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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

Nesting `vmap`

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References

Automatic Vectorization with vmap, JAX core contributors, 2024 (JAX Project) - Provides an introduction to vmap, illustrating its use for batching computations and explaining the in_axes parameter for handling multiple input dimensions, including nesting.
JAX: Composable transformations of Python+NumPy programs, James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Skye Wanderman-Milne, and Adam Paszke, 2018 SysML '18: Proceedings of the 1st Systems for Machine Learning Workshop (ACM) DOI: 10.1145/3278972.3278996 - Presents the core design principles and architecture of JAX, detailing how its functional transformations, including vmap, enable efficient and composable numerical computing.

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