dot and lax.conv. Those ops have a precision parameter which can be used to simulate true 32-bit, with a cost of possibly slower runtime.
Supported platforms Instructions
See the documentation for information on alternative installation strategies. These include compiling from source, installing with Docker, using other versions of CUDA, a community-supported conda build, and answers to some frequently-asked questions.
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.
Google X maintains the neural network library Equinox. This is used as the foundation for several other libraries in the JAX ecosystem.
To cite this repository:
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.
For details about the JAX API, see the reference documentation.
For getting started as a JAX developer, see the developer documentation.
JAX provides a unified NumPy-like interface to computations that run on CPU, GPU, or TPU, in local or distributed settings. JAX features built-in Just-In-Time (JIT) compilation via Open XLA, an open-source machine learning compiler ecosystem. JAX functions support efficient evaluation of gradients via its automatic differentiation transformations.
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