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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

Limitations and Considerations

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References

Automatic differentiation in JAX, JAX core contributors, 2024 - Official documentation explaining jax.grad and other automatic differentiation transformations, covering the types of functions it supports and how to handle multi-output differentiation.
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Andreas Griewank and Andrea Walther, 2008 (Society for Industrial and Applied Mathematics (SIAM)) DOI: 10.1137/1.9780898717711 - A foundational text providing a comprehensive mathematical and algorithmic treatment of automatic differentiation, relevant for understanding non-differentiable operations and numerical precision.
Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Chapter 8 discusses optimization algorithms and provides excellent explanations of vanishing and exploding gradients, and numerical stability issues relevant to deep learning.
The Sharp Bits of JAX, JAX core contributors, 2024 - Explains JAX's functional programming model, tracing mechanism, and how these aspects interact with Python control flow and side effects, providing context for grad limitations.

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