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Guide to high-performance numerical computing for ML / AI

🧬 JAX Complete Guide

Visitors

JAX is a high-performance research and training framework that combines a NumPy-style API with automatic differentiation, JIT compilation, vectorization, and distributed execution.

  • Advanced
  • Updated Oct 1, 2026
  • ~3 min read
  • 8 sections
  • 4 code examples
  • Web IDE lab included
🧬

JAX Web IDE

Run code in the browser with nothing to install and learn through step-by-step examples.

Open the Web IDE β†’
High-performance matrix operationsAutomatic differentiationJIT compilationResearch model experiments

Related frameworks & environments

🐍Python AIβ†’πŸ”₯PyTorchβ†’TFTensorFlowβ†’

Contents

0 / 10
  1. How to use this guide
  2. Architecture diagrams
  3. What is JAX?
  4. Installation
  5. Automatic differentiation
  6. JIT compilation
  7. Vectorization
  8. JAX design
  9. Operating standards
  10. Verification strategy
Contents 10 sections
  1. How to use this guide
  2. Architecture diagrams
  3. What is JAX?
  4. Installation
  5. Automatic differentiation
  6. JIT compilation
  7. Vectorization
  8. JAX design
  9. Operating standards
  10. Verification strategy

How to use this guide

How to read it

Understanding JAX as a real-world workflow

JAX is a high-performance research and training framework that combines a NumPy-style API with automatic differentiation, JIT compilation, vectorization, and distributed execution. Rather than listing concepts, this guide is organized so you can follow the content in the order you have to make decisions on a real project.

Key perspective

AI / LLM systems

Look beyond the model and the prompt: connect the data flow, evaluation, and post-deployment operating metrics in one view.

High-performance matrix operationsAutomatic differentiationJIT compilationResearch model experiments

Architecture diagrams

To make what you read stick, it helps to capture the flow as a picture first. The two diagrams below are reference maps you can keep coming back to while learning JAX.

Learning flow

Rendering diagram…

Architecture view

Rendering diagram…

What is JAX?

When you first open JAX, the big picture matters more than individual commands. This section starts with the problems the concepts ahead were created to solve.

JAX is a library that offers GPU/TPU acceleration, automatic differentiation, and JIT compilation with NumPy-like syntax. It is often used for large-scale model research and high-performance numerical experiments.
FunctionDescription
gradComputes the gradient of a function automatically.
jitCompiles a function with XLA to run it fast.
vmapVectorizes over the batch dimension automatically.
pmapRuns in parallel across several devices.

Installation

Here you look at Installation alongside real code. Rather than copying the example as-is, read it with an eye on the inputs, the outputs, and the parts most likely to change.

On a CPU-only machine the jax[cpu] package is enough; to use a GPU/TPU you have to install a specific CUDA build. The first step is to check which compute devices were actually detected with jax.devices().
BASH
uv venv
source .venv/bin/activate
uv pip install "jax[cpu]"
python -c "import jax; print(jax.devices())"

Automatic differentiation

Here you look at Automatic differentiation alongside real code. Rather than copying the example as-is, read it with an eye on the inputs, the outputs, and the parts most likely to change.

jax.grad takes a pure function and returns a new function that computes its derivative. There is no need to modify the original function; just wrap it with grad() where the derivative is needed.
PYTHON
import jax
import jax.numpy as jnp

def loss(w):
    return jnp.sum((w - 3.0) ** 2)

grad_loss = jax.grad(loss)
print(grad_loss(jnp.array([1.0, 2.0, 4.0])))

Tip

The function jax.grad differentiates must be a pure function with no side effects for the result to be guaranteed correct.

JIT compilation

Here you look at JIT compilation alongside real code. Rather than copying the example as-is, read it with an eye on the inputs, the outputs, and the parts most likely to change.

Pure functions that are called often can be compiled with jit to cut their execution cost.
PYTHON
@jax.jit
def matmul(a, b):
    return a @ b

x = jnp.ones((1024, 1024))
print(matmul(x, x).shape)

Vectorization

Here you look at Vectorization alongside real code. Rather than copying the example as-is, read it with an eye on the inputs, the outputs, and the parts most likely to change.

vmap extends a single-sample function into a batch function.
PYTHON
def predict(w, x):
    return jnp.dot(w, x)

batched_predict = jax.vmap(predict, in_axes=(None, 0))

JAX practical design

JAX practical design is a point where the options diverge. Using the table to compare what each approach is for and how it differs in operation makes later decisions much easier.

JAX has to be designed on the premise of pure functions and immutable data. Passing the random key, model params, and optimizer state explicitly makes extension with jit/vmap/pmap easy.
Decision pointQuestion to askPractical guideline
BoundariesWhich parts of the JAX code are most likely to change?Separate input/output, configuration, external integrations, and the core rules.
StateWhere is state created and where does it go away?Make the owner and lifecycle of state visible in the code.
FailureWhat does the caller receive on failure?Decide the timeout, fallback, and error contract first.

JAX operating standards

This section covers JAX operating standards from a practical perspective. Instead of memorizing the concept, focus on the situations in which you would reach for it.

Measure jit compile time and run time separately. Frequent shape changes raise the recompilation cost, so stabilizing the batch shape matters.

Tip

  • stable batch shape
  • PRNG key discipline
  • jit compile cache
  • gradient sanity check

JAX verification strategy

JAX verification strategy is a point where the options diverge. Using the table to compare what each approach is for and how it differs in operation makes later decisions much easier.

Verify numerical stability, dtype differences, gradient checks, and deterministic use of PRNG keys.
Quality axisHow to verifyDefinition of done
CorrectnessAutomate the normal/failure cases.The core scenarios pass reproducibly.
Regression preventionWhen fixing a bug, leave the same case behind as a test.The same failure is not deployed again.
OperabilityCheck the logs, metrics, and alerts.There is a path for tracing the cause when a problem occurs.
← Previous guideTensorFlow