<h1><img src="" alt="Nx" width="400"></h1>

[![Package](]( [![Documentation](](

Nx is a multi-dimensional tensors library for Elixir with multi-staged compilation to the CPU/GPU. Its high-level features are:

  * Typed multi-dimensional tensors, where the tensors can be unsigned integers (`u8`, `u16`, `u32`, `u64`), signed integers (`s8`, `s16`, `s32`, `s64`), floats (`f16`, `f32`, `f64`), brain floats (`bf16`), and complex numbers (`c64`, `c128`);

  * Named tensors, allowing developers to give names to each dimension, leading to more readable and less error prone codebases;

  * Automatic differentiation, also known as autograd. The `grad` function provides reverse-mode differentiation, useful for simulations, training probabilistic models, etc;

  * Auto-vectorization and auto-batching, which allow developers to elegantly transform numerical code that only work on specific dimensions, into code that efficiently runs on higher dimensions in parallel

  * Numerical definitions, known as `defn`, is a subset of Elixir that is compilable to multiple targets, including GPUs. See [EXLA]( for just-in-time (JIT) compilation for CPUs/GPUs/TPUs and [Torchx]( or [Candlex]( for CPUs/GPUs support;

  * Built-in distributed² serving: encapsulate complex numerical pipelines into `Nx.Serving`. Servings provide batching, streaming, and partitioning out of the box. You can distribute servings over multiple CPU cores and GPU devices, as well as over a cluster of machines;

  * Support for data streaming and hooks, allowing developers to send and receive data from CPUs/GPUs/TPUs while computations are running;

  * Support for linear algebra primitives via `Nx.LinAlg`;

You can find planned enhancements and features in the issues tracker. If you need one particular feature to move forward, don't hesitate to let us know and give us feedback.

For Python developers, `Nx` packages features from [`Numpy`](, [`JAX`](, [HuggingFace Pipelines](, and TorchServing/TensorServing, but packaged into a single unified library and developer experience.

See [the Nx organization on GitHub]( to learn about other Numerical Elixir projects.

## Community

Developers interested in Numerical Elixir can join the community and interact in the following places:

  * For general discussion on Numerical Elixir and Machine Learning, [join the #machine-learning channel in the Erlang Ecosystem Foundation Slack]( (click on the link on the sidebar on the right)

  * For bugs and pull requests, use the [issues tracker](

  * For feature requests and Nx-specific discussion, [join the Nx mailing list](

Nx discussion is also welcome on any of the Elixir-specific forums and chats maintained by the community.

## Support

In order to support Nx, you might:

  * Become a supporting member or a sponsor of the Erlang Ecosystem Foundation. The Nx project is part of the [Machine Learning WG](

  * Nx's mascot is the Numbat, a marsupial native to southern Australia. Unfortunately the Numbat are endangered and it is estimated to be fewer than 1000 left. If you enjoy this project, consider donating to Numbat conservation efforts, such as [Project Numbat]( and [Australian Wildlife Conservancy]( The Project Numbat website also contains Numbat related swag.

## Installation

In order to use `Nx`, you will need Elixir installed. Then create an Elixir project via the `mix` build tool:

$ mix new my_app

Then you can add `Nx` as dependency in your `mix.exs`:

def deps do
    {:nx, "~> 0.5"}

If you are using Livebook or IEx, you can instead run:

  {:nx, "~> 0.5"}

## Examples

Let's create a tensor:

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.shape(t)
{2, 2}

To implement [the Softmax function](
using this library:

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.divide(Nx.exp(t), Nx.sum(Nx.exp(t)))
    [0.032058604061603546, 0.08714432269334793],
    [0.23688282072544098, 0.6439142227172852]

By default, `Nx` uses pure Elixir code. Since Elixir is a functional and immutable language, each operation above makes a copy of the tensor, which is quite innefficient. You can use either [EXLA](, [Torchx]( or [Candlex]( backends for an improvement in performance, often over 3 orders of magnitude, as well as the ability to work on the data in the GPU. See the README of those projects for more information.

## Numerical definitions

`Nx` also comes with numerical definitions, called `defn`, which is a subset of Elixir tailored for numerical computations. For example, it overrides Elixir's default operators so they are tensor-aware:

defmodule MyModule do
  import Nx.Defn

  defn softmax(t) do
    Nx.exp(t) / Nx.sum(Nx.exp(t))

You can now invoke it as:

MyModule.softmax(Nx.tensor([1, 2, 3]))

`defn` relies on a technique called multi-stage programming, which is built on top of Elixir functional and meta-programming capabilities: we transform Elixir code to build a graph of your numerical definitions. This brings two important capabilities:

  1. We can transform this graph to provide features such as automatic differentiation, type lowering, and more

  2. We support custom compilers, which can compile said definitions to run on the CPU and GPU just-in-time

For example, [using the `EXLA` compiler](, which provides bindings to Google's XLA:

will_jit = EXLA.jit(&MyModule.softmax/1)

Once `softmax` is called, `EXLA` will emit a just-in-time and high-specialized compiled version of the code, tailored to the input tensors type and shape. By setting the `XLA_TARGET` environment variable to `cuda` or `rocm`, the code can be compiled for the GPU. For reference, here are some benchmarks of the function above when called with a tensor of one million random float values:

Name                       ips        average  deviation         median         99th %
xla gpu f32 keep      15308.14      0.0653 ms    ±29.01%      0.0638 ms      0.0758 ms
xla gpu f64 keep       4550.59        0.22 ms     ±7.54%        0.22 ms        0.33 ms
xla cpu f32             434.21        2.30 ms     ±7.04%        2.26 ms        2.69 ms
xla gpu f32             398.45        2.51 ms     ±2.28%        2.50 ms        2.69 ms
xla gpu f64             190.27        5.26 ms     ±2.16%        5.23 ms        5.56 ms
xla cpu f64             168.25        5.94 ms     ±5.64%        5.88 ms        7.35 ms
elixir f32                3.22      311.01 ms     ±1.88%      309.69 ms      340.27 ms
elixir f64                3.11      321.70 ms     ±1.44%      322.10 ms      328.98 ms

xla gpu f32 keep      15308.14
xla gpu f64 keep       4550.59 - 3.36x slower +0.154 ms
xla cpu f32             434.21 - 35.26x slower +2.24 ms
xla gpu f32             398.45 - 38.42x slower +2.44 ms
xla gpu f64             190.27 - 80.46x slower +5.19 ms
xla cpu f64             168.25 - 90.98x slower +5.88 ms
elixir f32                3.22 - 4760.93x slower +310.94 ms
elixir f64                3.11 - 4924.56x slower +321.63 ms

See the [`bench`]( and [`examples`]( directory inside the EXLA project for more information.

Many of Elixir's features are supported inside `defn`, such as the pipe operator, aliases, conditionals, pattern-matching, and more. It also brings exclusive features to numerical definitions, such as `while` loops, automatic differentiation via the `grad` function, hooks to inspect data running on the GPU, and more.

## Working with processes

Elixir runs on the Erlang Virtual Machine, which runs your code inside lightweight thread of executions called "processes". Sending tensors between processes is done by sharing, no copying is required. The tensors are then [refcounted]( and garbage collected once all processes no longer hold a reference to them.

Nx also allows developers to run different Erlang VM processes, each against a different GPU device. For using, with EXLA, one could do:

Nx.default_backend({EXLA.Backend, client: :cuda, device_id: 1})


will_jit = EXLA.jit(&MyModule.softmax/1, client: :cuda, device_id: 1)

And, from that moment on, all operations will happen within a particular GPU instance. You can then use Elixir's message-passing abilities to coordinate the necessary work across processes.

## License

Copyright (c) 2020 Dashbit

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at [](

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
See the License for the specific language governing permissions and
limitations under the License.