Getting Started with JAX
Chapter 1: Introduction to JAX
What is JAX?
JAX vs NumPy
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.jitHow JIT Works: Tracing and Compilation
Python Control Flow and
jitStatic vs Traced Values
Common Challenges with
jitHands-on Practical: Applying
jitQuiz for Chapter 2
Chapter 3: Automatic Differentiation with
gradUnderstanding Gradients
Introducing
jax.gradHow 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
vmapThe Concept of Vectorization
Introducing
jax.vmapMapping over Specific Arguments (
in_axes, out_axes)Handling Multiple Batched Arguments
Nesting
vmapCombining
vmap with jit and gradPerformance Considerations for
vmapHands-on Practical: Vectorizing Functions
Quiz for Chapter 4
Chapter 5: Parallelization Across Devices with
pmapIntroduction to Data Parallelism (SPMD)
Introducing
jax.pmapMapping Data to Devices (
in_axes, out_axes)Device Meshes and Axis Names
Collective Operations (
lax.psum, lax.pmean, etc.)Combining
pmap with other TransformationsDebugging
pmapped FunctionsHands-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
Differentiating with Respect to Arguments
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jax.grad, JAX core developers, 2023 - Official documentation detailing thejax.gradfunction, including the use of theargnumsparameter for targeted differentiation.- Evaluating Derivatives: Principles and Techniques for Algorithmic Differentiation, Andreas Griewank, Andrea Walther, 2008 (Society for Industrial and Applied Mathematics (SIAM)) DOI: 10.1137/1.9780898717761 - A comprehensive textbook explaining the fundamental principles and various techniques of automatic differentiation.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Provides foundational knowledge on gradient-based optimization methods and backpropagation in machine learning, where targeted differentiation is crucial.
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