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Getting Started with JAX

Chapter 1: Introduction to JAX

Core Design Philosophy: Function Transformations

Installation and Setup

Working with JAX Arrays

Device Management: CPU, GPU, TPU

Practice: Basic Array Operations

Quiz for Chapter 1

Chapter 2: Accelerating Functions with JIT Compilation

The Need for Speed: Why Compile?

Introducing jax.jit

How JIT Works: Tracing and Compilation

Python Control Flow and jit

Static vs Traced Values

Common Challenges with jit

Hands-on Practical: Applying jit

Quiz for Chapter 2

Chapter 3: Automatic Differentiation with grad

Understanding Gradients

Introducing jax.grad

How Autodiff Works: Reverse Mode

Differentiating with Respect to Arguments

Higher-Order Derivatives (grad of grad)

Value and Gradient (jax.value_and_grad)

Differentiation and Control Flow

Limitations and Considerations

Hands-on Practical: Computing Gradients

Quiz for Chapter 3

Chapter 4: Automatic Vectorization with vmap

The Concept of Vectorization

Introducing jax.vmap

Mapping over Specific Arguments (in_axes, out_axes)

Handling Multiple Batched Arguments

Combining vmap with jit and grad

Performance Considerations for vmap

Hands-on Practical: Vectorizing Functions

Quiz for Chapter 4

Chapter 5: Parallelization Across Devices with pmap

Introduction to Data Parallelism (SPMD)

Introducing jax.pmap

Mapping Data to Devices (in_axes, out_axes)

Device Meshes and Axis Names

Collective Operations (lax.psum, lax.pmean, etc.)

Combining pmap with other Transformations

Debugging pmapped Functions

Hands-on Practical: Parallel Computation

Quiz for Chapter 5

Chapter 6: Managing State in JAX

Functional Purity and Side Effects

The Challenge of State in Functional Code

Pattern: Explicit State Passing

Using PyTrees for Structured State

Example: Stateful Counter

Example: Simple Optimizer State

Combining State Management with Transformations

Practice: Implementing Stateful Functions

Quiz for Chapter 6

Chapter 2: Accelerating Functions with JIT Compilation

While JAX provides a familiar NumPy-like API, standard Python execution can be slow for the intensive numerical computations common in scientific computing and machine learning, particularly when targeting accelerators like GPUs or TPUs. To achieve high performance, JAX relies on compilation.

This chapter focuses on jax.jit, the Just-In-Time compilation transformation. You will learn how jit converts Python functions into optimized executables tailored for your hardware. We will cover:

The basic application of jax.jit as a decorator or function.
How JIT compilation works through a process called tracing.
The implications of tracing for Python control flow (loops, conditionals).
How to handle static versus dynamic values within compiled functions.
Common mistakes and considerations when using jit.

By the end of this chapter, you will be able to use jax.jit to significantly speed up your JAX computations.

Sections

2.1 The Need for Speed: Why Compile?
2.2 Introducing `jax.jit`
2.3 How JIT Works: Tracing and Compilation
2.4 Python Control Flow and `jit`
2.5 Static vs Traced Values
2.6 Common Challenges with `jit`
2.7 Hands-on Practical: Applying `jit`

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