Understand JAX itself

Who this path is for

Curious JAX users who can already use grad and jit and want to diagnose transformation behavior.

Preparation

Shared foundations and advanced autodiff

Your first useful artifact

An annotated jaxpr that explains a computation and a changed input shape.

How to study

Start by connecting each jaxpr primitive to the function that produced it. Revisit directional derivatives and the chain rule before studying JVPs, VJPs and custom rules. Keep an independent derivative reference beside every transformation. Finish the derivative audit, then extend the tiny interpreter in the synthesis assessment and explain its unsupported cases.

Course phases and lessons

1. Setup & first steps

   Run a saved program and explain its environment, array output and device placement. Start on one CPU, practice sharding on four logical CPU devices, and learn how to get a TPU running, launch a TPU job, and run course experiments on TPU in parallel from Phase 00 onward.

   • Set up your learning workspace
   • Meet your arrays and devices
   • Practice with four virtual CPU devices
   • Move your experiment to a TPU
2. Arrays & pure functions

   Treat every axis as part of a contract. Work through normalization, broadcasting and immutable updates, then diagnose mistakes that still return plausible numbers.

   • From NumPy to jax.numpy
   • Shapes, broadcasting, and dtypes
   • Pure functions and explicit inputs
   • Immutable updates and indexing
3. JAX transformations

   Begin with a scalar function, then differentiate it, batch it and compile it. Compare each transformed result with a simple reference so you can explain what changed.

   • Your first gradient
   • Losses and value_and_grad
   • Batch a function with vmap
   • Compile a function with jit
   • Tracing, static arguments, and recompilation
4. State, randomness & control flow

   Make randomness, parameters and loop state explicit. Learn how to repeat an experiment without accidentally reusing randomness or mutating a caller’s state.

   • Random keys without surprises
   • Pytrees and structured parameters
   • Compiled loops with lax.scan
   • Branches with lax.cond
5. Math & optimization

   Connect geometry and probability to the updates in a training loop. Begin with linear algebra, gradient checks and gradient descent, then investigate conditioning, curvature, likelihoods, regularization and optimizer behavior.

   • Vectors, norms, and projections
   • Linear algebra and loss intuition
   • Least squares, rank, and conditioning
   • The chain rule, Jacobians, and directions
   • Gradient checking and numerical accuracy
   • Curvature, Hessians, and learning rates
   • Write gradient descent yourself
   • Probability, likelihood, and stable losses
   • Regularization and honest validation
   • Minibatches, expectation, and gradient noise
   • Optimize with Optax
   • Adam, clipping, and learning-rate schedules
6. Autodiff & JAX internals

   Trace functions into jaxpr, check forward and reverse sensitivities, write exact custom derivatives and compile a small transformation with explicit supported primitives.

   • Read your first jaxpr
   • JVPs, VJPs, and higher-order derivatives
   • Custom derivative rules
   • Lowering, compilation, and a tiny transformation

Audit derivatives and a tiny transformation

A guided project is available for this route.

Connect a jaxpr to your function and numerically verify the derivative rule.

• An annotated jaxpr linking primitives and shapes to the original function
• Directional and adjoint derivative checks on changed inputs
• A custom derivative or transformation with a deliberate unsupported case and explicit rejection

Read the portfolio project guide

Work through the synthesis assessment

Use this path in your learning workspace