Julia for python

jax is a successor to classic python+numpy autograd. It includes various code optimisation, jit-compilations, differentiating and vectorizing.

So, a numerical library with certain high performance machine-learning affordances. Note, it is not a deep learning framework per se, but rather the producer species at lowest trophic level of a deep learning ecosystem. For information frameworks built upon it, (or I suppose, in this metaphor predator species) read on to later sections.

The official pitch:

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.

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. Another is vmap for automatic vectorization, 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!

AFAICT the conda installation command is

conda install -c conda-forge jaxlib

Neat examples


Jax has idioms that are not obvious. For me it was not clear how to use batch vectorizing and functional-style application of structures:

Sabrina J. Mielke, From PyTorch to JAX: towards neural net frameworks that purify stateful code

Maybe you decided to look at libraries like flax, trax, or haiku and what you see at least in the ResNet examples looks not too dissimilar from any other framework: define some layers, run some trainers… but what is it that actually happens there? What’s the route from these tiny numpy functions to training big hierarchical neural nets?

That’s the niche this post is trying to fill. We will:

  1. quickly recap a stateful LSTM-LM implementation in a tape-based gradient framework, specifically PyTorch,
  2. see how PyTorch-style coding relies on mutating state, learn about mutation-free pure functions and build (pure) zappy one-liners in JAX,
  3. step-by-step go from individual parameters to medium-size modules by registering them as pytree nodes,
  4. combat growing pains by building fancy scaffolding, and controlling context to extract initialized parameters purify functions and
  5. realize that we could get that easily in a framework like DeepMind’s haiku using its transform mechanism.

Sabrina Mielke’s explanation of the JAX toolchain in context taught me how to think about it better.

One thing I see often in examples is

from jax.config import config

Do I need to care about it? tl;dr omnistaging is good and necessary and also switched on by default on recent jax, so that line is simply being careful and likely unneeded.

Deep learning frameworks

OK, elegant linear algebra is all well and good, but can I also have some standard neural network libraries with convnets and dropout layers and SGD all that standard machinery? Yes! In fact I can have a huge menu of very similar libraries, and now all the computation time I saved by using jax must be spent on working out which flavour of jax libraries I actually want. That sounds snarky because it is; I’m not a huge fan of any of these frameworks. All of them have friction between the pure and beautiful functional style of jax code and the object-oriented conveniences that deep learning people are used to. the exception is Stax, but that looks vaguely abandoned. Equinox claims to address this problem but I have not tested it yet.


Flax was I think the de facto standard deep learning library for jax, and may be still.

Flax is a high-performance neural network library for JAX that is designed for flexibility: Try new forms of training by forking an example and by modifying the training loop, not by adding features to a framework.

Flax is being developed in close collaboration with the JAX team and comes with everything you need to start your research, including:

  • Neural network API (flax.linen): Dense, Conv, {Batch|Layer|Group} Norm, Attention, Pooling, {LSTM|GRU} Cell, Dropout

  • Utilities and patterns: replicated training, serialization and checkpointing, metrics, prefetching on device

  • Educational examples that work out of the box: MNIST, LSTM seq2seq, Graph Neural Networks, Sequence Tagging

  • Fast, tuned large-scale end-to-end examples: CIFAR10, ResNet on ImageNet, Transformer LM1b

I think the google brain team has moved on but this now has momentum? e.g. Why do some modules assume batching and other not? No hints) but it more or less can be cargo-culted and you can ignore the quirks except sometimes.

See also the WIP documentation notebooks Those answered some of my questions, but I still have questions left over due to various annoying rough edges and non-obvious gotchas. For example, if you miss a parameter needed for a given model, the error is FilteredStackTrace: AssertionError: Need PRNG for "params".

There are some good examples in the repository.

I have the vague feeling that this will be abandoned for a more polished interface soon. Still seems actively developed.

Light learning rate scheduling is supported natively.


Rob Salomone recommends stax which ships with jax. It has an alarming disclaimer:

You likely do not mean to import this module! Stax is intended as an example library only. There are a number of other much more fully-featured neural network libraries for JAX…

Documentation seems absent. Here are some examples of stax in action

Unique value proposition: stax attempts to be stay close to Jax’s functional style, unlike the more object-oriented contenders.


google/trax: Trax — Deep Learning with Clear Code and Speed

Trax is an end-to-end library for deep learning that focuses on clear code and speed. It is actively used and maintained in the Google Brain team. This notebook (run it in colab) shows how to use Trax and where you can find more information.

Trax includes basic models (like ResNet, LSTM, Transformer) and RL algorithms (like REINFORCE, A2C, PPO). It is also actively used for research and includes new models like the Reformer and new RL algorithms like AWR. Trax has bindings to a large number of deep learning datasets, including Tensor2Tensor and TensorFlow datasets.

You can use Trax either as a library from your own python scripts and notebooks or as a binary from the shell, which can be more convenient for training large models. It runs without any changes on CPUs, GPUs and TPUs.


Kidger and Garcia (2021):

JAX and PyTorch are two popular Python autodifferentiation frameworks. JAX is based around pure functions and functional programming. PyTorch has popularised the use of an object-oriented (OO) class-based syntax for defining parameterised functions, such as neural networks. That this seems like a fundamental difference means current libraries for building parameterised functions in JAX have either rejected the OO approach entirely (Stax) or have introduced OO-to-functional transformations, multiple new abstractions, and been limited in the extent to which they integrate with JAX (Flax, Haiku, Objax). Either way this OO/ functional difference has been a source of tension. Here, we introduce Equinox, a small neural network library showing how a PyTorch-like class-based approach may be admitted without sacrificing JAX-like functional programming. We provide two main ideas. One: parameterised functions are themselves represented as PyTrees, which means that the parameterisation of a function is transparent to the JAX framework. Two: we filter a PyTree to isolate just those components that should be treated when transforming (jit, grad or vmap-ing) a higher-order function of a parameterised function – such as a loss function applied to a model. Overall Equinox resolves the above tension without introducing any new program- matic abstractions: only PyTrees and transformations, just as with regular JAX. Equinox is available at https://github.com/patrick-kidger/equinox

Inference boilerplate stuff


Optax is a gradient processing and optimization library for JAX. It is designed to facilitate research by providing building blocks that can be recombined in custom ways in order to optimise parametric models such as, but not limited to, deep neural networks.

Our goals are to

  • Provide readable, well-tested, efficient implementations of core components,

  • Improve researcher productivity by making it possible to combine low level ingredients into custom optimiser (or other gradient processing components).

  • Accelerate adoption of new ideas by making it easy for anyone to contribute.

We favour focusing on small composable building blocks that can be effectively combined into custom solutions. Others may build upon these basic components more complicated abstractions. Whenever reasonable, implementations prioritise readability and structuring code to match standard equations, over code reuse.


Elegy seems to be a pytorch-lightning-like library in an object-oriented style.

Main Features

  • 😀 Easy-to-use: Elegy provides a Keras-like high-level API that makes it very easy to use for most common tasks.
  • 💪‍ Flexible: Elegy provides a Pytorch Lightning-like low-level API that offers maximum flexibility when needed.
  • 🔌 Compatible: Elegy supports various frameworks and data sources including Flax & Haiku Modules, Optax Optimizers, TensorFlow Datasets, Pytorch DataLoaders, and more.

Elegy is built on top of Treex and Treeo and reexports their APIs for convenience.

Getting Started | Examples | Documentation

What is included?

  • A Model class with an Estimator-like API.
  • A callbacks module with common Keras callbacks.

From Treex

  • A Module class.
  • A nn module for with common layers.
  • A losses module with common loss functions.
  • A metrics module with common metrics.

A lot of the design choices here are not for me; it resembles the annoying parts of pytorch-lightning, which vexes me because they could have just kept the good bits when rewriting for the more elegant jax.

Probabilistic programming frameworks


Numpyro seems to be the dominant probabilistic programming system. It is a jax port/implementation/something of the pytorch classic, Pyro.

More fringe but possibly interesting, jax-md does molecular dynamics. ladax “LADAX: Layers of distributions using FLAX/JAX” does some kind of latent RV something.


The creators of Stheno eem to be Invenia, some of whose staff I am connected to in various indirect ways. It targets jax as one of several backends via a generic backend library, wesselb/lab: A generic interface for linear algebra backends.

Placeholder; details TBD.

graph networks

Differential equations

Trying to do inference with differential equations? Can’t use julia? Jax might do instead.


Diffrax is a JAX-based library providing numerical differential equation solvers.



TF2JAX is an experimental library for converting TensorFlow functions/graphs to JAX functions.


Jax natively handles multi-GPU, via pmap, but how ot use it? The haiku example makes it clearer.


How do we get networks into and out of the Jax ecosystem?


Blondel, Mathieu, Quentin Berthet, Marco Cuturi, Roy Frostig, Stephan Hoyer, Felipe Llinares-López, Fabian Pedregosa, and Jean-Philippe Vert. 2021. Efficient and Modular Implicit Differentiation.” arXiv:2105.15183 [Cs, Math, Stat], October.
Hessel, Matteo, David Budden, Fabio Viola, Mihaela Rosca, Eren Sezener, and Tom Hennigan. 2020. Optax: Composable Gradient Transformation and Optimisation, in JAX!
Kidger, Patrick, and Cristian Garcia. 2021. Equinox: Neural Networks in JAX via Callable PyTrees and Filtered Transformations.” arXiv:2111.00254 [Cs], October.
Krämer, Nicholas, Nathanael Bosch, Jonathan Schmidt, and Philipp Hennig. 2021. Probabilistic ODE Solutions in Millions of Dimensions.” arXiv.

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